Method and apparatus for improved high order modulation
View Patent ↗Methods, systems and software are provided for high order signal modulation based on improved signal constellation and bit labeling designs for enhanced performance characteristics, including decreased power consumption. According to the improved signal constellation and bit labeling designs for enhanced performance characteristics, designs for 8-ary, 16-ary, 32-ary and 64-ary signal constellations are provided. According to an 8-ary constellation, improved bit labeling and bit coordinates are provided for a 1+7APSK signal constellation. According to a 16-ary constellation, improved bit labeling and bit coordinates are provided for a 6+10APSK signal constellation. According to three 32-ary constellations, improved bit labeling and bit coordinates are provided for a 16+16APSK signal constellation and two 4+12+16APSK signal constellations. According to two 64-ary constellations, improved bit labeling and bit coordinates are provided for an 8+16+20+20APSK signal constellation and a 12+16+16+20APSK signal constellation.
1. A method, comprising:
modulating a signal, through a modulation device, based at least in part on an 8-ary, 1+7APSK signal constellation, having an outer ring with 7 bit positions, in accordance with the following bit labeling and [x, y] bit coordinate positions:
Bit Label
[x, y] Coordinates
000
[0.0, 0.0]
001
[{square root over ((8.0 * ε χ /7.0)}, 0.0]
010
[{square root over (8.0 * ε χ /7.0)} * cos (4.0 * π/7.0),
{square root over (8.0 * ε χ /7.0)} * sin (4.0 * π/7.0)]
011
[{square root over (8.0 * ε χ /7.0)}* cos (2.0 * π/7.0),
{square root over (8.0 * ε χ /7.0)} * sin (2.0 * π/7.0)]
100
[{square root over (8.0 * ε χ /7.0)} * cos (12.0 * π/7.0),
{square root over (8.0 * ε χ /7.0)} * sin (12.0 * π/7.0)]
101
[{square root over (8.0 * ε χ /7.0)} * cos (10.0 * π/7.0),
{square root over (8.0 * ε χ /7.0)} * sin (10.0 * π/7.0)]
110
[{square root over (8.0 * ε χ /7.0)} * cos (6.0 * π/7.0),
{square root over (8.0 * ε χ /7.0)} * sin (6.0 * π/7.0)]
111
[{square root over (8.0 * ε χ /7.0)} * cos (8.0 * π/7.0),
{square root over (8.0 * ε χ /7.0)} * sin (8.0 * π/7.0)]
where ε x represents average energy per symbol, and
wherein each of the [x, y] bit coordinate positions is rotated by a same rotation factor (from 0 to 359°, inclusive), and/or each bit label is altered by interchanging the 0's and 1's, and/or a uniform swapping of bit positions is applied within each bit label.
2. An apparatus, comprising:
a modulation device configured to modulate a signal based at least in part on an 8-ary, 1+7APSK signal constellation, having an outer ring with 7 bit positions, in accordance with the following bit labeling and [x, y] bit coordinate positions:
Bit Label
[x, y] Coordinates
000
[0.0, 0.0]
001
[{square root over ((8.0 * ε χ /7.0)} , 0.0]
010
[{square root over (8.0 * ε χ /7.0)} * cos (4.0 * π/7.0), {square root over (8.0 * ε χ /7.0)} * sin (4.0 * π/7.0)]
011
[{square root over (8.0 * ε χ /7.0)} * cos (2.0 * π/7.0), {square root over (8.0 * ε χ /7.0)} * sin (2.0 * π/7.0)]
100
[{square root over (8.0 * ε χ /7.0)} * cos (12.0 * π/7.0), {square root over (8.0 * ε χ /7.0)} * sin (12.0 * π/7.0)]
101
[{square root over (8.0 * ε χ /7.0)} * cos (10.0 * π/7.0), {square root over (8.0 * ε χ /7.0)} * sin (10.0 * π/7.0)]
110
[{square root over (8.0 * ε χ /7.0)} * cos (6.0 * π/7.0), {square root over (8.0 * ε χ /7.0)} * sin (6.0 * π/7.0)]
111
[{square root over (8.0 * ε χ /7.0)} * cos (8.0 * π/7.0), {square root over (8.0 * ε χ /7.0)} * sin (8.0 * π/7.0)]
where ε x represents average energy per symbol, and
wherein each of the [x, y] bit coordinate positions is rotated by a same rotation factor (from 0 to 359°, inclusive), and/or each bit label is altered by interchanging the 0's and 1's, and/or a uniform swapping of bit positions is applied within each bit label.
3. A method, comprising:
demodulating a signal, through a demodulation device, wherein the signal was modulated based at least in part on an 8-ary, 1+7APSK signal constellation, having an outer ring with 7 bit positions, in accordance with the following bit labeling and [x, y] bit coordinate positions:
Bit Label
[x, y] Coordinates
000
[0.0, 0.0]
001
[{square root over ((8.0 * ε χ /7.0)} , 0.0]
010
[{square root over (8.0 * ε χ /7.0)} * cos (4.0 * π/7.0), {square root over (8.0 * ε χ /7.0)} * sin (4.0 * π/7.0)]
011
[{square root over (8.0 * ε χ /7.0)} * cos (2.0 * π/7.0), {square root over (8.0 * ε χ /7.0)} * sin (2.0 * π/7.0)]
100
[{square root over (8.0 * ε χ /7.0)} * cos (12.0 * π/7.0), {square root over (8.0 * ε χ /7.0)} * sin (12.0 * π/7.0)]
101
[{square root over (8.0 * ε χ /7.0)} * cos (10.0 * π/7.0), {square root over (8.0 * ε χ /7.0)} * sin (10.0 * π/7.0)]
110
[{square root over (8.0 * ε χ /7.0)} * cos (6.0 * π/7.0), {square root over (8.0 * ε χ /7.0)} * sin (6.0 * π/7.0)]
111
[{square root over (8.0 * ε χ /7.0)} * cos (8.0 * π/7.0), {square root over (8.0 * ε χ /7.0)} * sin (8.0 * π/7.0)]
where ε x represents average energy per symbol, and
wherein each of the [x, y] bit coordinate positions is rotated by a same rotation factor (from 0 to 359°, inclusive), and/or each bit label is altered by interchanging the 0's and 1's, and/or a uniform swapping of bit positions is applied within each bit label.
4. An apparatus, comprising:
a demodulation device configured to demodulate a signal, wherein the signal was modulated based at least in part on an 8-ary, 1+7APSK signal constellation, having an outer ring with 7 bit positions, in accordance with the following bit labeling and [x, y] bit coordinate positions:
Bit Label
[x, y] Coordinates
000
[0.0, 0.0]
001
[{square root over ((8.0 * ε χ /7.0)}, 0.0]
010
[{square root over (8.0 * ε χ /7.0)} * cos (4.0 * π/7.0),
{square root over (8.0 * ε χ /7.0)} * sin (4.0 * π/7.0)]
011
[{square root over (8.0 * ε χ /7.0)}* cos (2.0 * π/7.0),
{square root over (8.0 * ε χ /7.0)} * sin (2.0 * π/7.0)]
100
[{square root over (8.0 * ε χ /7.0)} * cos (12.0 * π/7.0),
{square root over (8.0 * ε χ /7.0)} * sin (12.0 * π/7.0)]
101
[{square root over (8.0 * ε χ /7.0)} * cos (10.0 * π/7.0),
{square root over (8.0 * ε χ /7.0)} * sin (10.0 * π/7.0)]
110
[{square root over (8.0 * ε χ /7.0)} * cos (6.0 * π/7.0),
{square root over (8.0 * ε χ /7.0)} * sin (6.0 * π/7.0)]
111
[{square root over (8.0 * ε χ /7.0)} * cos (8.0 * π/7.0),
{square root over (8.0 * ε χ /7.0)} * sin (8.0 * π/7.0)]
where ε x represents average energy per symbol, and
wherein each of the [x, y] bit coordinate positions is rotated by a same rotation factor (from 0 to 359°, inclusive), and/or each bit label is altered by interchanging the 0's and 1's, and/or a uniform swapping of bit positions is applied within each bit label.
5. A method, comprising:
modulating a signal, through a modulation device, based at least in part on an 16-ary, 6+10APSK signal constellation, having an inner ring with 6 bit positions and an outer ring with 10 bit positions.
6. The method according to claim 5 , wherein the bit positions of the inner and outer rings are in accordance with the following bit labeling and [x, y] bit coordinate positions:
Bit
Label
[x, y] Coordinates
0000
[R1 * {square root over (ε χ )}, 0.0]
0001
[R1 * {square root over (ε χ )} * cos (5.0 * π/3.0), R1 * {square root over (ε χ )} * sin (5.0 * π/3.0)]
0010
[R1 * {square root over (ε χ )} * cos (π/3.0), R1 * {square root over (ε χ )} * sin (π/3.0)]
0011
[R2 * {square root over (ε χ )} * cos (13.0 * π/30.0), R2 * {square root over (ε χ )} * sin (13.0 * π/30.0)]
0100
[R2 * {square root over (ε χ )} * cos (55.0 * π/30.0), R2 * {square root over (ε χ )} * sin (55.0 * π/30.0)]
0101
[R2 * {square root over (ε χ )} * cos (49.0 * π/30.0), R2 * {square root over (ε χ )} * sin (49.0 * π/30.0)]
0110
[R2 * {square root over (ε χ )} * cos (π/30.0), R2 * {square root over (ε χ )} * sin (π/30.0)]
0111
[R2 * {square root over (ε χ )} * cos (7.0 * π/30.0), R2 * {square root over (ε χ )} * sin (7.0 * π/30.0)]
1000
[−R1 * {square root over (ε χ )}, 0.0]
1001
[R1 * {square root over (ε χ )} * cos (4.0 * π/3.0), R1 * {square root over (ε χ )} * sin (4.0 * π/3.0)]
1010
[R1 * {square root over (ε χ )} * cos (2.0 * π/3.0), R1 * {square root over (ε χ )} * sin (2.0 * π/3.0)]
1011
[R2 * {square root over (ε χ )} * cos (19.0 * π/30.0), R2 * {square root over (ε χ )} * sin (19.0 * π/30.0)]
1100
[R2 * {square root over (ε χ )} * cos (37.0 * π/30.0), R2 * {square root over (ε χ )} * sin (37.0 * π/30.0)]
1101
[R2 * {square root over (ε χ )} * cos (43.0 * π/30.0), R2 * {square root over (ε χ )} * sin (43.0 * π/30.0)]
1110
[R2 * {square root over (ε χ )} * cos (31.0 * π/30.0), R2 * {square root over (ε χ )} * sin (31.0 * π/30.0)]
1111
[R2 * {square root over (ε χ )} * cos (25.0 * π/30.0), R2 * {square root over (ε χ )} * sin (25.0 * π/30.0)]
where ε x represents average energy per symbol, 6*R1 2 +10*R2 2 =16, and R1 represents the radius of the inner ring and R2 represents the radius of the outer ring, and
wherein each of the [x, y] bit coordinate positions is rotated by a same rotation factor (from 0 to 359°, inclusive), and/or each bit label is altered by interchanging the 0's and 1's, and/or a uniform swapping of bit positions is applied within each bit label.
7. An apparatus, comprising:
a modulation device configured to modulate a signal based at least in part on an 16-ary, 6+10APSK signal constellation, having an inner ring with 6 bit positions and an outer ring with 10 bit positions.
8. The apparatus according to claim 7 , wherein the bit positions of the inner and outer rings are in accordance with the following bit labeling and [x, y] bit coordinate positions:
Bit
Label
[x, y] Coordinates
0000
[R1 * {square root over (ε χ )}, 0.0]
0001
[R1 * {square root over (ε χ )} * cos (5.0 * π/3.0), R1 * {square root over (ε χ )} * sin (5.0 * π/3.0)]
0010
[R1 * {square root over (ε χ )} * cos (π/3.0), R1 * {square root over (ε χ )} * sin (π/3.0)]
0011
[R2 * {square root over (ε χ )} * cos (13.0 * π/30.0), R2 * {square root over (ε χ )} * sin (13.0 * π/30.0)]
0100
[R2 * {square root over (ε χ )} * cos (55.0 * π/30.0), R2 * {square root over (ε χ )} * sin (55.0 * π/30.0)]
0101
[R2 * {square root over (ε χ )} * cos (49.0 * π/30.0), R2 * {square root over (ε χ )} * sin (49.0 * π/30.0)]
0110
[R2 * {square root over (ε χ )} * cos (π/30.0), R2 * {square root over (ε χ )} * sin (π/30.0)]
0111
[R2 * {square root over (ε χ )} * cos (7.0 * π/30.0), R2 * {square root over (ε χ )} * sin (7.0 * π/30.0)]
1000
[−R1 * {square root over (ε χ )}, 0.0]
1001
[R1 * {square root over (ε χ )} * cos (4.0 * π/3.0), R1 * {square root over (ε χ )} * sin (4.0 * π/3.0)]
1010
[R1 * {square root over (ε χ )} * cos (2.0 * π/3.0), R1 * {square root over (ε χ )} * sin (2.0 * π/3.0)]
1011
[R2 * {square root over (ε χ )} * cos (19.0 * π/30.0), R2 * {square root over (ε χ )} * sin (19.0 * π/30.0)]
1100
[R2 * {square root over (ε χ )} * cos (37.0 * π/30.0), R2 * {square root over (ε χ )} * sin (37.0 * π/30.0)]
1101
[R2 * {square root over (ε χ )} * cos (43.0 * π/30.0), R2 * {square root over (ε χ )} * sin (43.0 * π/30.0)]
1110
[R2 * {square root over (ε χ )} * cos (31.0 * π/30.0), R2 * {square root over (ε χ )} * sin (31.0 * π/30.0)]
1111
[R2 * {square root over (ε χ )} * cos (25.0 * π/30.0), R2 * {square root over (ε χ )} * sin (25.0 * π/30.0)]
where ε x represents average energy per symbol, 6*R1 2 +10*R2 2 =16, and R1 represents the radius of the inner ring and R2 represents the radius of the outer ring, and
wherein each of the [x, y] bit coordinate positions is rotated by a same rotation factor (from 0 to 359°, inclusive), and/or each bit label is altered by interchanging the 0's and 1's, and/or a uniform swapping of bit positions is applied within each bit label.
9. A method, comprising:
demodulating a signal, through a demodulation device, wherein the signal was modulated based at least in part on an 16-ary, 6+10APSK signal constellation, having an inner ring with 6 bit positions and an outer ring with 10 bit positions.
10. The method according to claim 9 , wherein the bit positions of the inner and outer rings are in accordance with the following bit labeling and [x, y] bit coordinate positions:
Bit
Label
[x, y] Coordinates
0000
[R1 * {square root over (ε χ )}, 0.0]
0001
[R1 * {square root over (ε χ )} * cos (5.0 * π/3.0), R1 * {square root over (ε χ )} * sin (5.0 * π/3.0)]
0010
[R1 * {square root over (ε χ )} * cos (π/3.0), R1 * {square root over (ε χ )} * sin (π/3.0)]
0011
[R2 * {square root over (ε χ )} * cos (13.0 * π/30.0), R2 * {square root over (ε χ )} * sin (13.0 * π/30.0)]
0100
[R2 * {square root over (ε χ )} * cos (55.0 * π/30.0), R2 * {square root over (ε χ )} * sin (55.0 * π/30.0)]
0101
[R2 * {square root over (ε χ )} * cos (49.0 * π/30.0), R2 * {square root over (ε χ )} * sin (49.0 * π/30.0)]
0110
[R2 * {square root over (ε χ )} * cos (π/30.0), R2 * {square root over (ε χ )} * sin (π/30.0)]
0111
[R2 * {square root over (ε χ )} * cos (7.0 * π/30.0), R2 * {square root over (ε χ )} * sin (7.0 * π/30.0)]
1000
[−R1 * {square root over (ε χ )}, 0.0]
1001
[R1 * {square root over (ε χ )} * cos (4.0 * π/3.0), R1 * {square root over (ε χ )} * sin (4.0 * π/3.0)]
1010
[R1 * {square root over (ε χ )} * cos (2.0 * π/3.0), R1 * {square root over (ε χ )} * sin (2.0 * π/3.0)]
1011
[R2 * {square root over (ε χ )} * cos (19.0 * π/30.0), R2 * {square root over (ε χ )} * sin (19.0 * π/30.0)]
1100
[R2 * {square root over (ε χ )} * cos (37.0 * π/30.0), R2 * {square root over (ε χ )} * sin (37.0 * π/30.0)]
1101
[R2 * {square root over (ε χ )} * cos (43.0 * π/30.0), R2 * {square root over (ε χ )} * sin (43.0 * π/30.0)]
1110
[R2 * {square root over (ε χ )} * cos (31.0 * π/30.0), R2 * {square root over (ε χ )} * sin (31.0 * π/30.0)]
1111
[R2 * {square root over (ε χ )} * cos (25.0 * π/30.0), R2 * {square root over (ε χ )} * sin (25.0 * π/30.0)]
where ε x represents average energy per symbol, 6*R1 2 +10*R2 2 =16, and R1 represents the radius of the inner ring and R2 represents the radius of the outer ring, and
wherein each of the [x, y] bit coordinate positions is rotated by a same rotation factor (from 0 to 359°, inclusive), and/or each bit label is altered by interchanging the 0's and 1's, and/or a uniform swapping of bit positions is applied within each bit label.
11. An apparatus, comprising:
a demodulation device configured to demodulate a signal, wherein the signal was modulated based at least in part on an 16-ary, 6+10APSK signal constellation, having an inner ring with 6 bit positions and an outer ring with 10 bit positions.
12. The apparatus according to claim 11 , wherein the bit positions of the inner and outer rings are in accordance with the following bit labeling and [x, y] bit coordinate positions:
Bit
Label
[x, y] Coordinates
0000
[R1 * {square root over (ε χ )}, 0.0]
0001
[R1 * {square root over (ε χ )} * cos (5.0 * π/3.0), R1 * {square root over (ε χ )} * sin (5.0 * π/3.0)]
0010
[R1 * {square root over (ε χ )} * cos (π/3.0), R1 * {square root over (ε χ )} * sin (π/3.0)]
0011
[R2 * {square root over (ε χ )} * cos (13.0 * π/30.0), R2 * {square root over (ε χ )} * sin (13.0 * π/30.0)]
0100
[R2 * {square root over (ε χ )} * cos (55.0 * π/30.0), R2 * {square root over (ε χ )} * sin (55.0 * π/30.0)]
0101
[R2 * {square root over (ε χ )} * cos (49.0 * π/30.0), R2 * {square root over (ε χ )} * sin (49.0 * π/30.0)]
0110
[R2 * {square root over (ε χ )} * cos (π/30.0), R2 * {square root over (ε χ )} * sin (π/30.0)]
0111
[R2 * {square root over (ε χ )} * cos (7.0 * π/30.0), R2 * {square root over (ε χ )} * sin (7.0 * π/30.0)]
1000
[−R1 * {square root over (ε χ )}, 0.0]
1001
[R1 * {square root over (ε χ )} * cos (4.0 * π/3.0), R1 * {square root over (ε χ )} * sin (4.0 * π/3.0)]
1010
[R1 * {square root over (ε χ )} * cos (2.0 * π/3.0), R1 * {square root over (ε χ )} * sin (2.0 * π/3.0)]
1011
[R2 * {square root over (ε χ )} * cos (19.0 * π/30.0), R2 * {square root over (ε χ )} * sin (19.0 * π/30.0)]
1100
[R2 * {square root over (ε χ )} * cos (37.0 * π/30.0), R2 * {square root over (ε χ )} * sin (37.0 * π/30.0)]
1101
[R2 * {square root over (ε χ )} * cos (43.0 * π/30.0), R2 * {square root over (ε χ )} * sin (43.0 * π/30.0)]
1110
[R2 * {square root over (ε χ )} * cos (31.0 * π/30.0), R2 * {square root over (ε χ )} * sin (31.0 * π/30.0)]
1111
[R2 * {square root over (ε χ )} * cos (25.0 * π/30.0), R2 * {square root over (ε χ )} * sin (25.0 * π/30.0)]
where ε x represents average energy per symbol, 6*R1 2 +10*R2 2 =16, and R1 represents the radius of the inner ring and R2 represents the radius of the outer ring, and
wherein each of the [x, y] bit coordinate positions is rotated by a same rotation factor (from 0 to 359°, inclusive), and/or each bit label is altered by interchanging the 0's and 1's, and/or a uniform swapping of bit positions is applied within each bit label.
13. A method, comprising:
modulating a signal, through a modulation device, based at least in part on an 32-ary, 16+16APSK signal constellation, having an inner ring with 16 bit positions and an outer ring with 16 bit positions.
14. The method according to claim 13 , wherein the bit positions of the inner and outer rings are in accordance with the following bit labeling and [x, y] bit coordinate positions:
Bit Label
[x, y] Coordinates
00000
[R1 * {square root over (ε χ )} * cos(π/16.0), R1 * {square root over (ε χ )} * sin(π/16.0)]
00001
[R1 * {square root over (ε χ )} * cos(3.0 * π/16.0), R1 * {square root over (ε χ )} * sin(3.0 * π/16.0)]
00010
[R1 * {square root over (ε χ )} * sin(π/16.0), R1 * {square root over (ε χ )} * cos(π/16.0)]
00011
[R1 * {square root over (ε χ )} * sin(3.0 * π/16.0), R1 * {square root over (ε χ )} * cos(3.0 * π/16.0)]
00100
[R1 * {square root over (ε χ )} * cos(π/16.0), −R1 * {square root over (ε χ )} * sin(π/16.0)]
00101
[R1 * {square root over (ε χ )} * cos(3.0 * π/16.0), −R1 * {square root over (ε χ )} * sin(3.0 * π/16.0)]
00110
[R1 * {square root over (ε χ )} * sin(π/16.0), −R1 * {square root over (ε χ )} * cos(π/16.0)]
00111
[R1 * {square root over (ε χ )} * sin(3.0 *π/16.0), −R1 * {square root over (ε χ )} * cos(3.0 * π/16.0)]
01000
[−R1 * {square root over (ε χ )} * cos(π/16.0), R1 * {square root over (ε χ )} * sin(π/16.0)]
01001
[−R1 * {square root over (ε χ )} * cos(3.0 * π/16.0), R1 * {square root over (ε χ )} * sin(3.0 * π/16.0)]
01010
[−R1 * {square root over (ε χ )} * sin(π/16.0), R1 * {square root over (ε χ )} * cos(π/16.0)]
01011
[−R1 * {square root over (ε χ )} * sin(3.0 * π/16.0), R1 * {square root over (ε χ )} * cos(3.0 * π/16.0)]
01100
[−R1 * {square root over (ε χ )} * cos(π/16.0), −R1 * {square root over (ε χ )} * sin(π/16.0)]
01101
[−R1 * {square root over (ε χ )} * cos(3.0 * π/16.0), −R1 * {square root over (ε χ )} * sin(3.0 * π/16.0)]
01110
[−R1 * {square root over (ε χ )} * sin(π/16.0), −R1 * {square root over (ε χ )} * cos(π/16.0)]
01111
[−R1 * {square root over (ε χ )} * sin(3.0 * π/16.0), −R1 * {square root over (ε χ )} * cos(3.0 * π/16.0)]
10000
[R2 * {square root over (ε χ )} * cos(π/16.0), R2 * {square root over (ε χ )} * sin(π/16.0)]
10001
[R2 * {square root over (ε χ )} * cos(3.0 * π/16.0), R2 * {square root over (ε χ )} * sin(3.0 * π/16.0)]
10010
[R2 * {square root over (ε χ )} * sin(π/16.0), R2 * {square root over (ε χ )} * cos(π/16.0)]
10011
[R2 * {square root over (ε χ )} * sin(3.0 * π/16.0), R2 * {square root over (ε χ )} * cos(3.0 * π/16.0)]
10100
[R2 * {square root over (ε χ )} * cos(π/16.0), −R2 * {square root over (ε χ )} * sin(π/16.0)]
10101
[R2 * {square root over (ε χ )} * cos(3.0 * π/16.0), −R2 * {square root over (ε χ )} * sin(3.0 * π/16.0)]
10110
[R2 * {square root over (ε χ )} * sin(π/16.0), −R2 * {square root over (ε χ )} * cos(π/16.0)]
10111
[R2 * {square root over (ε χ )} * sin(3.0 * π/16.0), −R2 * {square root over (ε χ )} * cos(3.0 * π/16.0)]
11000
[−R2 * {square root over (ε χ )} * cos(π/16.0), R2 * {square root over (ε χ )} * sin(π/16.0)]
11001
[−R2 * {square root over (ε χ )} * cos(3.0 * π/16.0), R2 * {square root over (ε χ )} * sin(3.0 * π/16.0)]
11010
[−R2 * {square root over (ε χ )} * sin(π/16.0), R2 * {square root over (ε χ )} * cos(π/16.0)]
11011
[−R2 * {square root over (ε χ )} * sin(3.0 * π/16.0), R2 * {square root over (ε χ )} * cos(3.0 * π/16.0)]
11100
[−R2 * {square root over (ε χ )} * cos(π/16.0), −R2 * {square root over (ε χ )} * sin(π/16.0)]
11101
[−R2 * {square root over (ε χ )} * cos(3.0 * π/16.0), −R2 * {square root over (ε χ )} * sin(3.0 * π/16.0)]
11110
[−R2 * {square root over (ε χ )} * sin(π/16.0), −R2 * {square root over (ε χ )} * cos(π/16.0)]
11111
[−R2 * {square root over (ε χ )} * sin(3.0 * π/16.0), −R2 * {square root over (ε χ )} * cos(3.0 * π/16.0)]
where ε x represents average energy per symbol, R1 2 +R2 2 =2, and R1 represents the radius of the inner ring and R2 represents the radius of the outer ring, and
wherein each of the [x, y] bit coordinate positions is rotated by a same rotation factor (from 0 to 359°, inclusive), and/or each bit label is altered by interchanging the 0's and 1's, and/or a uniform swapping of bit positions is applied within each bit label.
15. An apparatus, comprising:
a modulation device configured to modulate a signal based at least in part on an 32-ary, 16+16APSK signal constellation, having an inner ring with 16 bit positions and an outer ring with 16 bit positions.
16. The apparatus according to claim 15 , wherein the bit positions of the inner and outer rings are in accordance with the following bit labeling and [x, y] bit coordinate positions:
Bit Label
[x, y] Coordinates
00000
[R1 * {square root over (ε χ )} * cos(π/16.0), R1 * {square root over (ε χ )} * sin(π/16.0)]
00001
[R1 * {square root over (ε χ )} * cos(3.0 * π/16.0), R1 * {square root over (ε χ )} * sin(3.0 * π/16.0)]
00010
[R1 * {square root over (ε χ )} * sin(π/16.0), R1 * {square root over (ε χ )} * cos(π/16.0)]
00011
[R1 * {square root over (ε χ )} * sin(3.0 * π/16.0), R1 * {square root over (ε χ )} * cos(3.0 * π/16.0)]
00100
[R1 * {square root over (ε χ )} * cos(π/16.0), −R1 * {square root over (ε χ )} * sin(π/16.0)]
00101
[R1 * {square root over (ε χ )} * cos(3.0 * π/16.0), −R1 * {square root over (ε χ )} * sin(3.0 * π/16.0)]
00110
[R1 * {square root over (ε χ )} * sin(π/16.0), −R1 * {square root over (ε χ )} * cos(π/16.0)]
00111
[R1 * {square root over (ε χ )} * sin(3.0 * π/16.0), −R1 * {square root over (ε χ )} * cos(3.0 * π/16.0)]
01000
[−R1 * {square root over (ε χ )} * cos(π/16.0), R1 * {square root over (ε χ )} * sin(π/16.0)]
01001
[−R1 * {square root over (ε χ )} * cos(3.0 * π/16.0), R1 * {square root over (ε χ )} * sin(3.0 * π/16.0)]
01010
[−R1 * {square root over (ε χ )} * sin(π/16.0), R1 * {square root over (ε χ )} * cos(π/16.0)]
01011
[−R1 * {square root over (ε χ )} * sin(3.0 * π/16.0), R1 * {square root over (ε χ )} * cos(3.0 * π/16.0)]
01100
[−R1 * {square root over (ε χ )} * cos(π/16.0), −R1 * {square root over (ε χ )} * sin(π/16.0)]
01101
[−R1 * {square root over (ε χ )} * cos(3.0 * π/16.0), −R1 * {square root over (ε χ )} * sin(3.0 * π/16.0)]
01110
[−R1 * {square root over (ε χ )} * sin(π/16.0), −R1 * {square root over (ε χ )} * cos(π/16.0)]
01111
[−R1 * {square root over (ε χ )} * sin(3.0 * π/16.0), −R1 * {square root over (ε χ )} * cos(3.0 * π/16.0)]
10000
[R2 * {square root over (ε χ )} * cos(π/16.0), R2 * {square root over (ε χ )} * sin(π/16.0)]
10001
[R2 * {square root over (ε χ )} * cos(3.0 * π/16.0), R2 * {square root over (ε χ )} * sin(3.0 * π/16.0)]
10010
[R2 * {square root over (ε χ )} * sin(π/16.0), R2 * {square root over (ε χ )} * cos(π/16.0)]
10011
[R2 * {square root over (ε χ )} * sin(3.0 * π/16.0), R2 * {square root over (ε χ )} * cos(3.0 * π/16.0)]
10100
[R2 * {square root over (ε χ )} * cos(π/16.0), −R2 * {square root over (ε χ )} * sin(π/16.0)]
10101
[R2 * {square root over (ε χ )} * cos(3.0 * π/16.0), −R2 * {square root over (ε χ )} * sin(3.0 * π/16.0)]
10110
[R2 * {square root over (ε χ )} * sin(π/16.0), −R2 * {square root over (ε χ )} * cos(π/16.0)]
10111
[R2 * {square root over (ε χ )} * sin(3.0 * π/16.0), −R2 * {square root over (ε χ )} * cos(3.0 * π/16.0)]
11000
[−R2 * {square root over (ε χ )} * cos(π/16.0), R2 * {square root over (ε χ )} * sin(π/16.0)]
11001
[−R2 * {square root over (ε χ )} * cos(3.0 * π/16.0), R2 * {square root over (ε χ )} * sin(3.0 * π/16.0)]
11010
[−R2 * {square root over (ε χ )} * sin(π/16.0), R2 * {square root over (ε χ )} * cos(π/16.0)]
11011
[−R2 * {square root over (ε χ )} * sin(3.0 * π/16.0), R2 * {square root over (ε χ )} * cos(3.0 * π/16.0)]
11100
[−R2 * {square root over (ε χ )} * cos(π/16.0), −R2 * {square root over (ε χ )} * sin(π/16.0)]
11101
[−R2 * {square root over (ε χ )} * cos(3.0 * π/16.0), −R2 * {square root over (ε χ )} * sin(3.0 * π/16.0)]
11110
[−R2 * {square root over (ε χ )} * sin(π/16.0), −R2 * {square root over (ε χ )} * cos(π/16.0)]
11111
[−R2 * {square root over (ε χ )} * sin(3.0 * π/16.0), −R2 * {square root over (ε χ )} * cos(3.0 * π/16.0)]
where ε x represents average energy per symbol, R1 2 +R2 2 =2, and R1 represents the radius of the inner ring and R2 represents the radius of the outer ring, and
wherein each of the [x, y] bit coordinate positions is rotated by a same rotation factor (from 0 to 359°, inclusive), and/or each bit label is altered by interchanging the 0's and 1's, and/or a uniform swapping of bit positions is applied within each bit label.
17. A method, comprising:
demodulating a signal, through a demodulation device, wherein the signal was modulated based at least in part on an 32-ary, 16+16APSK signal constellation, having an inner ring with 16 bit positions and an outer ring with 16 bit positions.
18. The method according to claim 17 , wherein the bit positions of the inner and outer rings are in accordance with the following bit labeling and [x, y] bit coordinate positions:
Bit Label
[x, y] Coordinates
00000
[R1 * {square root over (ε χ )} * cos(π/16.0), R1 * {square root over (ε χ )} * sin(π/16.0)]
00001
[R1 * {square root over (ε χ )} * cos(3.0 * π/16.0), R1 * {square root over (ε χ )} * sin(3.0 * π/16.0)]
00010
[R1 * {square root over (ε χ )} * sin(π/16.0), R1 * {square root over (ε χ )} * cos(π/16.0)]
00011
[R1 * {square root over (ε χ )} * sin(3.0 * π/16.0), R1 * {square root over (ε χ )} * cos(3.0 * π/16.0)]
00100
[R1 * {square root over (ε χ )} * cos(π/16.0), −R1 * {square root over (ε χ )} * sin(π/16.0)]
00101
[R1 * {square root over (ε χ )} * cos(3.0 * π/16.0), −R1 * {square root over (ε χ )} * sin(3.0 * π/16.0)]
00110
[R1 * {square root over (ε χ )} * sin(π/16.0), −R1 * {square root over (ε χ )} * cos(π/16.0)]
00111
[R1 * {square root over (ε χ )} * sin(3.0 * π/16.0), −R1 * {square root over (ε χ )} * cos(3.0 * π/16.0)]
01000
[−R1 * {square root over (ε χ )} * cos(π/16.0), R1 * {square root over (ε χ )} * sin(π/16.0)]
01001
[−R1 * {square root over (ε χ )} * cos(3.0 * π/16.0), R1 * {square root over (ε χ )} * sin(3.0 * π/16.0)]
01010
[−R1 * {square root over (ε χ )} * sin(π/16.0), R1 * {square root over (ε χ )} * cos(π/16.0)]
01011
[−R1 * {square root over (ε χ )} * sin(3.0 * π/16.0), R1 * {square root over (ε χ )} * cos(3.0 * π/16.0)]
01100
[−R1 * {square root over (ε χ )} * cos(π/16.0), −R1 * {square root over (ε χ )} * sin(π/16.0)]
01101
[−R1 * {square root over (ε χ )} * cos(3.0 * π/16.0), −R1 * {square root over (ε χ )} * sin(3.0 * π/16.0)]
01110
[−R1 * {square root over (ε χ )} * sin(π/16.0), −R1 * {square root over (ε χ )} * cos(π/16.0)]
01111
[−R1 * {square root over (ε χ )} * sin(3.0 * π/16.0), −R1 * {square root over (ε χ )} * cos(3.0 * π/16.0)]
10000
[R2 * {square root over (ε χ )} * cos(π/16.0), R2 * {square root over (ε χ )} * sin(π/16.0)]
10001
[R2 * {square root over (ε χ )} * cos(3.0 * π/16.0), R2 * {square root over (ε χ )} * sin(3.0 * π/16.0)]
10010
[R2 * {square root over (ε χ )} * sin(π/16.0), R2 * {square root over (ε χ )} * cos(π/16.0)]
10011
[R2 * {square root over (ε χ )} * sin(3.0 * π/16.0), R2 * {square root over (ε χ )} * cos(3.0 * π/16.0)]
10100
[R2 * {square root over (ε χ )} * cos(π/16.0), −R2 * {square root over (ε χ )} * sin(π/16.0)]
10101
[R2 * {square root over (ε χ )} * cos(3.0 * π/16.0), −R2 * {square root over (ε χ )} * sin(3.0 * π/16.0)]
10110
[R2 * {square root over (ε χ )} * sin(π/16.0), −R2 * {square root over (ε χ )} * cos(π/16.0)]
10111
[R2 * {square root over (ε χ )} * sin(3.0 * π/16.0), −R2 * {square root over (ε χ )} * cos(3.0 * π/16.0)]
11000
[−R2 * {square root over (ε χ )} * cos(π/16.0), R2 * {square root over (ε χ )} * sin(π/16.0)]
11001
[−R2 * {square root over (ε χ )} * cos(3.0 * π/16.0), R2 * {square root over (ε χ )} * sin(3.0 * π/16.0)]
11010
[−R2 * {square root over (ε χ )} * sin(π/16.0), R2 * {square root over (ε χ )} * cos(π/16.0)]
11011
[−R2 * {square root over (ε χ )} * sin(3.0 * π/16.0), R2 * {square root over (ε χ )} * cos(3.0 * π/16.0)]
11100
[−R2 * {square root over (ε χ )} * cos(π/16.0), −R2 * {square root over (ε χ )} * sin(π/16.0)]
11101
[−R2 * {square root over (ε χ )} * cos(3.0 * π/16.0), −R2 * {square root over (ε χ )} * sin(3.0 * π/16.0)]
11110
[−R2 * {square root over (ε χ )} * sin(π/16.0), −R2 * {square root over (ε χ )} * cos(π/16.0)]
11111
[−R2 * {square root over (ε χ )} * sin(3.0 * π/16.0), −R2 * {square root over (ε χ )} * cos(3.0 * π/16.0)]
where ε x represents average energy per symbol, R1 2 +R2 2 =2, and R1 represents the radius of the inner ring and R2 represents the radius of the outer ring, and
wherein each of the [x, y] bit coordinate positions is rotated by a same rotation factor (from 0 to 359°, inclusive), and/or each bit label is altered by interchanging the 0's and 1's, and/or a uniform swapping of bit positions is applied within each bit label.
19. An apparatus, comprising:
a demodulation device configured to demodulate a signal, wherein the signal was modulated based at least in part on an 32-ary, 16+16APSK signal constellation, having an inner ring with 16 bit positions and an outer ring with 16 bit positions.
20. The apparatus according to claim 19 , wherein the bit positions of the inner and outer rings are in accordance with the following bit labeling and [x, y] bit coordinate positions:
Bit Label
[x, y] Coordinates
00000
[R1 * {square root over (ε χ )} * cos(π/16.0), R1 * {square root over (ε χ )} * sin(π/16.0)]
00001
[R1 * {square root over (ε χ )} * cos(3.0 * π/16.0), R1 * {square root over (ε χ )} * sin(3.0 * π/16.0)]
00010
[R1 * {square root over (ε χ )} * sin(π/16.0), R1 * {square root over (ε χ )} * cos(π/16.0)]
00011
[R1 * {square root over (ε χ )} * sin(3.0 * π/16.0), R1 * {square root over (ε χ )} * cos(3.0 * π/16.0)]
00100
[R1 * {square root over (ε χ )} * cos(π/16.0), −R1 * {square root over (ε χ )} * sin(π/16.0)]
00101
[R1 * {square root over (ε χ )} * cos(3.0 * π/16.0), −R1 * {square root over (ε χ )} * sin(3.0 * π/16.0)]
00110
[R1 * {square root over (ε χ )} * sin(π/16.0), −R1 * {square root over (ε χ )} * cos(π/16.0)]
00111
[R1 * {square root over (ε χ )} * sin(3.0 * π/16.0), −R1 * {square root over (ε χ )} * cos(3.0 * π/16.0)]
01000
[−R1 * {square root over (ε χ )} * cos(π/16.0), R1 * {square root over (ε χ )} * sin(π/16.0)]
01001
[−R1 * {square root over (ε χ )} * cos(3.0 * π/16.0), R1 * {square root over (ε χ )} * sin(3.0 * π/16.0)]
01010
[−R1 * {square root over (ε χ )} * sin(π/16.0), R1 * {square root over (ε χ )} * cos(π/16.0)]
01011
[−R1 * {square root over (ε χ )} * sin(3.0 * π/16.0), R1 * {square root over (ε χ )} * cos(3.0 * π/16.0)]
01100
[−R1 * {square root over (ε χ )} * cos(π/16.0), −R1 * {square root over (ε χ )} * sin(π/16.0)]
01101
[−R1 * {square root over (ε χ )} * cos(3.0 * π/16.0), −R1 * {square root over (ε χ )} * sin(3.0 * π/16.0)]
01110
[−R1 * {square root over (ε χ )} * sin(π/16.0), −R1 * {square root over (ε χ )} * cos(π/16.0)]
01111
[−R1 * {square root over (ε χ )} * sin(3.0 * π/16.0), −R1 * {square root over (ε χ )} * cos(3.0 * π/16.0)]
10000
[R2 * {square root over (ε χ )} * cos(π/16.0), R2 * {square root over (ε χ )} * sin(π/16.0)]
10001
[R2 * {square root over (ε χ )} * cos(3.0 * π/16.0), R2 * {square root over (ε χ )} * sin(3.0 * π/16.0)]
10010
[R2 * {square root over (ε χ )} * sin(π/16.0), R2 * {square root over (ε χ )} * cos(π/16.0)]
10011
[R2 * {square root over (ε χ )} * sin(3.0 * π/16.0), R2 * {square root over (ε χ )} * cos(3.0 * π/16.0)]
10100
[R2 * {square root over (ε χ )} * cos(π/16.0), −R2 * {square root over (ε χ )} * sin(π/16.0)]
10101
[R2 * {square root over (ε χ )} * cos(3.0 * π/16.0), −R2 * {square root over (ε χ )} * sin(3.0 * π/16.0)]
10110
[R2 * {square root over (ε χ )} * sin(π/16.0), −R2 * {square root over (ε χ )} * cos(π/16.0)]
10111
[R2 * {square root over (ε χ )} * sin(3.0 * π/16.0), −R2 * {square root over (ε χ )} * cos(3.0 * π/16.0)]
11000
[−R2 * {square root over (ε χ )} * cos(π/16.0), R2 * {square root over (ε χ )} * sin(π/16.0)]
11001
[−R2 * {square root over (ε χ )} * cos(3.0 * π/16.0), R2 * {square root over (ε χ )} * sin(3.0 * π/16.0)]
11010
[−R2 * {square root over (ε χ )} * sin(π/16.0), R2 * {square root over (ε χ )} * cos(π/16.0)]
11011
[−R2 * {square root over (ε χ )} * sin(3.0 * π/16.0), R2 * {square root over (ε χ )} * cos(3.0 * π/16.0)]
11100
[−R2 * {square root over (ε χ )} * cos(π/16.0), −R2 * {square root over (ε χ )} * sin(π/16.0)]
11101
[−R2 * {square root over (ε χ )} * cos(3.0 * π/16.0), −R2 * {square root over (ε χ )} * sin(3.0 * π/16.0)]
11110
[−R2 * {square root over (ε χ )} * sin(π/16.0), −R2 * {square root over (ε χ )} * cos(π/16.0)]
11111
[−R2 * {square root over (ε χ )} * sin(3.0 * π/16.0), −R2 * {square root over (ε χ )} * cos(3.0 * π/16.0)]
where ε x represents average energy per symbol, R1 2 +R2 2 =2, and R1 represents the radius of the inner ring and R2 represents the radius of the outer ring, and
wherein each of the [x, y] bit coordinate positions is rotated by a same rotation factor (from 0 to 359°, inclusive), and/or each bit label is altered by interchanging the 0's and 1's, and/or a uniform swapping of bit positions is applied within each bit label.
21. A method, comprising:
modulating a signal, through a modulation device, based at least in part on an 32-ary, 4+12+16APSK signal constellation, having an inner ring with 4 bit positions, a middle ring with 12 bit positions and an outer ring with 16 bit positions, in accordance with the following bit labeling and [x, y] bit coordinate positions:
Bit Label
[x, y] Coordinates
00000
[−R3 * {square root over (ε χ )} * cos(5.0 * π/16.0), R3 * {square root over (ε χ )} * cos(3.0 * π/16.0)]
00001
[−R3 * {square root over (ε χ )} * cos(7.0 * π/16.0), R3 * {square root over (ε χ )} * cos(π/16.0)]
00010
[R3 * {square root over (ε χ )} * cos(5.0 * π/16.0), R3 * {square root over (ε χ )} * cos(3.0 * π/16.0)]
00011
[R3 * {square root over (ε χ )} * cos(7.0 * π/16.0), R3 * {square root over (ε χ )} * cos(π/16.0)]
00100
[−R2 * {square root over (ε χ )} * sin(π/4.0), R2 * {square root over (ε χ )} * sin(π/4.0)]
00101
[−R2 * {square root over (ε χ )} * sin(π/12.0), R2 * {square root over (ε χ )} * sin(5.0 * π/12.0)]
00110
[R2 * {square root over (ε χ )} * sin(π/4.0), R2 * {square root over (ε χ )} * sin(π/4.0)]
00111
[R2 * {square root over (ε χ )} * sin(π/12.0), R2 * {square root over (ε χ )} * sin(5.0 * π/12.0)]
01000
[−R3 * {square root over (ε χ )} * cos(3.0 * π/16.0), R3 * {square root over (ε χ )} * cos(5.0 * π/16.0)]
01001
[−R3 * {square root over (ε χ )} * cos(π/16.0), R3 * {square root over (ε χ )} * cos(7.0 * π/16.0)]
01010
[R3 * {square root over (ε χ )} * cos(3.0 * π/16.0), R3 * {square root over (ε χ )} * cos(5.0 * π/16.0)]
01011
[R3 * {square root over (ε χ )} * cos(π/16.0), R3 * {square root over (ε χ )} * cos(7.0 * π/16.0)]
01100
[−R2 * {square root over (ε χ )} * sin(5.0 * π/12.0), R2 * {square root over (ε χ )} * sin(π/12.0)]
01101
[−R1 * {square root over (ε χ )} * sin(π/4.0), R1 * {square root over (ε χ )} * sin(π/4.0)]
01110
[R2 * {square root over (ε χ )} * sin(5.0 * π/12.0), R2 * {square root over (ε χ )} * sin(π/12.0)]
01111
[R1 * {square root over (ε χ )} * sin(π/4.0), R1 * {square root over (ε χ )} * sin(π/4.0)]
10000
[−R3 * {square root over (ε χ )} * cos(5.0 * π/16.0), −R3 * {square root over (ε χ )} * cos(3.0 * π/16.0)]
10001
[−R3 * {square root over (ε χ )} * cos(7.0 * π/16.0), −R3 * {square root over (ε χ )} * cos(π/16.0)]
10010
[R3 * {square root over (ε χ )} * cos(5.0 * π/16.0), −R3 * {square root over (ε χ )} * cos(3.0 * π/16.0)]
10011
[R3 * {square root over (ε χ )} * cos(7.0 * π/16.0), −R3 * {square root over (ε χ )} * cos(π/16.0)]
10100
[−R2 * {square root over (ε χ )} * sin(π/4.0), −R2 * {square root over (ε χ )} * sin(π/4.0)]
10101
[−R2 * {square root over (ε χ )} * sin(π/12.0), −R2 * {square root over (ε χ )} * sin(5.0 * π/12.0)]
10110
[R2 * {square root over (ε χ )} * sin(π/4.0), −R2 * {square root over (ε χ )} * sin(π/4.0)]
10111
[R2 * {square root over (ε χ )} * sin(π/12.0), −R2 * {square root over (ε χ )} * sin(5.0 * π/12.0)]
11000
[−R3 * {square root over (ε χ )} * cos(3.0 * π/16.0), −R3 * {square root over (ε χ )} * cos(5.0 * π/16.0)]
11001
[−R3 * {square root over (ε χ )} * cos(π/16.0), −R3 * {square root over (ε χ )} * cos(7.0 * π/16.0)]
11010
[R3 * {square root over (ε χ )} * cos(3.0 * π/16.0), −R3 * {square root over (ε χ )} * cos(5.0 * π/16.0)]
11011
[R3 * {square root over (ε χ )} * cos(π/16.0), −R3 * {square root over (ε χ )} * cos(7.0 * π/16.0)]
11100
[−R2 * {square root over (ε χ )} * sin(5.0 * π/12.0), −R2 * {square root over (ε χ )} * sin(π/12.0)]
11101
[−R1 * {square root over (ε χ )} * sin(π/4.0), −R1 * {square root over (ε χ )} * sin(π/4.0)]
11110
[R2 * {square root over (ε χ )} * sin(5.0 * π/12.0), −R2 * {square root over (ε χ )} * sin(π/12.0)]
11111
[R1 * {square root over (ε χ )} * sin(π/4.0), −R1 * {square root over (ε χ )} * sin(π/4.0)]
where ε x represents average energy per symbol, 4*R1 2 +12*R2 2 +16*R3 2 =32, and R1 represents the radius of the inner ring, R2 represents the radius of the middle ring and R3 represents the radius of the outer ring, and
wherein each of the [x, y] bit coordinate positions is rotated by a same rotation factor (from 0 to 359°, inclusive), and/or each bit label is altered by interchanging the 0's and 1's, and/or a uniform swapping of bit positions is applied within each bit label.
22. An apparatus, comprising:
a modulation device configured to modulate a signal based at least in part on an 32-ary, 4+12+16APSK signal constellation, having an inner ring with 4 bit positions, a middle ring with 12 bit positions and an outer ring with 16 bit positions, in accordance with the following bit labeling and [x, y] bit coordinate positions:
Bit
Label
[x, y] Coordinates
00000
[−R3 * {square root over (ε x )} * cos(5.0 * π/16.0), R3 * {square root over (ε x )} * cos(3.0 * π/16.0)]
00001
[−R3 * {square root over (ε x )} * cos(7.0 * π/16.0), R3 * {square root over (ε x )} * cos(π/16.0)]
00010
[R3 * {square root over (ε x )} * cos(5.0 * π/16.0), R3 * {square root over (ε x )} * cos(3.0 * π/16.0)]
00011
[R3 * {square root over (ε x )} * cos(7.0 * π/16.0), R3 * {square root over (ε x )} * cos(π/16.0)]
00100
[−R2 * {square root over (ε x )} * sin(π/4.0), R2 * {square root over (ε x )} * sin(π/4.0)]
00101
[−R2 * {square root over (ε x )} * sin(π/12.0), R2 * {square root over (ε x )} * sin(5.0 * π/12.0)]
00110
[R2 * {square root over (ε x )} * sin(π/4.0), R2 * {square root over (ε x )} * sin(π/4.0)]
00111
[R2 * {square root over (ε x )} * sin(π/12.0), R2 * {square root over (ε x )} * sin(5.0 * π/12.0)]
01000
[−R3 * {square root over (ε x )} * cos(3.0 * π/16.0), R3 * {square root over (ε x )} * cos(5.0 * π/16.0)]
01001
[−R3 * {square root over (ε x )} * cos(π/16.0), R3 * {square root over (ε x )} * cos(7.0 * π/16.0)]
01010
[R3 * {square root over (ε x )} * cos(3.0 * π/16.0), R3 * {square root over (ε x )} * cos(5.0 * π/16.0)]
01011
[R3 * {square root over (ε x )} * cos(π/16.0), R3 * {square root over (ε x )} * cos(7.0 * π/16.0)]
01100
[−R2 * {square root over (ε x )} * sin(5.0 * π/12.0), R2 * {square root over (ε x )} * sin(π/12.0)]
01101
[−R1 * {square root over (ε x )} * sin(π/4.0), R1 * {square root over (ε x )} * sin(π/4.0)]
01110
[R2 * {square root over (ε x )} * sin(5.0 * π/12.0), R2 * {square root over (ε x )} * sin(π/12.0)]
01111
[R1 * {square root over (ε x )} * sin(π/4.0), R1 * {square root over (ε x )} * sin(π/4.0)]
10000
[−R3 * {square root over (ε x )} * cos(5.0 * π/16.0), −R3 * {square root over (ε x )} * cos(3.0 * π/16.0)]
10001
[−R3 * {square root over (ε x )} * cos(7.0 * π/16.0), −R3 * {square root over (ε x )} * cos(π/16.0)]
10010
[R3 * {square root over (ε x )} * cos(5.0 * π/16.0), −R3 * {square root over (ε x )} * cos(3.0 * π/16.0)]
10011
[R3 * {square root over (ε x )} * cos(7.0 * π/16.0), −R3 * {square root over (ε x )} * cos(π/16.0)]
10100
[−R2 * {square root over (ε x )} * sin(π/4.0), −R2 * {square root over (ε x )} * sin(π/4.0)]
10101
[−R2 * {square root over (ε x )} * sin(π/12.0), −R2 * {square root over (ε x )} * sin(5.0 * π/12.0)]
10110
[R2 * {square root over (ε x )} * sin(π/4.0), −R2 * {square root over (ε x )} * sin(π/4.0)]
10111
[R2 * {square root over (ε x )} * sin(π/12.0), −R2 * {square root over (ε x )} * sin(5.0 * π/12.0)]
11000
[−R3 * {square root over (ε x )} * cos(3.0 * π/16.0), −R3 * {square root over (ε x )} * cos(5.0 * π/16.0)]
11001
[−R3 * {square root over (ε x )} * cos(π/16.0), −R3 * {square root over (ε x )} * cos(7.0 * π/16.0)]
11010
[R3 * {square root over (ε x )} * cos(3.0 * π/16.0), −R3 * {square root over (ε x )} * cos(5.0 * π/16.0)]
11011
[R3 * {square root over (ε x )} * cos(π/16.0), −R3 * {square root over (ε x )} * cos(7.0 * π/16.0)]
11100
[−R2 * {square root over (ε x )} * sin(5.0 * π/12.0), −R2 * {square root over (ε x )} * sin(π/12.0)]
11101
[−R1 * {square root over (ε x )} * sin(π/4.0), −R1 * {square root over (ε x )} * sin(π/4.0)]
11110
[R2 * {square root over (ε x )} * sin(5.0 * π/12.0), −R2 * {square root over (ε x )} * sin(π/12.0)]
11111
[R1 * {square root over (ε x )} * sin(π/4.0), −R1 * {square root over (ε x )} * sin(π/4.0)]
where ε x represents average energy per symbol, 4*R1 2 +12*R2 2 +16*R3 2 =32, and R1 represents the radius of the inner ring, R2 represents the radius of the middle ring and R3 represents the radius of the outer ring, and
wherein each of the [x, y] bit coordinate positions is rotated by a same rotation factor (from 0 to 359°, inclusive), and/or each bit label is altered by interchanging the 0's and 1's, and/or a uniform swapping of bit positions is applied within each bit label.
23. A method, comprising:
demodulating a signal, through a demodulation device, wherein the signal was modulated based at least in part on an 32-ary, 4+12+16APSK signal constellation, having an inner ring with 4 bit positions, a middle ring with 12 bit positions and an outer ring with 16 bit positions, in accordance with the following bit labeling and [x, y] bit coordinate positions:
Bit
Label
[x, y] Coordinates
00000
[−R3 * {square root over (ε x )} * cos(5.0 * π/16.0), R3 * {square root over (ε x )} * cos(3.0 * π/16.0)]
00001
[−R3 * {square root over (ε x )} * cos(7.0 * π/16.0), R3 * {square root over (ε x )} * cos(π/16.0)]
00010
[R3 * {square root over (ε x )} * cos(5.0 * π/16.0), R3 * {square root over (ε x )} * cos(3.0 * π/16.0)]
00011
[R3 * {square root over (ε x )} * cos(7.0 * π/16.0), R3 * {square root over (ε x )} * cos(π/16.0)]
00100
[−R2 * {square root over (ε x )} * sin(π/4.0), R2 * {square root over (ε x )} * sin(π/4.0)]
00101
[−R2 * {square root over (ε x )} * sin(π/12.0), R2 * {square root over (ε x )} * sin(5.0 * π/12.0)]
00110
[R2 * {square root over (ε x )} * sin(π/4.0), R2 * {square root over (ε x )} * sin(π/4.0)]
00111
[R2 * {square root over (ε x )} * sin(π/12.0), R2 * {square root over (ε x )} * sin(5.0 * π/12.0)]
01000
[−R3 * {square root over (ε x )} * cos(3.0 * π/16.0), R3 * {square root over (ε x )} * cos(5.0 * π/16.0)]
01001
[−R3 * {square root over (ε x )} * cos(π/16.0), R3 * {square root over (ε x )} * cos(7.0 * π/16.0)]
01010
[R3 * {square root over (ε x )} * cos(3.0 * π/16.0), R3 * {square root over (ε x )} * cos(5.0 * π/16.0)]
01011
[R3 * {square root over (ε x )} * cos(π/16.0), R3 * {square root over (ε x )} * cos(7.0 * π/16.0)]
01100
[−R2 * {square root over (ε x )} * sin(5.0 * π/12.0), R2 * {square root over (ε x )} * sin(π/12.0)]
01101
[−R1 * {square root over (ε x )} * sin(π/4.0), R1 * {square root over (ε x )} * sin(π/4.0)]
01110
[R2 * {square root over (ε x )} * sin(5.0 * π/12.0), R2 * {square root over (ε x )} * sin(π/12.0)]
01111
[R1 * {square root over (ε x )} * sin(π/4.0), R1 * {square root over (ε x )} * sin(π/4.0)]
10000
[−R3 * {square root over (ε x )} * cos(5.0 * π/16.0), −R3 * {square root over (ε x )} * cos(3.0 * π/16.0)]
10001
[−R3 * {square root over (ε x )} * cos(7.0 * π/16.0), −R3 * {square root over (ε x )} * cos(π/16.0)]
10010
[R3 * {square root over (ε x )} * cos(5.0 * π/16.0), −R3 * {square root over (ε x )} * cos(3.0 * π/16.0)]
10011
[R3 * {square root over (ε x )} * cos(7.0 * π/16.0), −R3 * {square root over (ε x )} * cos(π/16.0)]
10100
[−R2 * {square root over (ε x )} * sin(π/4.0), −R2 * {square root over (ε x )} * sin(π/4.0)]
10101
[−R2 * {square root over (ε x )} * sin(π/12.0), −R2 * {square root over (ε x )} * sin(5.0 * π/12.0)]
10110
[R2 * {square root over (ε x )} * sin(π/4.0), −R2 * {square root over (ε x )} * sin(π/4.0)]
10111
[R2 * {square root over (ε x )} * sin(π/12.0), −R2 * {square root over (ε x )} * sin(5.0 * π/12.0)]
11000
[−R3 * {square root over (ε x )} * cos(3.0 * π/16.0), −R3 * {square root over (ε x )} * cos(5.0 * π/16.0)]
11001
[−R3 * {square root over (ε x )} * cos(π/16.0), −R3 * {square root over (ε x )} * cos(7.0 * π/16.0)]
11010
[R3 * {square root over (ε x )} * cos(3.0 * π/16.0), −R3 * {square root over (ε x )} * cos(5.0 * π/16.0)]
11011
[R3 * {square root over (ε x )} * cos(π/16.0), −R3 * {square root over (ε x )} * cos(7.0 * π/16.0)]
11100
[−R2 * {square root over (ε x )} * sin(5.0 * π/12.0), −R2 * {square root over (ε x )} * sin(π/12.0)]
11101
[−R1 * {square root over (ε x )} * sin(π/4.0), −R1 * {square root over (ε x )} * sin(π/4.0)]
11110
[R2 * {square root over (ε x )} * sin(5.0 * π/12.0), −R2 * {square root over (ε x )} * sin(π/12.0)]
11111
[R1 * {square root over (ε x )} * sin(π/4.0), −R1 * {square root over (ε x )} * sin(π/4.0)]
where ε x represents average energy per symbol, 4*R1 2 +12*R2 2 +16*R3 2 =32, and R1 represents the radius of the inner ring, R2 represents the radius of the middle ring and R3 represents the radius of the outer ring, and
wherein each of the [x, y] bit coordinate positions is rotated by a same rotation factor (from 0 to 359°, inclusive), and/or each bit label is altered by interchanging the 0's and 1's, and/or a uniform swapping of bit positions is applied within each bit label.
24. An apparatus, comprising:
a demodulation device configured to demodulate a signal, wherein the signal was modulated based at least in part on an 32-ary, 4+12+16APSK signal constellation, having an inner ring with 4 bit positions, a middle ring with 12 bit positions and an outer ring with 16 bit positions, in accordance with the following bit labeling and [x, y] bit coordinate positions:
Bit
Label
[x, y] Coordinates
00000
[−R3 * {square root over (ε x )} * cos(5.0 * π/16.0), R3 * {square root over (ε x )} * cos(3.0 * π/16.0)]
00001
[−R3 * {square root over (ε x )} * cos(7.0 * π/16.0), R3 * {square root over (ε x )} * cos(π/16.0)]
00010
[R3 * {square root over (ε x )} * cos(5.0 * π/16.0), R3 * {square root over (ε x )} * cos(3.0 * π/16.0)]
00011
[R3 * {square root over (ε x )} * cos(7.0 * π/16.0), R3 * {square root over (ε x )} * cos(π/16.0)]
00100
[−R2 * {square root over (ε x )} * sin(π/4.0), R2 * {square root over (ε x )} * sin(π/4.0)]
00101
[−R2 * {square root over (ε x )} * sin(π/12.0), R2 * {square root over (ε x )} * sin(5.0 * π/12.0)]
00110
[R2 * {square root over (ε x )} * sin(π/4.0), R2 * {square root over (ε x )} * sin(π/4.0)]
00111
[R2 * {square root over (ε x )} * sin(π/12.0), R2 * {square root over (ε x )} * sin(5.0 * π/12.0)]
01000
[−R3 * {square root over (ε x )} * cos(3.0 * π/16.0), R3 * {square root over (ε x )} * cos(5.0 * π/16.0)]
01001
[−R3 * {square root over (ε x )} * cos(π/16.0), R3 * {square root over (ε x )} * cos(7.0 * π/16.0)]
01010
[R3 * {square root over (ε x )} * cos(3.0 * π/16.0), R3 * {square root over (ε x )} * cos(5.0 * π/16.0)]
01011
[R3 * {square root over (ε x )} * cos(π/16.0), R3 * {square root over (ε x )} * cos(7.0 * π/16.0)]
01100
[−R2 * {square root over (ε x )} * sin(5.0 * π/12.0), R2 * {square root over (ε x )} * sin(π/12.0)]
01101
[−R1 * {square root over (ε x )} * sin(π/4.0), R1 * {square root over (ε x )} * sin(π/4.0)]
01110
[R2 * {square root over (ε x )} * sin(5.0 * π/12.0), R2 * {square root over (ε x )} * sin(π/12.0)]
01111
[R1 * {square root over (ε x )} * sin(π/4.0), R1 * {square root over (ε x )} * sin(π/4.0)]
10000
[−R3 * {square root over (ε x )} * cos(5.0 * π/16.0), −R3 * {square root over (ε x )} * cos(3.0 * π/16.0)]
10001
[−R3 * {square root over (ε x )} * cos(7.0 * π/16.0), −R3 * {square root over (ε x )} * cos(π/16.0)]
10010
[R3 * {square root over (ε x )} * cos(5.0 * π/16.0), −R3 * {square root over (ε x )} * cos(3.0 * π/16.0)]
10011
[R3 * {square root over (ε x )} * cos(7.0 * π/16.0), −R3 * {square root over (ε x )} * cos(π/16.0)]
10100
[−R2 * {square root over (ε x )} * sin(π/4.0), −R2 * {square root over (ε x )} * sin(π/4.0)]
10101
[−R2 * {square root over (ε x )} * sin(π/12.0), −R2 * {square root over (ε x )} * sin(5.0 * π/12.0)]
10110
[R2 * {square root over (ε x )} * sin(π/4.0), −R2 * {square root over (ε x )} * sin(π/4.0)]
10111
[R2 * {square root over (ε x )} * sin(π/12.0), −R2 * {square root over (ε x )} * sin(5.0 * π/12.0)]
11000
[−R3 * {square root over (ε x )} * cos(3.0 * π/16.0), −R3 * {square root over (ε x )} * cos(5.0 * π/16.0)]
11001
[−R3 * {square root over (ε x )} * cos(π/16.0), −R3 * {square root over (ε x )} * cos(7.0 * π/16.0)]
11010
[R3 * {square root over (ε x )} * cos(3.0 * π/16.0), −R3 * {square root over (ε x )} * cos(5.0 * π/16.0)]
11011
[R3 * {square root over (ε x )} * cos(π/16.0), −R3 * {square root over (ε x )} * cos(7.0 * π/16.0)]
11100
[−R2 * {square root over (ε x )} * sin(5.0 * π/12.0), −R2 * {square root over (ε x )} * sin(π/12.0)]
11101
[−R1 * {square root over (ε x )} * sin(π/4.0), −R1 * {square root over (ε x )} * sin(π/4.0)]
11110
[R2 * {square root over (ε x )} * sin(5.0 * π/12.0), −R2 * {square root over (ε x )} * sin(π/12.0)]
11111
[R1 * {square root over (ε x )} * sin(π/4.0), −R1 * {square root over (ε x )} * sin(π/4.0)]
where ε x represents average energy per symbol, 4*R1 2 +12*R2 2 +16*R3 2 =32, and R1 represents the radius of the inner ring, R2 represents the radius of the middle ring and R3 represents the radius of the outer ring, and
wherein each of the [x, y] bit coordinate positions is rotated by a same rotation factor (from 0 to 359°, inclusive), and/or each bit label is altered by interchanging the 0's and 1's, and/or a uniform swapping of bit positions is applied within each bit label.
25. A method, comprising:
modulating a signal, through a modulation device, based at least in part on an 32-ary, 4+12+16APSK signal constellation, having an inner ring with 4 bit positions, a middle ring with 12 bit positions and an outer ring with 16 bit positions, in accordance with the following bit labeling and [x, y] bit coordinate positions:
Bit Label
[x, y] Coordinates
00000
[−R3 * {square root over (ε x )} * sin(π/4.0), R3 * {square root over (ε x )} * sin(π/4.0)]
00001
[−R3 * {square root over (ε x )} * sin(π/8.0), R3 * {square root over (ε x )} * cos(π/8.0)]
00010
[R3 * {square root over (ε x )} * sin(π/8.0), R3 * {square root over (ε x )} * cos(π/8.0)]
00011
[0, R3 * {square root over (ε x )}]
00100
[−R2 * {square root over (ε x )} * sin(π/4.0), R2 * {square root over (ε x )} * sin(π/4.0)]
00101
[−R2 * {square root over (ε x )} * sin(π/12.0), R2 * {square root over (ε x )} * sin(5.0 * π/12.0)]
00110
[R2 * {square root over (ε x )} * sin(π/4.0), R2 * {square root over (ε x )} * sin(π/4.0)]
00111
[R2 * {square root over (ε x )} * sin(π/12.0), R2 * {square root over (ε x )} * sin(5.0 * π/12.0)]
01000
[−R3 * {square root over (ε x )} * cos(π/8.0), R3 * {square root over (ε x )} * sin(π/8.0)]
01001
[−R3 * {square root over (ε x )}, 0]
01010
[R3 * {square root over (ε x )} * sin(π/4.0), R3 * {square root over (ε x )} * sin(π/4.0)]
01011
[R3 * {square root over (ε x )} * cos(π/8.0), R3 * {square root over (ε x )} * sin(π/8.0)]
01100
[−R2 * {square root over (ε x )} * sin(5.0 * π/12.0), R2 * {square root over (ε x )} * sin(π/12.0)]
01101
[−R1 * {square root over (ε x )} * sin(π/4.0), R1 * {square root over (ε x )} * sin(π/4.0)]
01110
[R2 * {square root over (ε x )} * sin(5.0 * π/12.0), R2 * {square root over (ε x )} * sin(π/12.0)]
01111
[R1 * {square root over (ε x )} * sin(π/4.0), R1 * {square root over (ε x )} * sin(π/4.0)]
10000
[−R3 * {square root over (ε x )} * sin(π/8.0), −R3 * {square root over (ε x )} * cos(π/8.0)]
10001
[0, −R3 * {square root over (ε x )}]
10010
[R3 * {square root over (ε x )} * sin(π/4.0), −R3 * {square root over (ε x )} * sin(π/4.0)]
10011
[R3 * {square root over (ε x )} * sin(π/8.0), −R3 * {square root over (ε x )} * cos(π/8.0)]
10100
[−R2 * {square root over (ε x )} * sin(π/4.0), −R2 * {square root over (ε x )} * sin(π/4.0)]
10101
[−R2 * {square root over (ε x )} * sin(π/12.0), −R2 * {square root over (ε x )} * sin(5.0 * π/12.0)]
10110
[R2 * {square root over (ε x )} * sin(π/4.0), −R2 * {square root over (ε x )} * sin(π/4.0)]
10111
[R2 * {square root over (ε x )} * sin(π/12.0), −R2 * {square root over (ε x )} * sin(5.0 * π/12.0)]
11000
[−R3 * {square root over (ε x )} * sin(π/4.0), −R3 * {square root over (ε x )} * sin(π/4.0)]
11001
[−R3 * {square root over (ε x )} * cos(π/8.0), −R3 * {square root over (ε x )} * sin(π/8.0)]
11010
[R3 * {square root over (ε x )} * cos(π/8.0), −R3 * {square root over (ε x )} * sin(π/8.0)]
11011
[R3 * {square root over (ε x )}, 0]
11100
[−R2 * {square root over (ε x )} * sin(5.0 * π/12.0), −R2 * {square root over (ε x )} * sin(π/12.0)]
11101
[−R1 * {square root over (ε x )} * sin(π/4.0), −R1 * {square root over (ε x )} * sin(π/4.0)]
11110
[R2 * {square root over (ε x )} * sin(5.0 * π/12.0), −R2 * {square root over (ε x )} * sin(π/12.0)]
11111
[R1 * {square root over (ε x )} * sin(π/4.0), −R1 * {square root over (ε x )} * sin(π/4.0)]
where ε x represents average energy per symbol, 4*R1 2 +12*R2 2 +16*R3 2 =32, and R1 represents the radius of the inner ring, R2 represents the radius of the middle ring and R3 represents the radius of the outer ring, and
wherein each of the [x, y] bit coordinate positions is rotated by a same rotation factor (from 0 to 359°, inclusive), and/or each bit label is altered by interchanging the 0's and 1's, and/or a uniform swapping of bit positions is applied within each bit label.
26. An apparatus, comprising:
a modulation device configured to modulate a signal based at least in part on an 32-ary, 4+12+16APSK signal constellation, having an inner ring with 4 bit positions, a middle ring with 12 bit positions and an outer ring with 16 bit positions, in accordance with the following bit labeling and [x, y] bit coordinate positions:
Bit Label
[x, y] Coordinates
00000
[−R3 * {square root over (ε x )} * sin(π/4.0), R3 * {square root over (ε x )} * sin(π/4.0)]
00001
[−R3 * {square root over (ε x )} * sin(π/8.0), R3 * {square root over (ε x )} * cos(π/8.0)]
00010
[R3 * {square root over (ε x )} * sin(π/8.0), R3 * {square root over (ε x )} * cos(π/8.0)]
00011
[0, R3 * {square root over (ε x )}]
00100
[−R2 * {square root over (ε x )} * sin(π/4.0), R2 * {square root over (ε x )} * sin(π/4.0)]
00101
[−R2 * {square root over (ε x )} * sin(π/12.0), R2 * {square root over (ε x )} * sin(5.0 * π/12.0)]
00110
[R2 * {square root over (ε x )} * sin(π/4.0), R2 * {square root over (ε x )} * sin(π/4.0)]
00111
[R2 * {square root over (ε x )} * sin(π/12.0), R2 * {square root over (ε x )} * sin(5.0 * π/12.0)]
01000
[−R3 * {square root over (ε x )} * cos(π/8.0), R3 * {square root over (ε x )} * sin(π/8.0)]
01001
[−R3 * {square root over (ε x )}, 0]
01010
[R3 * {square root over (ε x )} * sin(π/4.0), R3 * {square root over (ε x )} * sin(π/4.0)]
01011
[R3 * {square root over (ε x )} * cos(π/8.0), R3 * {square root over (ε x )} * sin(π/8.0)]
01100
[−R2 * {square root over (ε x )} * sin(5.0 * π/12.0), R2 * {square root over (ε x )} * sin(π/12.0)]
01101
[−R1 * {square root over (ε x )} * sin(π/4.0), R1 * {square root over (ε x )} * sin(π/4.0)]
01110
[R2 * {square root over (ε x )} * sin(5.0 * π/12.0), R2 * {square root over (ε x )} * sin(π/12.0)]
01111
[R1 * {square root over (ε x )} * sin(π/4.0), R1 * {square root over (ε x )} * sin(π/4.0)]
10000
[−R3 * {square root over (ε x )} * sin(π/8.0), −R3 * {square root over (ε x )} * cos(π/8.0)]
10001
[0, −R3 * {square root over (ε x )}]
10010
[R3 * {square root over (ε x )} * sin(π/4.0), −R3 * {square root over (ε x )} * sin(π/4.0)]
10011
[R3 * {square root over (ε x )} * sin(π/8.0), −R3 * {square root over (ε x )} * cos(π/8.0)]
10100
[−R2 * {square root over (ε x )} * sin(π/4.0), −R2 * {square root over (ε x )} * sin(π/4.0)]
10101
[−R2 * {square root over (ε x )} * sin(π/12.0), −R2 * {square root over (ε x )} * sin(5.0 * π/12.0)]
10110
[R2 * {square root over (ε x )} * sin(π/4.0), −R2 * {square root over (ε x )} * sin(π/4.0)]
10111
[R2 * {square root over (ε x )} * sin(π/12.0), −R2 * {square root over (ε x )} * sin(5.0 * π/12.0)]
11000
[−R3 * {square root over (ε x )} * sin(π/4.0), −R3 * {square root over (ε x )} * sin(π/4.0)]
11001
[−R3 * {square root over (ε x )} * cos(π/8.0), −R3 * {square root over (ε x )} * sin(π/8.0)]
11010
[R3 * {square root over (ε x )} * cos(π/8.0), −R3 * {square root over (ε x )} * sin(π/8.0)]
11011
[R3 * {square root over (ε x )}, 0]
11100
[−R2 * {square root over (ε x )} * sin(5.0 * π/12.0), −R2 * {square root over (ε x )} * sin(π/12.0)]
11101
[−R1 * {square root over (ε x )} * sin(π/4.0), −R1 * {square root over (ε x )} * sin(π/4.0)]
11110
[R2 * {square root over (ε x )} * sin(5.0 * π/12.0), −R2 * {square root over (ε x )} * sin(π/12.0)]
11111
[R1 * {square root over (ε x )} * sin(π/4.0), −R1 * {square root over (ε x )} * sin(π/4.0)]
where ε x represents average energy per symbol, 4*R1 2 +12*R2 2 +16*R3 2 =32, and R1 represents the radius of the inner ring, R2 represents the radius of the middle ring and R3 represents the radius of the outer ring, and
wherein each of the [x, y] bit coordinate positions is rotated by a same rotation factor (from 0 to 359°, inclusive), and/or each bit label is altered by interchanging the 0's and 1's, and/or a uniform swapping of bit positions is applied within each bit label.
27. A method, comprising:
demodulating a signal, through a demodulation device, wherein the signal was modulated based at least in part on an 32-ary, 4+12+16APSK signal constellation, having an inner ring with 4 bit positions, a middle ring with 12 bit positions and an outer ring with 16 bit positions, in accordance with the following bit labeling and [x, y] bit coordinate positions:
Bit Label
[x, y] Coordinates
00000
[−R3 * {square root over (ε x )} * sin(π/4.0), R3 * {square root over (ε x )} * sin(π/4.0)]
00001
[−R3 * {square root over (ε x )} * sin(π/8.0), R3 * {square root over (ε x )} * cos(π/8.0)]
00010
[R3 * {square root over (ε x )} * sin(π/8.0), R3 * {square root over (ε x )} * cos(π/8.0)]
00011
[0, R3 * {square root over (ε x )}]
00100
[−R2 * {square root over (ε x )} * sin(π/4.0), R2 * {square root over (ε x )} * sin(π/4.0)]
00101
[−R2 * {square root over (ε x )} * sin(π/12.0), R2 * {square root over (ε x )} * sin(5.0 * π/12.0)]
00110
[R2 * {square root over (ε x )} * sin(π/4.0), R2 * {square root over (ε x )} * sin(π/4.0)]
00111
[R2 * {square root over (ε x )} * sin(π/12.0), R2 * {square root over (ε x )} * sin(5.0 * π/12.0)]
01000
[−R3 * {square root over (ε x )} * cos(π/8.0), R3 * {square root over (ε x )} * sin(π/8.0)]
01001
[−R3 * {square root over (ε x )}, 0]
01010
[R3 * {square root over (ε x )} * sin(π/4.0), R3 * {square root over (ε x )} * sin(π/4.0)]
01011
[R3 * {square root over (ε x )} * cos(π/8.0), R3 * {square root over (ε x )} * sin(π/8.0)]
01100
[−R2 * {square root over (ε x )} * sin(5.0 * π/12.0), R2 * {square root over (ε x )} * sin(π/12.0)]
01101
[−R1 * {square root over (ε x )} * sin(π/4.0), R1 * {square root over (ε x )} * sin(π/4.0)]
01110
[R2 * {square root over (ε x )} * sin(5.0 * π/12.0), R2 * {square root over (ε x )} * sin(π/12.0)]
01111
[R1 * {square root over (ε x )} * sin(π/4.0), R1 * {square root over (ε x )} * sin(π/4.0)]
10000
[−R3 * {square root over (ε x )} * sin(π/8.0), −R3 * {square root over (ε x )} * cos(π/8.0)]
10001
[0, −R3 * {square root over (ε x )}]
10010
[R3 * {square root over (ε x )} * sin(π/4.0), −R3 * {square root over (ε x )} * sin(π/4.0)]
10011
[R3 * {square root over (ε x )} * sin(π/8.0), −R3 * {square root over (ε x )} * cos(π/8.0)]
10100
[−R2 * {square root over (ε x )} * sin(π/4.0), −R2 * {square root over (ε x )} * sin(π/4.0)]
10101
[−R2 * {square root over (ε x )} * sin(π/12.0), −R2 * {square root over (ε x )} * sin(5.0 * π/12.0)]
10110
[R2 * {square root over (ε x )} * sin(π/4.0), −R2 * {square root over (ε x )} * sin(π/4.0)]
10111
[R2 * {square root over (ε x )} * sin(π/12.0), −R2 * {square root over (ε x )} * sin(5.0 * π/12.0)]
11000
[−R3 * {square root over (ε x )} * sin(π/4.0), −R3 * {square root over (ε x )} * sin(π/4.0)]
11001
[−R3 * {square root over (ε x )} * cos(π/8.0), −R3 * {square root over (ε x )} * sin(π/8.0)]
11010
[R3 * {square root over (ε x )} * cos(π/8.0), −R3 * {square root over (ε x )} * sin(π/8.0)]
11011
[R3 * {square root over (ε x )}, 0]
11100
[−R2 * {square root over (ε x )} * sin(5.0 * π/12.0), −R2 * {square root over (ε x )} * sin(π/12.0)]
11101
[−R1 * {square root over (ε x )} * sin(π/4.0), −R1 * {square root over (ε x )} * sin(π/4.0)]
11110
[R2 * {square root over (ε x )} * sin(5.0 * π/12.0), −R2 * {square root over (ε x )} * sin(π/12.0)]
11111
[R1 * {square root over (ε x )} * sin(π/4.0), −R1 * {square root over (ε x )} * sin(π/4.0)]
where ε x represents average energy per symbol, 4*R1 2 +12*R2 2 +16*R3 2 =32, and R1 represents the radius of the inner ring, R2 represents the radius of the middle ring and R3 represents the radius of the outer ring, and
wherein each of the [x, y] bit coordinate positions is rotated by a same rotation factor (from 0 to 359°, inclusive), and/or each bit label is altered by interchanging the 0's and 1's, and/or a uniform swapping of bit positions is applied within each bit label.
28. An apparatus, comprising:
a demodulation device configured to demodulate a signal, wherein the signal was modulated based at least in part on an 32-ary, 4+12+16APSK signal constellation, having an inner ring with 4 bit positions, a middle ring with 12 bit positions and an outer ring with 16 bit positions, in accordance with the following bit labeling and [x, y] bit coordinate positions:
Bit Label
[x, y] Coordinates
00000
[−R3 * {square root over (ε x )} * sin(π/4.0), R3 * {square root over (ε x )} * sin(π/4.0)]
00001
[−R3 * {square root over (ε x )} * sin(π/8.0), R3 * {square root over (ε x )} * cos(π/8.0)]
00010
[R3 * {square root over (ε x )} * sin(π/8.0), R3 * {square root over (ε x )} * cos(π/8.0)]
00011
[0, R3 * {square root over (ε x )}]
00100
[−R2 * {square root over (ε x )} * sin(π/4.0), R2 * {square root over (ε x )} * sin(π/4.0)]
00101
[−R2 * {square root over (ε x )} * sin(π/12.0), R2 * {square root over (ε x )} * sin(5.0 * π/12.0)]
00110
[R2 * {square root over (ε x )} * sin(π/4.0), R2 * {square root over (ε x )} * sin(π/4.0)]
00111
[R2 * {square root over (ε x )} * sin(π/12.0), R2 * {square root over (ε x )} * sin(5.0 * π/12.0)]
01000
[−R3 * {square root over (ε x )} * cos(π/8.0), R3 * {square root over (ε x )} * sin(π/8.0)]
01001
[−R3 * {square root over (ε x )}, 0]
01010
[R3 * {square root over (ε x )} * sin(π/4.0), R3 * {square root over (ε x )} * sin(π/4.0)]
01011
[R3 * {square root over (ε x )} * cos(π/8.0), R3 * {square root over (ε x )} * sin(π/8.0)]
01100
[−R2 * {square root over (ε x )} * sin(5.0 * π/12.0), R2 * {square root over (ε x )} * sin(π/12.0)]
01101
[−R1 * {square root over (ε x )} * sin(π/4.0), R1 * {square root over (ε x )} * sin(π/4.0)]
01110
[R2 * {square root over (ε x )} * sin(5.0 * π/12.0), R2 * {square root over (ε x )} * sin(π/12.0)]
01111
[R1 * {square root over (ε x )} * sin(π/4.0), R1 * {square root over (ε x )} * sin(π/4.0)]
10000
[−R3 * {square root over (ε x )} * sin(π/8.0), −R3 * {square root over (ε x )} * cos(π/8.0)]
10001
[0, −R3 * {square root over (ε x )}]
10010
[R3 * {square root over (ε x )} * sin(π/4.0), −R3 * {square root over (ε x )} * sin(π/4.0)]
10011
[R3 * {square root over (ε x )} * sin(π/8.0), −R3 * {square root over (ε x )} * cos(π/8.0)]
10100
[−R2 * {square root over (ε x )} * sin(π/4.0), −R2 * {square root over (ε x )} * sin(π/4.0)]
10101
[−R2 * {square root over (ε x )} * sin(π/12.0), −R2 * {square root over (ε x )} * sin(5.0 * π/12.0)]
10110
[R2 * {square root over (ε x )} * sin(π/4.0), −R2 * {square root over (ε x )} * sin(π/4.0)]
10111
[R2 * {square root over (ε x )} * sin(π/12.0), −R2 * {square root over (ε x )} * sin(5.0 * π/12.0)]
11000
[−R3 * {square root over (ε x )} * sin(π/4.0), −R3 * {square root over (ε x )} * sin(π/4.0)]
11001
[−R3 * {square root over (ε x )} * cos(π/8.0), −R3 * {square root over (ε x )} * sin(π/8.0)]
11010
[R3 * {square root over (ε x )} * cos(π/8.0), −R3 * {square root over (ε x )} * sin(π/8.0)]
11011
[R3 * {square root over (ε x )}, 0]
11100
[−R2 * {square root over (ε x )} * sin(5.0 * π/12.0), −R2 * {square root over (ε x )} * sin(π/12.0)]
11101
[−R1 * {square root over (ε x )} * sin(π/4.0), −R1 * {square root over (ε x )} * sin(π/4.0)]
11110
[R2 * {square root over (ε x )} * sin(5.0 * π/12.0), −R2 * {square root over (ε x )} * sin(π/12.0)]
11111
[R1 * {square root over (ε x )} * sin(π/4.0), −R1 * {square root over (ε x )} * sin(π/4.0)]
where ε x represents average energy per symbol, 4*R1 2 +12*R2 2 +16*R3 2 =32, and R1 represents the radius of the inner ring, R2 represents the radius of the middle ring and R3 represents the radius of the outer ring, and
wherein each of the [x, y] bit coordinate positions is rotated by a same rotation factor (from 0 to 359°, inclusive), and/or each bit label is altered by interchanging the 0's and 1's, and/or a uniform swapping of bit positions is applied within each bit label.
29. A method, comprising:
modulating a signal, through a modulation device, based at least in part on an 64-ary, 8+16+20+20APSK signal constellation, having an inner ring with 8 bit positions, a first middle ring with 16 bit positions, a second middle ring with 20 bit positions and an outer ring with 20 bit positions.
30. The method according to claim 29 , wherein the bit positions of the inner, first middle, second middle and outer rings are in accordance with the following bit labeling and [x, y] bit coordinate positions:
Bit
Label
[x, y] Coordinates
000000
[R2 * {square root over (ε x )} * cos(25.0 * π/16.0), R2 * {square root over (ε x )} * sin(25.0 * π/16.0)]
000001
[R4 * {square root over (ε x )} * cos(35.0 * π/20.0), R4 * {square root over (ε x )} * sin(35.0 * π/20.0)]
000010
[R2 * {square root over (ε x )} * cos(27.0 * π/16.0), R2 * {square root over (ε x )} * sin(27.0 * π/16.0)]
000011
[R3 * {square root over (ε x )} * cos(35.0 * π/20.0), R3 * {square root over (ε x )} * sin(35.0 * π/20.0)]
000100
[R4 * {square root over (ε x )} * cos(31.0 * π/20.0), R4 * {square root over (ε x )} * sin(31.0 * π/20.0)]
000101
[R4 * {square root over (ε x )} * cos(33.0 * π/20.0), R4 * {square root over (ε x )} * sin(33.0 * π/20.0)]
000110
[R3 * {square root over (ε x )} * cos(31.0 * π/20.0), R3 * {square root over (ε x )} * sin(31.0 * π/20.0)]
000111
[R3 * {square root over (ε x )} * cos(33.0 * π/20.0), R3 * {square root over (ε x )} * sin(33.0 * π/20.0)]
001000
[R2 * {square root over (ε x )} * cos(23.0 * π/16.0), R2 * {square root over (ε x )} * sin(23.0 * π/16.0)]
001001
[R4 * {square root over (ε x )} * cos(25.0 * π/20.0), R4 * {square root over (ε x )} * sin(25.0 * π/20.0)]
001010
[R2 * {square root over (ε x )} * cos(21.0 * π/16.0), R2 * {square root over (ε x )} * sin(21.0 * π/16.0)]
001011
[R3 * {square root over (ε x )} * cos(25.0 * π/20.0), R3 * {square root over (ε x )} * sin(25.0 * π/20.0)]
001100
[R4 * {square root over (ε x )} * cos(29.0 * π/20.0), R4 * {square root over (ε x )} * sin(29.0 * π/20.0)]
001101
[R4 * {square root over (ε x )} * cos(27.0 * π/20.0), R4 * {square root over (ε x )} * sin(27.0 * π/20.0)]
001110
[R3 * {square root over (ε x )} * cos (29.0 * π/20.0), R3 * {square root over (ε x )} * sin(29.0 * π/20.0)]
001111
[R3 * {square root over (ε x )} * cos(27.0 * π/20.0), R3 * {square root over (ε x )} * sin(27.0 * π/20.0)]
010000
[R1 * {square root over (ε x )} * cos(13.0 * π/8.0), R1 * {square root over (ε x )} * sin(13.0 * π/8.0)]
010001
[R4 * {square root over (ε x )} * cos(37.0 * π/20.0), R4 * {square root over (ε x )} * sin(37.0 * π/20.0)]
010010
[R2 * {square root over (ε x )} * cos(29.0 * π/16.0), R2 * {square root over (ε x )} * sin(29.0 * π/16.0)]
010011
[R3 * {square root over (ε x )} * cos(37.0 * π/20.0), R3 * {square root over (ε x )} * sin(37.0 * π/20.0)]
010100
[R1 * {square root over (ε x )} * cos(15.0 * π/8.0), R1 * {square root over (ε x )} * sin(15.0 * π/8.0)]
010101
[R4 * {square root over (ε x )} * cos(39.0 * π/20.0), R4 * {square root over (ε x )} * sin(39.0 * π/20.0)]
010110
[R2 * {square root over (ε x )} * cos(31.0 * π/16.0), R2 * {square root over (ε x )} * sin(31.0 * π/16.0)]
010111
[R3 * {square root over (ε x )} * cos(39.0 * π/20.0), R3 * {square root over (ε x )} * sin(39.0 * π/20.0)]
011000
[R1 * {square root over (ε x )} * cos(11.0 * π/8.0), R1 * {square root over (ε x )} * sin(11.0 * π/8.0)]
011001
[R4 * {square root over (ε x )} * cos(23.0 * π/20.0), R4 * {square root over (ε x )} * sin(23.0 * π/20.0)]
011010
[R2 * {square root over (ε x )} * cos(19.0 * π/16.0), R2 * {square root over (ε x )} * sin(19.0 * π/16.0)]
011011
[R3 * {square root over (ε x )} * cos(23.0 * π/20.0), R3 * {square root over (ε x )} * sin(23.0 * π/20.0)]
011100
[R1 * {square root over (ε x )} * cos(9.0 * π/8.0), R1 * {square root over (ε x )} * sin(9.0 * π/8.0)]
011101
[R4 * {square root over (ε x )} * cos(21.0 * π/20.0), R4 * {square root over (ε x )} * sin(21.0 * π/20.0)]
011110
[R2 * {square root over (ε x )} * cos(17.0 * π/16.0), R2 * {square root over (ε x )} * sin(17.0 * π/16.0)]
011111
[R3 * {square root over (ε x )} * cos(21.0 * π/20.0), R3 * {square root over (ε x )} * sin(21.0 * π/20.0)]
100000
[R2 * {square root over (ε x )} * cos(7.0 * π/16.0), R2 * {square root over (ε x )} * sin(7.0 * π/16.0)]
100001
[R4 * {square root over (ε x )} * cos(5.0 * π/20.0), R4 * {square root over (ε x )} * sin(5.0 * π/20.0)]
100010
[R2 * {square root over (ε x )} * cos(5.0 * π/16.0), R2 * {square root over (ε x )} * sin(5.0 * π/16.0)]
100011
[R3 * {square root over (ε x )} * cos(5.0 * π/20.0), R3 * {square root over (ε x )} * sin(5.0 * π/20.0)]
100100
[R4 * {square root over (ε x )} * cos(9.0 * π/20.0), R4 * {square root over (ε x )} * sin(9.0 * π/20.0)]
100101
[R4 * {square root over (ε x )} * cos(7.0 * π/20.0), R4 * {square root over (ε x )} * sin(7.0 * π/20.0)]
100110
[R3 * {square root over (ε x )} * cos(9.0 * π/20.0), R3 * {square root over (ε x )} * sin(9.0 * π/20.0)]
100111
[R3 * {square root over (ε x )} * cos(7.0 * π/20.0), R3 * {square root over (ε x )} * sin(7.0 * π/20.0)]
101000
[R2 * {square root over (ε x )} * cos(9.0 * π/16.0), R2 * {square root over (ε x )} * sin(9.0 * π/16.0)]
101001
[R4 * {square root over (ε x )} * cos(15.0 * π/20.0), R4 * {square root over (ε x )} * sin(15.0 * π/20.0)]
101010
[R2 * {square root over (ε x )} * cos(11.0 * π/16.0), R2 * {square root over (ε x )} * sin(11.0 * π/16.0)]
101011
[R3 * {square root over (ε x )} * cos(15.0 * π/20.0), R3 * {square root over (ε x )} * sin(15.0 * π/20.0)]
101100
[R4 * {square root over (ε x )} * cos(11.0 * π/20.0), R4 * {square root over (ε x )} * sin(11.0 * π/20.0)]
101101
[R4 * {square root over (ε x )} * cos(13.0 * π/20.0), R4 * {square root over (ε x )} * sin(13.0 * π/20.0)]
101110
[R3 * {square root over (ε x )} * cos(11.0 * π/20.0), R3 * {square root over (ε x )} * sin(11.0 * π/20.0)]
101111
[R3 * {square root over (ε x )} * cos(13.0 * π/20.0), R3 * {square root over (ε x )} * sin(13.0 * π/20.0)]
110000
[R1 * {square root over (ε x )} * cos(3.0 * π/8.0), R1 * {square root over (ε x )} * sin(3.0 * π/8.0)]
110001
[R4 * {square root over (ε x )} * cos(3.0 * π/20.0), R4 * {square root over (ε x )} * sin(3.0 * π/20.0)]
110010
[R2 * {square root over (ε x )} * cos(3.0 * π/16.0), R2 * {square root over (ε x )} * sin(3.0 * π/16.0)]
110011
[R3 * {square root over (ε x )} * cos(3.0 * π/20.0), R3 * {square root over (ε x )} * sin(3.0 * π/20.0)]
110100
[R1 * {square root over (ε x )} * cos(π/8.0), R1 * {square root over (ε x )} * sin(π/8.0)]
110101
[R4 * {square root over (ε x )} * cos(π/20.0), R4 * {square root over (ε x )} * sin(π/20.0)]
110110
[R2 * {square root over (ε x )} * cos(π/16.0), R2 * {square root over (ε x )} * sin(π/16.0)]
110111
[R3 * {square root over (ε x )} * cos(π/20.0), R3 * {square root over (ε x )} * sin(π/20.0)]
111000
[R1 * {square root over (ε x )} * cos(5.0 * π/8.0), R1 * {square root over (ε x )} * sin(5.0 * π/8.0)]
111001
[R4 * {square root over (ε x )} * cos(17.0 * π/20.0), R4 * {square root over (ε x )} * sin(17.0 * π/20.0)]
111010
[R2 * {square root over (ε x )} * cos(13.0 * π/16.0), R2 * {square root over (ε x )} * sin(13.0 * π/16.0)]
111011
[R3 * {square root over (ε x )} * cos(17.0 * π/20.0), R3 * {square root over (ε x )} * sin(17.0 * π/20.0)]
111100
[R1 * {square root over (ε x )} * cos(7.0 * π/8.0), R1 * {square root over (ε x )} * sin(7.0 * π/8.0)]
111101
[R4 * {square root over (ε x )} * cos(19.0 * π/20.0), R4 * {square root over (ε x )} * sin(19.0 * π/20.0)]
111110
[R2 * {square root over (ε x )} * cos(15.0 * π/16.0), R2 * {square root over (ε x )} * sin(15.0 * π/16.0)]
111111
[R3 * {square root over (ε x )} * cos(19.0 * π/20.0), R3 * {square root over (ε x )} * sin(19.0 * π/20.0)]
where ε x represents average energy per symbol, 8*R1 2 +16*R2 2 +20*R3 2 +20*R4 2 =64, and R1 represents the radius of the inner ring, R2 represents the radius of the first middle ring, R3 represents the radius of the second middle ring and R4 represents the radius of the outer ring, and
wherein each of the [x, y] bit coordinate positions is rotated by a same rotation factor (from 0 to 359°, inclusive), and/or each bit label is altered by interchanging the 0's and 1's, and/or a uniform swapping of bit positions is applied within each bit label.
31. An apparatus, comprising:
a modulation device configured to modulate a signal based at least in part on an 64-ary, 8+16+20+20APSK signal constellation, having an inner ring with 8 bit positions, a first middle ring with 16 bit positions, a second middle ring with 20 bit positions and an outer ring with 20 bit positions.
32. The apparatus according to claim 31 , wherein the bit positions of the inner, first middle, second middle and outer rings are in accordance with the following bit labeling and [x, y] bit coordinate positions:
Bit
Label
[x, y] Coordinates
000000
[R2 * {square root over (ε x )} * cos(25.0 * π/16.0), R2 * {square root over (ε x )} * sin(25.0 * π/16.0)]
000001
[R4 * {square root over (ε x )} * cos(35.0 * π/20.0), R4 * {square root over (ε x )} * sin(35.0 * π/20.0)]
000010
[R2 * {square root over (ε x )} * cos(27.0 * π/16.0), R2 * {square root over (ε x )} * sin(27.0 * π/16.0)]
000011
[R3 * {square root over (ε x )} * cos(35.0 * π/20.0), R3 * {square root over (ε x )} * sin(35.0 * π/20.0)]
000100
[R4 * {square root over (ε x )} * cos(31.0 * π/20.0), R4 * {square root over (ε x )} * sin(31.0 * π/20.0)]
000101
[R4 * {square root over (ε x )} * cos(33.0 * π/20.0), R4 * {square root over (ε x )} * sin(33.0 * π/20.0)]
000110
[R3 * {square root over (ε x )} * cos(31.0 * π/20.0), R3 * {square root over (ε x )} * sin(31.0 * π/20.0)]
000111
[R3 * {square root over (ε x )} * cos(33.0 * π/20.0), R3 * {square root over (ε x )} * sin(33.0 * π/20.0)]
001000
[R2 * {square root over (ε x )} * cos(23.0 * π/16.0), R2 * {square root over (ε x )} * sin(23.0 * π/16.0)]
001001
[R4 * {square root over (ε x )} * cos(25.0 * π/20.0), R4 * {square root over (ε x )} * sin(25.0 * π/20.0)]
001010
[R2 * {square root over (ε x )} * cos(21.0 * π/16.0), R2 * {square root over (ε x )} * sin(21.0 * π/16.0)]
001011
[R3 * {square root over (ε x )} * cos(25.0 * π/20.0), R3 * {square root over (ε x )} * sin(25.0 * π/20.0)]
001100
[R4 * {square root over (ε x )} * cos(29.0 * π/20.0), R4 * {square root over (ε x )} * sin(29.0 * π/20.0)]
001101
[R4 * {square root over (ε x )} * cos(27.0 * π/20.0), R4 * {square root over (ε x )} * sin(27.0 * π/20.0)]
001110
[R3 * {square root over (ε x )} * cos(29.0 * π/20.0), R3 * {square root over (ε x )} * sin(29.0 * π/20.0)]
001111
[R3 * {square root over (ε x )} * cos(27.0 * π/20.0), R3 * {square root over (ε x )} * sin(27.0 * π/20.0)]
010000
[R1 * {square root over (ε x )} * cos(13.0 * π/8.0), R1 * {square root over (ε x )} * sin(13.0 * π/8.0)]
010001
[R4 * {square root over (ε x )} * cos(37.0 * π/20.0), R4 * {square root over (ε x )} * sin(37.0 * π/20.0)]
010010
[R2 * {square root over (ε x )} * cos(29.0 * π/16.0), R2 * {square root over (ε x )} * sin(29.0 * π/16.0)]
010011
[R3 * {square root over (ε x )} * cos(37.0 * π/20.0), R3 * {square root over (ε x )} * sin(37.0 * π/20.0)]
010100
[R1 * {square root over (ε x )} * cos(15.0 * π/8.0), R1 * {square root over (ε x )} * sin(15.0 * π/8.0)]
010101
[R4 * {square root over (ε x )} * cos(39.0 * π/20.0), R4 * {square root over (ε x )} * sin(39.0 * π/20.0)]
010110
[R2 * {square root over (ε x )} * cos(31.0 * π/16.0), R2 * {square root over (ε x )} * sin(31.0 * π/16.0)]
010111
[R3 * {square root over (ε x )} * cos(39.0 * π/20.0), R3 * {square root over (ε x )} * sin(39.0 * π/20.0)]
011000
[R1 * {square root over (ε x )} * cos(11.0 * π/8.0), R1 * {square root over (ε x )} * sin(11.0 * π/8.0)]
011001
[R4 * {square root over (ε x )} * cos(23.0 * π/20.0), R4 * {square root over (ε x )} * sin(23.0 * π/20.0)]
011010
[R2 * {square root over (ε x )} * cos(19.0 * π/16.0), R2 * {square root over (ε x )} * sin(19.0 * π/16.0)]
011011
[R3 * {square root over (ε x )} * cos(23.0 * π/20.0), R3 * {square root over (ε x )} * sin(23.0 * π/20.0)]
011100
[R1 * {square root over (ε x )} * cos(9.0 * π/8.0), R1 * {square root over (ε x )} * sin(9.0 * π/8.0)]
011101
[R4 * {square root over (ε x )} * cos(21.0 * π/20.0), R4 * {square root over (ε x )} * sin(21.0 * π/20.0)]
011110
[R2 * {square root over (ε x )} * cos(17.0 * π/16.0), R2 * {square root over (ε x )} * sin(17.0 * π/16.0)]
011111
[R3 * {square root over (ε x )} * cos(21.0 * π/20.0), R3 * {square root over (ε x )} * sin(21.0 * π/20.0)]
100000
[R2 * {square root over (ε x )} * cos(7.0 * π/16.0), R2 * {square root over (ε x )} * sin(7.0 * π/16.0)]
100001
[R4 * {square root over (ε x )} * cos(5.0 * π/20.0), R4 * {square root over (ε x )} * sin(5.0 * π/20.0)]
100010
[R2 * {square root over (ε x )} * cos(5.0 * π/16.0), R2 * {square root over (ε x )} * sin(5.0 * π/16.0)]
100011
[R3 * {square root over (ε x )} * cos(5.0 * π/20.0), R3 * {square root over (ε x )} * sin(5.0 * π/20.0)]
100100
[R4 * {square root over (ε x )} * cos(9.0 * π/20.0), R4 * {square root over (ε x )} * sin(9.0 * π/20.0)]
100101
[R4 * {square root over (ε x )} * cos(7.0 * π/20.0), R4 * {square root over (ε x )} * sin(7.0 * π/20.0)]
100110
[R3 * {square root over (ε x )} * cos(9.0 * π/20.0), R3 * {square root over (ε x )} * sin(9.0 * π/20.0)]
100111
[R3 * {square root over (ε x )} * cos(7.0 * π/20.0), R3 * {square root over (ε x )} * sin(7.0 * π/20.0)]
101000
[R2 * {square root over (ε x )} * cos(9.0 * π/16.0), R2 * {square root over (ε x )} * sin(9.0 * π/16.0)]
101001
[R4 * {square root over (ε x )} * cos(15.0 * π/20.0), R4 * {square root over (ε x )} * sin(15.0 * π/20.0)]
101010
[R2 * {square root over (ε x )} * cos(11.0 * π/16.0), R2 * {square root over (ε x )} * sin(11.0 * π/16.0)]
101011
[R3 * {square root over (ε x )} * cos(15.0 * π/20.0), R3 * {square root over (ε x )} * sin(15.0 * π/20.0)]
101100
[R4 * {square root over (ε x )} * cos(11.0 * π/20.0), R4 * {square root over (ε x )} * sin(11.0 * π/20.0)]
101101
[R4 * {square root over (ε x )} * cos(13.0 * π/20.0), R4 * {square root over (ε x )} * sin(13.0 * π/20.0)]
101110
[R3 * {square root over (ε x )} * cos(11.0 * π/20.0), R3 * {square root over (ε x )} * sin(11.0 * π/20.0)]
101111
[R3 * {square root over (ε x )} * cos(13.0 * π/20.0), R3 * {square root over (ε x )} * sin(13.0 * π/20.0)]
110000
[R1 * {square root over (ε x )} * cos(3.0 * π/8.0), R1 * {square root over (ε x )} * sin(3.0 * π/8.0)]
110001
[R4 * {square root over (ε x )} * cos(3.0 * π/20.0), R4 * {square root over (ε x )} * sin(3.0 * π/20.0)]
110010
[R2 * {square root over (ε x )} * cos(3.0 * π/16.0), R2 * {square root over (ε x )} * sin(3.0 * π/16.0)]
110011
[R3 * {square root over (ε x )} * cos(3.0 * π/20.0), R3 * {square root over (ε x )} * sin(3.0 * π/20.0)]
110100
[R1 * {square root over (ε x )} * cos(π/8.0), R1 * {square root over (ε x )} * sin(π/8.0)]
110101
[R4 * {square root over (ε x )} * cos(π/20.0), R4 * {square root over (ε x )} * sin(π/20.0)]
110110
[R2 * {square root over (ε x )} * cos(π/16.0), R2 * {square root over (ε x )} * sin(π/16.0)]
110111
[R3 * {square root over (ε x )} * cos(π/20.0), R3 * {square root over (ε x )} * sin(π/20.0)]
111000
[R1 * {square root over (ε x )} * cos(5.0 * π/8.0), R1 * {square root over (ε x )} * sin(5.0 * π/8.0)]
111001
[R4 * {square root over (ε x )} * cos(17.0 * π/20.0), R4 * {square root over (ε x )} * sin(17.0 * π/20.0)]
111010
[R2 * {square root over (ε x )} * cos(13.0 * π/16.0), R2 * {square root over (ε x )} * sin(13.0 * π/16.0)]
111011
[R3 * {square root over (ε x )} * cos(17.0 * π/20.0), R3 * {square root over (ε x )} * sin(17.0 * π/20.0)]
111100
[R1 * {square root over (ε x )} * cos(7.0 * π/8.0), R1 * {square root over (ε x )} * sin(7.0 * π/8.0)]
111101
[R4 * {square root over (ε x )} * cos(19.0 * π/20.0), R4 * {square root over (ε x )} * sin(19.0 * π/20.0)]
111110
[R2 * {square root over (ε x )} * cos(15.0 * π/16.0), R2 * {square root over (ε x )} * sin(15.0 * π/16.0)]
111111
[R3 * {square root over (ε x )} * cos(19.0 * π/20.0), R3 * {square root over (ε x )} * sin(19.0 * π/20.0)]
where ε x represents average energy per symbol, 8*R1 2 +16*R2 2 +20*R3 2 +20*R4 2 =64, and R1 represents the radius of the inner ring, R2 represents the radius of the first middle ring, R3 represents the radius of the second middle ring and R4 represents the radius of the outer ring, and
wherein each of the [x, y] bit coordinate positions is rotated by a same rotation factor (from 0 to 359°, inclusive), and/or each bit label is altered by interchanging the 0's and 1's, and/or a uniform swapping of bit positions is applied within each bit label.
33. A method, comprising:
demodulating a signal, through a demodulation device, wherein the signal was modulated based at least in part on an 64-ary, 8+16+20+20APSK signal constellation, having an inner ring with 8 bit positions, a first middle ring with 16 bit positions, a second middle ring with 20 bit positions and an outer ring with 20 bit positions.
34. The method according to claim 33 , wherein the bit positions of the inner, first middle, second middle and outer rings are in accordance with the following bit labeling and [x, y] bit coordinate positions:
Bit
Label
[x, y] Coordinates
000000
[R2 * {square root over (ε x )} * cos(25.0 * π/16.0), R2 * {square root over (ε x )} * sin(25.0 * π/16.0)]
000001
[R4 * {square root over (ε x )} * cos(35.0 * π/20.0), R4 * {square root over (ε x )} * sin(35.0 * π/20.0)]
000010
[R2 * {square root over (ε x )} * cos(27.0 * π/16.0), R2 * {square root over (ε x )} * sin(27.0 * π/16.0)]
000011
[R3 * {square root over (ε x )} * cos(35.0 * π/20.0), R3 * {square root over (ε x )} * sin(35.0 * π/20.0)]
000100
[R4 * {square root over (ε x )} * cos(31.0 * π/20.0), R4 * {square root over (ε x )} * sin(31.0 * π/20.0)]
000101
[R4 * {square root over (ε x )} * cos(33.0 * π/20.0), R4 * {square root over (ε x )} * sin(33.0 * π/20.0)]
000110
[R3 * {square root over (ε x )} * cos(31.0 * π/20.0), R3 * {square root over (ε x )} * sin(31.0 * π/20.0)]
000111
[R3 * {square root over (ε x )} * cos(33.0 * π/20.0), R3 * {square root over (ε x )} * sin(33.0 * π/20.0)]
001000
[R2 * {square root over (ε x )} * cos(23.0 * π/16.0), R2 * {square root over (ε x )} * sin(23.0 * π/16.0)]
001001
[R4 * {square root over (ε x )} * cos(25.0 * π/20.0), R4 * {square root over (ε x )} * sin(25.0 * π/20.0)]
001010
[R2 * {square root over (ε x )} * cos(21.0 * π/16.0), R2 * {square root over (ε x )} * sin(21.0 * π/16.0)]
001011
[R3 * {square root over (ε x )} * cos(25.0 * π/20.0), R3 * {square root over (ε x )} * sin(25.0 * π/20.0)]
001100
[R4 * {square root over (ε x )} * cos(29.0 * π/20.0), R4 * {square root over (ε x )} * sin(29.0 * π/20.0)]
001101
[R4 * {square root over (ε x )} * cos(27.0 * π/20.0), R4 * {square root over (ε x )} * sin(27.0 * π/20.0)]
001110
[R3 * {square root over (ε x )} * cos(29.0 * π/20.0), R3 * {square root over (ε x )} * sin(29.0 * π/20.0)]
001111
[R3 * {square root over (ε x )} * cos(27.0 * π/20.0), R3 * {square root over (ε x )} * sin(27.0 * π/20.0)]
010000
[R1 * {square root over (ε x )} * cos(13.0 * π/8.0), R1 * {square root over (ε x )} * sin(13.0 * π/8.0)]
010001
[R4 * {square root over (ε x )} * cos(37.0 * π/20.0), R4 * {square root over (ε x )} * sin(37.0 * π/20.0)]
010010
[R2 * {square root over (ε x )} * cos(29.0 * π/16.0), R2 * {square root over (ε x )} * sin(29.0 * π/16.0)]
010011
[R3 * {square root over (ε x )} * cos(37.0 * π/20.0), R3 * {square root over (ε x )} * sin(37.0 * π/20.0)]
010100
[R1 * {square root over (ε x )} * cos(15.0 * π/8.0), R1 * {square root over (ε x )} * sin(15.0 * π/8.0)]
010101
[R4 * {square root over (ε x )} * cos(39.0 * π/20.0), R4 * {square root over (ε x )} * sin(39.0 * π/20.0)]
010110
[R2 * {square root over (ε x )} * cos(31.0 * π/16.0), R2 * {square root over (ε x )} * sin(31.0 * π/16.0)]
010111
[R3 * {square root over (ε x )} * cos(39.0 * π/20.0), R3 * {square root over (ε x )} * sin(39.0 * π/20.0)]
011000
[R1 * {square root over (ε x )} * cos(11.0 * π/8.0), R1 * {square root over (ε x )} * sin(11.0 * π/8.0)]
011001
[R4 * {square root over (ε x )} * cos(23.0 * π/20.0), R4 * {square root over (ε x )} * sin(23.0 * π/20.0)]
011010
[R2 * {square root over (ε x )} * cos(19.0 * π/16.0), R2 * {square root over (ε x )} * sin(19.0 * π/16.0)]
011011
[R3 * {square root over (ε x )} * cos(23.0 * π/20.0), R3 * {square root over (ε x )} * sin(23.0 * π/20.0)]
011100
[R1 * {square root over (ε x )} * cos(9.0 * π/8.0), R1 * {square root over (ε x )} * sin(9.0 * π/8.0)]
011101
[R4 * {square root over (ε x )} * cos(21.0 * π/20.0), R4 * {square root over (ε x )} * sin(21.0 * π/20.0)]
011110
[R2 * {square root over (ε x )} * cos(17.0 * π/16.0), R2 * {square root over (ε x )} * sin(17.0 * π/16.0)]
011111
[R3 * {square root over (ε x )} * cos(21.0 * π/20.0), R3 * {square root over (ε x )} * sin(21.0 * π/20.0)]
100000
[R2 * {square root over (ε x )} * cos(7.0 * π/16.0), R2 * {square root over (ε x )} * sin(7.0 * π/16.0)]
100001
[R4 * {square root over (ε x )} * cos(5.0 * π/20.0), R4 * {square root over (ε x )} * sin(5.0 * π/20.0)]
100010
[R2 * {square root over (ε x )} * cos(5.0 * π/16.0), R2 * {square root over (ε x )} * sin(5.0 * π/16.0)]
100011
[R3 * {square root over (ε x )} * cos(5.0 * π/20.0), R3 * {square root over (ε x )} * sin(5.0 * π/20.0)]
100100
[R4 * {square root over (ε x )} * cos(9.0 * π/20.0), R4 * {square root over (ε x )} * sin(9.0 * π/20.0)]
100101
[R4 * {square root over (ε x )} * cos(7.0 * π/20.0), R4 * {square root over (ε x )} * sin(7.0 * π/20.0)]
100110
[R3 * {square root over (ε x )} * cos(9.0 * π/20.0), R3 * {square root over (ε x )} * sin(9.0 * π/20.0)]
100111
[R3 * {square root over (ε x )} * cos(7.0 * π/20.0), R3 * {square root over (ε x )} * sin(7.0 * π/20.0)]
101000
[R2 * {square root over (ε x )} * cos(9.0 * π/16.0), R2 * {square root over (ε x )} * sin(9.0 * π/16.0)]
101001
[R4 * {square root over (ε x )} * cos(15.0 * π/20.0), R4 * {square root over (ε x )} * sin(15.0 * π/20.0)]
101010
[R2 * {square root over (ε x )} * cos(11.0 * π/16.0), R2 * {square root over (ε x )} * sin(11.0 * π/16.0)]
101011
[R3 * {square root over (ε x )} * cos(15.0 * π/20.0), R3 * {square root over (ε x )} * sin(15.0 * π/20.0)]
101100
[R4 * {square root over (ε x )} * cos(11.0 * π/20.0), R4 * {square root over (ε x )} * sin(11.0 * π/20.0)]
101101
[R4 * {square root over (ε x )} * cos(13.0 * π/20.0), R4 * {square root over (ε x )} * sin(13.0 * π/20.0)]
101110
[R3 * {square root over (ε x )} * cos(11.0 * π/20.0), R3 * {square root over (ε x )} * sin(11.0 * π/20.0)]
101111
[R3 * {square root over (ε x )} * cos(13.0 * π/20.0), R3 * {square root over (ε x )} * sin(13.0 * π/20.0)]
110000
[R1 * {square root over (ε x )} * cos(3.0 * π/8.0), R1 * {square root over (ε x )} * sin(3.0 * π/8.0)]
110001
[R4 * {square root over (ε x )} * cos(3.0 * π/20.0), R4 * {square root over (ε x )} * sin(3.0 * π/20.0)]
110010
[R2 * {square root over (ε x )} * cos(3.0 * π/16.0), R2 * {square root over (ε x )} * sin(3.0 * π/16.0)]
110011
[R3 * {square root over (ε x )} * cos(3.0 * π/20.0), R3 * {square root over (ε x )} * sin(3.0 * π/20.0)]
110100
[R1 * {square root over (ε x )} * cos(π/8.0), R1 * {square root over (ε x )} * sin(π/8.0)]
110101
[R4 * {square root over (ε x )} * cos(π/20.0), R4 * {square root over (ε x )} * sin(π/20.0)]
110110
[R2 * {square root over (ε x )} * cos(π/16.0), R2 * {square root over (ε x )} * sin(π/16.0)]
110111
[R3 * {square root over (ε x )} * cos(π/20.0), R3 * {square root over (ε x )} * sin(π/20.0)]
111000
[R1 * {square root over (ε x )} * cos(5.0 * π/8.0), R1 * {square root over (ε x )} * sin(5.0 * π/8.0)]
111001
[R4 * {square root over (ε x )} * cos(17.0 * π/20.0), R4 * {square root over (ε x )} * sin(17.0 * π/20.0)]
111010
[R2 * {square root over (ε x )} * cos(13.0 * π/16.0), R2 * {square root over (ε x )} * sin(13.0 * π/16.0)]
111011
[R3 * {square root over (ε x )} * cos(17.0 * π/20.0), R3 * {square root over (ε x )} * sin(17.0 * π/20.0)]
111100
[R1 * {square root over (ε x )} * cos(7.0 * π/8.0), R1 * {square root over (ε x )} * sin(7.0 * π/8.0)]
111101
[R4 * {square root over (ε x )} * cos(19.0 * π/20.0), R4 * {square root over (ε x )} * sin(19.0 * π/20.0)]
111110
[R2 * {square root over (ε x )} * cos(15.0 * π/16.0), R2 * {square root over (ε x )} * sin(15.0 * π/16.0)]
111111
[R3 * {square root over (ε x )} * cos(19.0 * π/20.0), R3 * {square root over (ε x )} * sin(19.0 * π/20.0)]
where ε x represents average energy per symbol, 8*R1 2 +16*R2 2 +20*R3 2 +20*R4 2 =64, and R1 represents the radius of the inner ring, R2 represents the radius of the first middle ring, R3 represents the radius of the second middle ring and R4 represents the radius of the outer ring, and
wherein each of the [x, y] bit coordinate positions is rotated by a same rotation factor (from 0 to 359°, inclusive), and/or each bit label is altered by interchanging the 0's and 1's, and/or a uniform swapping of bit positions is applied within each bit label.
35. An apparatus, comprising:
a demodulation device configured to demodulate a signal, wherein the signal was modulated based at least in part on an 64-ary, 8+16+20+20APSK signal constellation, having an inner ring with 8 bit positions, a first middle ring with 16 bit positions, a second middle ring with 20 bit positions and an outer ring with 20 bit positions.
36. The apparatus according to claim 35 , wherein the bit positions of the inner, first middle, second middle and outer rings are in accordance with the following bit labeling and [x, y] bit coordinate positions:
Bit
Label
[x, y] Coordinates
000000
[R2 * {square root over (ε x )} * cos(25.0 * π/16.0), R2 * {square root over (ε x )} * sin(25.0 * π/16.0)]
000001
[R4 * {square root over (ε x )} * cos(35.0 * π/20.0), R4 * {square root over (ε x )} * sin(35.0 * π/20.0)]
000010
[R2 * {square root over (ε x )} * cos(27.0 * π/16.0), R2 * {square root over (ε x )} * sin(27.0 * π/16.0)]
000011
[R3 * {square root over (ε x )} * cos(35.0 * π/20.0), R3 * {square root over (ε x )} * sin(35.0 * π/20.0)]
000100
[R4 * {square root over (ε x )} * cos(31.0 * π/20.0), R4 * {square root over (ε x )} * sin(31.0 * π/20.0)]
000101
[R4 * {square root over (ε x )} * cos(33.0 * π/20.0), R4 * {square root over (ε x )} * sin(33.0 * π/20.0)]
000110
[R3 * {square root over (ε x )} * cos(31.0 * π/20.0), R3 * {square root over (ε x )} * sin(31.0 * π/20.0)]
000111
[R3 * {square root over (ε x )} * cos(33.0 * π/20.0), R3 * {square root over (ε x )} * sin(33.0 * π/20.0)]
001000
[R2 * {square root over (ε x )} * cos(23.0 * π/16.0), R2 * {square root over (ε x )} * sin(23.0 * π/16.0)]
001001
[R4 * {square root over (ε x )} * cos(25.0 * π/20.0), R4 * {square root over (ε x )} * sin(25.0 * π/20.0)]
001010
[R2 * {square root over (ε x )} * cos(21.0 * π/16.0), R2 * {square root over (ε x )} * sin(21.0 * π/16.0)]
001011
[R3 * {square root over (ε x )} * cos(25.0 * π/20.0), R3 * {square root over (ε x )} * sin(25.0 * π/20.0)]
001100
[R4 * {square root over (ε x )} * cos(29.0 * π/20.0), R4 * {square root over (ε x )} * sin(29.0 * π/20.0)]
001101
[R4 * {square root over (ε x )} * cos(27.0 * π/20.0), R4 * {square root over (ε x )} * sin(27.0 * π/20.0)]
001110
[R3 * {square root over (ε x )} * cos(29.0 * π/20.0), R3 * {square root over (ε x )} * sin(29.0 * π/20.0)]
001111
[R3 * {square root over (ε x )} * cos(27.0 * π/20.0), R3 * {square root over (ε x )} * sin(27.0 * π/20.0)]
010000
[R1 * {square root over (ε x )} * cos(13.0 * π/8.0), R1 * {square root over (ε x )} * sin(13.0 * π/8.0)]
010001
[R4 * {square root over (ε x )} * cos(37.0 * π/20.0), R4 * {square root over (ε x )} * sin(37.0 * π/20.0)]
010010
[R2 * {square root over (ε x )} * cos(29.0 * π/16.0), R2 * {square root over (ε x )} * sin(29.0 * π/16.0)]
010011
[R3 * {square root over (ε x )} * cos(37.0 * π/20.0), R3 * {square root over (ε x )} * sin(37.0 * π/20.0)]
010100
[R1 * {square root over (ε x )} * cos(15.0 * π/8.0), R1 * {square root over (ε x )} * sin(15.0 * π/8.0)]
010101
[R4 * {square root over (ε x )} * cos(39.0 * π/20.0), R4 * {square root over (ε x )} * sin(39.0 * π/20.0)]
010110
[R2 * {square root over (ε x )} * cos(31.0 * π/16.0), R2 * {square root over (ε x )} * sin(31.0 * π/16.0)]
010111
[R3 * {square root over (ε x )} * cos(39.0 * π/20.0), R3 * {square root over (ε x )} * sin(39.0 * π/20.0)]
011000
[R1 * {square root over (ε x )} * cos(11.0 * π/8.0), R1 * {square root over (ε x )} * sin(11.0 * π/8.0)]
011001
[R4 * {square root over (ε x )} * cos(23.0 * π/20.0), R4 * {square root over (ε x )} * sin(23.0 * π/20.0)]
011010
[R2 * {square root over (ε x )} * cos(19.0 * π/16.0), R2 * {square root over (ε x )} * sin(19.0 * π/16.0)]
011011
[R3 * {square root over (ε x )} * cos(23.0 * π/20.0), R3 * {square root over (ε x )} * sin(23.0 * π/20.0)]
011100
[R1 * {square root over (ε x )} * cos(9.0 * π/8.0), R1 * {square root over (ε x )} * sin(9.0 * π/8.0)]
011101
[R4 * {square root over (ε x )} * cos(21.0 * π/20.0), R4 * {square root over (ε x )} * sin(21.0 * π/20.0)]
011110
[R2 * {square root over (ε x )} * cos(17.0 * π/16.0), R2 * {square root over (ε x )} * sin(17.0 * π/16.0)]
011111
[R3 * {square root over (ε x )} * cos(21.0 * π/20.0), R3 * {square root over (ε x )} * sin(21.0 * π/20.0)]
100000
[R2 * {square root over (ε x )} * cos(7.0 * π/16.0), R2 * {square root over (ε x )} * sin(7.0 * π/16.0)]
100001
[R4 * {square root over (ε x )} * cos(5.0 * π/20.0), R4 * {square root over (ε x )} * sin(5.0 * π/20.0)]
100010
[R2 * {square root over (ε x )} * cos(5.0 * π/16.0), R2 * {square root over (ε x )} * sin(5.0 * π/16.0)]
100011
[R3 * {square root over (ε x )} * cos(5.0 * π/20.0), R3 * {square root over (ε x )} * sin(5.0 * π/20.0)]
100100
[R4 * {square root over (ε x )} * cos(9.0 * π/20.0), R4 * {square root over (ε x )} * sin(9.0 * π/20.0)]
100101
[R4 * {square root over (ε x )} * cos(7.0 * π/20.0), R4 * {square root over (ε x )} * sin(7.0 * π/20.0)]
100110
[R3 * {square root over (ε x )} * cos(9.0 * π/20.0), R3 * {square root over (ε x )} * sin(9.0 * π/20.0)]
100111
[R3 * {square root over (ε x )} * cos(7.0 * π/20.0), R3 * {square root over (ε x )} * sin(7.0 * π/20.0)]
101000
[R2 * {square root over (ε x )} * cos(9.0 * π/16.0), R2 * {square root over (ε x )} * sin(9.0 * π/16.0)]
101001
[R4 * {square root over (ε x )} * cos(15.0 * π/20.0), R4 * {square root over (ε x )} * sin(15.0 * π/20.0)]
101010
[R2 * {square root over (ε x )} * cos(11.0 * π/16.0), R2 * {square root over (ε x )} * sin(11.0 * π/16.0)]
101011
[R3 * {square root over (ε x )} * cos(15.0 * π/20.0), R3 * {square root over (ε x )} * sin(15.0 * π/20.0)]
101100
[R4 * {square root over (ε x )} * cos(11.0 * π/20.0), R4 * {square root over (ε x )} * sin(11.0 * π/20.0)]
101101
[R4 * {square root over (ε x )} * cos(13.0 * π/20.0), R4 * {square root over (ε x )} * sin(13.0 * π/20.0)]
101110
[R3 * {square root over (ε x )} * cos(11.0 * π/20.0), R3 * {square root over (ε x )} * sin(11.0 * π/20.0)]
101111
[R3 * {square root over (ε x )} * cos(13.0 * π/20.0), R3 * {square root over (ε x )} * sin(13.0 * π/20.0)]
110000
[R1 * {square root over (ε x )} * cos(3.0 * π/8.0), R1 * {square root over (ε x )} * sin(3.0 * π/8.0)]
110001
[R4 * {square root over (ε x )} * cos(3.0 * π/20.0), R4 * {square root over (ε x )} * sin(3.0 * π/20.0)]
110010
[R2 * {square root over (ε x )} * cos(3.0 * π/16.0), R2 * {square root over (ε x )} * sin(3.0 * π/16.0)]
110011
[R3 * {square root over (ε x )} * cos(3.0 * π/20.0), R3 * {square root over (ε x )} * sin(3.0 * π/20.0)]
110100
[R1 * {square root over (ε x )} * cos(π/8.0), R1 * {square root over (ε x )} * sin(π/8.0)]
110101
[R4 * {square root over (ε x )} * cos(π/20.0), R4 * {square root over (ε x )} * sin(π/20.0)]
110110
[R2 * {square root over (ε x )} * cos(π/16.0), R2 * {square root over (ε x )} * sin(π/16.0)]
110111
[R3 * {square root over (ε x )} * cos(π/20.0), R3 * {square root over (ε x )} * sin(π/20.0)]
111000
[R1 * {square root over (ε x )} * cos(5.0 * π/8.0), R1 * {square root over (ε x )} * sin(5.0 * π/8.0)]
111001
[R4 * {square root over (ε x )} * cos(17.0 * π/20.0), R4 * {square root over (ε x )} * sin(17.0 * π/20.0)]
111010
[R2 * {square root over (ε x )} * cos(13.0 * π/16.0), R2 * {square root over (ε x )} * sin(13.0 * π/16.0)]
111011
[R3 * {square root over (ε x )} * cos(17.0 * π/20.0), R3 * {square root over (ε x )} * sin(17.0 * π/20.0)]
111100
[R1 * {square root over (ε x )} * cos(7.0 * π/8.0), R1 * {square root over (ε x )} * sin(7.0 * π/8.0)]
111101
[R4 * {square root over (ε x )} * cos(19.0 * π/20.0), R4 * {square root over (ε x )} * sin(19.0 * π/20.0)]
111110
[R2 * {square root over (ε x )} * cos(15.0 * π/16.0), R2 * {square root over (ε x )} * sin(15.0 * π/16.0)]
111111
[R3 * {square root over (ε x )} * cos(19.0 * π/20.0), R3 * {square root over (ε x )} * sin(19.0 * π/20.0)]
where ε x represents average energy per symbol, 8*R1 2 +16*R2 2 +20*R3 2 +20*R4 2 =64, and R1 represents the radius of the inner ring, R2 represents the radius of the first middle ring, R3 represents the radius of the second middle ring and R4 represents the radius of the outer ring, and
wherein each of the [x, y] bit coordinate positions is rotated by a same rotation factor (from 0 to 359°, inclusive), and/or each bit label is altered by interchanging the 0's and 1's, and/or a uniform swapping of bit positions is applied within each bit label.
37. A method, comprising:
modulating a signal, through a modulation device, based at least in part on an 64-ary, 12+16+16+20APSK signal constellation, having an inner ring with 12 bit positions, a first middle ring with 16 bit positions, a second middle ring with 16 bit positions and an outer ring with 20 bit positions.
38. An apparatus, comprising:
a modulation device configured to modulate a signal based at least in part on an 64-ary, 12+16+16+20APSK signal constellation, having an inner ring with 12 bit positions, a first middle ring with 16 bit positions, a second middle ring with 16 bit positions and an outer ring with 20 bit positions.
39. A method, comprising:
demodulating a signal, through a demodulation device, wherein the signal was modulated based at least in part on an 64-ary, 12+16+16+20APSK signal constellation, having an inner ring with 12 bit positions, a first middle ring with 16 bit positions, a second middle ring with 16 bit positions and an outer ring with 20 bit positions.
40. An apparatus, comprising:
a demodulation device configured to demodulate a signal, wherein the signal was modulated based at least in part on an 64-ary, 12+16+16+20APSK signal constellation, having an inner ring with 12 bit positions, a first middle ring with 16 bit positions, a second middle ring with 16 bit positions and an outer ring with 20 bit positions.
41. A method, comprising:
modulating a signal, through a modulation device, based at least in part on a signal constellation having bit labeling and [x, y] bit coordinate positions in accordance with a one of the following tables:
TABLE 1
Bit Label
[x, y] Coordinates
000
[0.0, 0.0]
001
[{square root over ((8.0 * ε x /7.0,)} 0.0]
010
[{square root over (8.0 * ε x /7.0)} * cos(4.0 * π/7.0),
{square root over (8.0 * ε x /7.0 )} * sin(4.0 * π/7.0)]
011
[{square root over (8.0 * ε x /7.0)} * cos(2.0 * π/7.0),
{square root over (8.0 * ε x /7.0 )} * sin(2.0 * π/7.0)]
100
[{square root over (8.0 * ε x /7.0)} * cos(12.0 * π/7.0),
{square root over (8.0 * ε x /7.0 )} * sin(12.0 * π/7.0)]
101
[{square root over (8.0 * ε x /7.0)} * cos(10.0 * π/7.0),
{square root over (8.0 * ε x /7.0 )} * sin(10.0 * π/7.0)]
110
[{square root over (8.0 * ε x /7.0)} * cos(6.0 * π/7.0),
{square root over (8.0 * ε x /7.0 )} * sin(6.0 * π/7.0)]
111
[{square root over (8.0 * ε x /7.0)} * cos(8.0 * π/7.0),
{square root over (8.0 * ε x /7.0 )} * sin(8.0 * π/7.0)]
where ε x represents average energy per symbol;
TABLE 2
Bit
Label
[x, y] Coordinates
0000
[R1 * {square root over (ε x )}, 0.0]
0001
[R1 * {square root over (ε x )} * cos (5.0 * π/3.0), R1 * {square root over (ε x )} * sin (5.0 * π/3.0)]
0010
[R1 * {square root over (ε x )} * cos (π/3.0), R1 * {square root over (ε x )} * sin (π/3.0)]
0011
[R2 * {square root over (ε x )} * cos (13.0 * π/30.0), R2 * {square root over (ε x )} * sin (13.0 * π/30.0)]
0100
[R2 * {square root over (ε x )} * cos (55.0 * π/30.0), R2 * {square root over (ε x )} * sin (55.0 * π/30.0)]
0101
[R2 * {square root over (ε x )} * cos (49.0 * π/30.0), R2 * {square root over (ε x )} * sin (49.0 * π/30.0)]
0110
[R2 * {square root over (ε x )} * cos (π/30.0), R2 * {square root over (ε x )} * sin (π/30.0)]
0111
[R2 * {square root over (ε x )} * cos (7.0 * π/30.0), R2 * {square root over (ε x )} * sin (7.0 * π/30.0)]
1000
[−R1 * {square root over (ε x )}, 0.0]
1001
[R1 * {square root over (ε x )} * cos (4.0 * π/3.0), R1 * {square root over (ε x )} * sin (4.0 * π/3.0)]
1010
[R1 * {square root over (ε x )} * cos (2.0 * π/3.0), R1 * {square root over (ε x )} * sin (2.0 * π/3.0)]
1011
[R2 * {square root over (ε x )} * cos (19.0 * π/30.0), R2 * {square root over (ε x )} * sin (19.0 * π/30.0)]
1100
[R2 * {square root over (ε x )} * cos (37.0 * π/30.0), R2 * {square root over (ε x )} * sin (37.0 * π/30.0)]
1101
[R2 * {square root over (ε x )} * cos (43.0 * π/30.0), R2 * {square root over (ε x )} * sin (43.0 * π/30.0)]
1110
[R2 * {square root over (ε x )} * cos (31.0 * π/30.0), R2 * {square root over (ε x )} * sin (31.0 * π/30.0)]
1111
[R2 * {square root over (ε x )} * cos (25.0 * π/30.0), R2 * {square root over (ε x )} * sin (25.0 * π/30.0)]
where ε x represents average energy per symbol, 6*R1 2 +10*R2 2 =16, and R1 represents the radius of an inner ring of the constellation and R2 represents the radius of an outer ring of the constellation;
TABLE 3
Bit
Label
[x, y] Coordinates
00000
[R1 * {square root over (ε x )} * cos(π/16.0), R1 * {square root over (ε x )} * sin(π/16.0)]
00001
[R1 * {square root over (ε x )} * cos(3.0 * π/16.0), R1 * {square root over (ε x )} * sin(3.0 * π/16.0)]
00010
[R1 * {square root over (ε x )} * sin(π/16.0), R1 * {square root over (ε x )} * cos(π/16.0)]
00011
[R1 * {square root over (ε x )} * sin(3.0 * π/16.0), R1 * {square root over (ε x )} * cos(3.0 * π/16.0)]
00100
[R1 * {square root over (ε x )} * cos(π/16.0), −R1 * {square root over (ε x )} * sin(π/16.0)]
00101
[R1 * {square root over (ε x )} * cos(3.0 * π/16.0), −R1 * {square root over (ε x )} * sin(3.0 * π/16.0)]
00110
[R1 * {square root over (ε x )} * sin(π/16.0), −R1 * {square root over (ε x )} * cos(π/16.0)]
00111
[R1 * {square root over (ε x )} * sin(3.0 * π/16.0), −R1 * {square root over (ε x )} * cos(3.0 * π/16.0)]
01000
[−R1 * {square root over (ε x )} * cos(π/16.0), R1 * {square root over (ε x )} * sin(π/16.0)]
01001
[−R1 * {square root over (ε x )} * cos(3.0 * π/16.0), R1 * {square root over (ε x )} * sin(3.0 * π/16.0)]
01010
[−R1 * {square root over (ε x )} * sin(π/16.0), R1 * {square root over (ε x )} * cos(π/16.0)]
01011
[−R1 * {square root over (ε x )} * sin(3.0 * π/16.0), R1 * {square root over (ε x )} * cos(3.0 * π/16.0)]
01100
[−R1 * {square root over (ε x )} * cos(π/16.0), −R1 * {square root over (ε x )} * sin(π/16.0)]
01101
[−R1 * {square root over (ε x )} * cos(3.0 * π/16.0), −R1 * {square root over (ε x )} * sin(3.0 * π/16.0)]
01110
[−R1 * {square root over (ε x )} * sin(π/16.0), −R1 * {square root over (ε x )} * cos(π/16.0)]
01111
[−R1 * {square root over (ε x )} * sin(3.0 * π/16.0), −R1 * {square root over (ε x )} * cos(3.0 * π/16.0)]
10000
[R2 * {square root over (ε x )} * cos(π/16.0), R2 * {square root over (ε x )} * sin(π/16.0)]
10001
[R2 * {square root over (ε x )} * cos(3.0 * π/16.0), R2 * {square root over (ε x )} * sin(3.0 * π/16.0)]
10010
[R2 * {square root over (ε x )} * sin(π/16.0), R2 * {square root over (ε x )} * cos(π/16.0)]
10011
[R2 * {square root over (ε x )} * sin(3.0 * π/16.0), R2 * {square root over (ε x )} * cos(3.0 * π/16.0)]
10100
[R2 * {square root over (ε x )} * cos(π/16.0), −R2 * {square root over (ε x )} * sin(π/16.0)]
10101
[R2 * {square root over (ε x )} * cos(3.0 * π/16.0), −R2 * {square root over (ε x )} * sin(3.0 * π/16.0)]
10110
[R2 * {square root over (ε x )} * sin(π/16.0), −R2 * {square root over (ε x )} * cos(π/16.0)]
10111
[R2 * {square root over (ε x )} * sin(3.0 * π/16.0), −R2 * {square root over (ε x )} * cos(3.0 * π/16.0)]
11000
[−R2 * {square root over (ε x )} * cos(π/16.0), R2 * {square root over (ε x )} * sin(π/16.0)]
11001
[−R2 * {square root over (ε x )} * cos(3.0 * π/16.0), R2 * {square root over (ε x )} * sin(3.0 * π/16.0)]
11010
[−R2 * {square root over (ε x )} * sin(π/16.0), R2 * {square root over (ε x )} * cos(π/16.0)]
11011
[−R2 * {square root over (ε x )} * sin(3.0 * π/16.0), R2 * {square root over (ε x )} * cos(3.0 * π/16.0)]
11100
[−R2 * {square root over (ε x )} * cos(π/16.0), −R2 * {square root over (ε x )} * sin(π/16.0)]
11101
[−R2 * {square root over (ε x )} * cos(3.0 * π/16.0), −R2 * {square root over (ε x )} * sin(3.0 * π/16.0)]
11110
[−R2 * {square root over (ε x )} * sin(π/16.0), −R2 * {square root over (ε x )} * cos(π/16.0)]
11111
[−R2 * {square root over (ε x )} * sin(3.0 * π/16.0), −R2 * {square root over (ε x )} * cos(3.0 * π/16.0)]
where ε x represents average energy per symbol, R1 2 +R2 2 =2, and R1 represents the radius of an inner ring of the constellation and R2 represents the radius of an outer ring of the constellation;
TABLE 4
Bit
Label
[x, y] Coordinates
00000
[−R3 * {square root over (ε x )} * cos(5.0 * π/16.0), R3 * {square root over (ε x )} * cos(3.0 * π/16.0)]
00001
[−R3 * {square root over (ε x )} * cos(7.0 * π/16.0), R3 * {square root over (ε x )} * cos(π/16.0)]
00010
[R3 * {square root over (ε x )} * cos(5.0 * π/16.0), R3 * {square root over (ε x )} * cos(3.0 * π/16.0)]
00011
[R3 * {square root over (ε x )} * cos(7.0 * π/16.0), R3 * {square root over (ε x )} * cos(π/16.0)]
00100
[−R2 * {square root over (ε x )} * sin(π/4.0), R2 * {square root over (ε x )} * sin(π/4.0)]
00101
[−R2 * {square root over (ε x )} * sin(π/12.0), R2 * {square root over (ε)} x * sin(5.0 * π/12.0)]
00110
[R2 * {square root over (ε x )} * sin(π/4.0), R2 * {square root over (ε x )} * sin(π/4.0)]
00111
[R2 * {square root over (ε x )} * sin(π/12.0), R2 * {square root over (ε x )} * sin(5.0 * π/12.0)]
01000
[−R3 * {square root over (ε x )} * cos(3.0 * π/16.0), R3 * {square root over (ε x )} * cos(5.0 * π/16.0)]
01001
[−R3 * {square root over (ε x )}* cos(π/16.0), R3 * {square root over (ε x )} * cos(7.0 * π/16.0)]
01010
[R3 * {square root over (ε x )} * cos(3.0 * π/16.0), R3 * {square root over (ε x )} * cos(5.0 * π/16.0)]
01011
[R3 * {square root over (ε x )} * cos(π/16.0), R3 * {square root over (ε x )} * cos(7.0 * π/16.0)]
01100
[−R2 * {square root over (ε x )} * sin(5.0 * π/12.0), R2 * {square root over (ε x )} * sin(π/12.0)]
01101
[−R1 * {square root over (ε x )} * sin(π/4.0), R1 * {square root over (ε x )} * sin(π/4.0)]
01110
[R2 * {square root over (ε x )} * sin(5.0 * π/12.0), R2 * {square root over (ε x )} * sin(π/12.0)]
01111
[R1 * {square root over (ε x )} * sin(π/4.0), R1 * {square root over (ε x )}* sin(π/4.0)]
10000
[−R3 * {square root over (ε x )} * cos(5.0 * π/16.0), −R3 * {square root over (ε x )} * cos(3.0 * π/16.0)]
10001
[−R3 * {square root over (ε x )} * cos(7.0 * π/16.0), −R3 * {square root over (ε x )} * cos(π/16.0)]
10010
[R3 * {square root over (ε x )} * cos(5.0 * π/16.0), −R3 * {square root over (ε x )} * cos(3.0 * π/16.0)]
10011
[R3 * {square root over (ε x )} * cos(7.0 * π/16.0), −R3 * {square root over (ε x )} * cos(π/16.0)]
10100
[−R2 * {square root over (ε x )} * sin(π/4.0), −R2 * {square root over (ε x )} * sin(π/4.0)]
10101
[−R2 * {square root over (ε x )} * sin(π/12.0), −R2 * {square root over (ε x )} * sin(5.0 * π/12.0)]
10110
[R2 * {square root over (ε x )} * sin(π/4.0), −R2 * {square root over (ε x )} * sin(π/4.0)]
10111
[R2 * {square root over (ε x )} * sin(π/12.0), −R2 * {square root over (ε x )} * sin(5.0 * π/12.0)]
11000
[−R3 * {square root over (ε x )} * cos(3.0 * π/16.0), −R3 * {square root over (ε x )} * cos(5.0 * π/16.0)]
11001
[−R3 * {square root over (ε x )} * cos(π/16.0), −R3 * {square root over (ε x )} * cos(7.0 * π/16.0)]
11010
[R3 * {square root over (ε x )} * cos(3.0 * π/16.0), R3 * {square root over (ε x )} * cos(5.0 * π/16.0)]
11011
[R3 * {square root over (ε x )} * cos(π/16.0), −R3 * {square root over (ε x )} * cos(7.0 * π/16.0)]
11100
[−R2 * {square root over (ε x )} * sin(5.0 * π/12.0), −R2 * {square root over (ε x )} * sin(π/12.0)]
11101
[−R1 * {square root over (ε x )} * sin(π/4.0), −R1 * {square root over (ε x )} * sin(π/4.0)]
11110
[R2 * {square root over (ε x )} * sin(5.0 * π/12.0), −R2 * {square root over (ε x )} * sin(π/12.0)]
11111
[R1 * {square root over (ε x )} * sin(π/4.0), −R1 * {square root over (ε x )} * sin(π/4.0)]
where ε x represents average energy per symbol, 4*R1 2 +12*R2 2 +16*R3 2 =32, and R1 represents the radius of an inner ring of the constellation, R2 represents the radius of a middle ring of the constellation and R3 represents the radius of an outer ring of the constellation;
TABLE 5
Bit
Label
[x, y] Coordinates
00000
[−R3 * {square root over (ε x )} * sin(π/4.0), R3 * {square root over (ε x )} * sin(π/4.0)]
00001
[−R3 * {square root over (ε x )} * sin(π/8.0), R3 * {square root over (ε x )} * cos(π/8.0)]
00010
[R3 * {square root over (ε x )} * sin(π/8.0), R3 * {square root over (ε x )} * cos(π/8.0)]
00011
[0, R3 * {square root over (ε x )}]
00100
[−R2 * {square root over (ε x )} * sin(π/4.0), R2 * {square root over (ε x )} * sin(π/4.0)]
00101
[−R2 * {square root over (ε x )} * sin(π/12.0), R2 * {square root over (ε x )} * sin(5.0 * π/12.0)]
00110
[R2 * {square root over (ε x )} * sin(π/4.0), R2 * {square root over (ε x )} * sin(π/4.0)]
00111
[R2 * {square root over (ε x )} * sin(π/12.0), R2 * {square root over (ε x )} * sin(5.0 * π/12.0)]
01000
[−R3 * {square root over (ε x )} * cos(π/8.0), R3 * {square root over (ε x )} * sin(π/8.0)]
01001
[−R3 * {square root over (ε x )}, 0]
01010
[R3 * {square root over (ε x )} * sin(π/4.0), R3 * {square root over (ε x )} * sin(π/4.0)]
01011
[R3 * {square root over (ε x )} * cos(π/8.0), R3 {square root over (ε x )} * sin(π/8.0)]
01100
[−R2 * {square root over (ε x )} * sin(5.0 * π/12.0), R2 * {square root over (ε x )} * sin(π/12.0)]
01101
[−R1 * {square root over (ε x )} * sin(π/4.0), R1 * {square root over (ε x )} * sin(π/4.0)]
01110
[R2 * {square root over (ε x )} * sin(5.0 * π/12.0), R2 * {square root over (ε x )} * sin(π/12.0)]
01111
[R1 * {square root over (ε x )} * sin(π/4.0), R1 * {square root over (ε x )} * sin(π/4.0)]
10000
[−R3 * {square root over (ε x )} * sin(π/8.0), −R3 * {square root over (ε x )} * cos(π/8.0)]
10001
[0, −R3 * {square root over (ε x )}]
10010
[R3 * {square root over (ε x )} * sin(π/4.0), −R3 * {square root over (ε x )} * sin(π/4.0)]
10011
[R3 * {square root over (ε x )} * sin(π/8.0), −R3 * {square root over (ε x )} * cos(π/8.0)]
10100
[−R2 * {square root over (ε x )} * sin(π/4.0), −R2 * {square root over (ε x )} * sin(π/4.0)]
10101
[−R2 * {square root over (ε x )} * sin(π/12.0), −R2 * {square root over (ε x )} * sin(5.0 * π/12.0)]
10110
[R2 * {square root over (ε x )} * sin(π/4.0), −R2 * {square root over (ε x )} * sin(π/4.0)]
10111
[R2 * {square root over (ε x )} * sin(π/12.0), −R2 * {square root over (ε x )} * sin(5.0 * π/12.0)]
11000
[−R3 * {square root over (ε x )} * sin(π/4.0), −R3 * {square root over (ε x )} * sin(π/4.0)]
11001
[−R3 * {square root over (ε x )} * cos(π/8.0), −R3 * {square root over (ε x )} * sin(π/8.0)]
11010
[R3 * {square root over (ε x )} * cos(π/8.0), −R3 * {square root over (ε x )} * sin(π/8.0)]
11011
[R3 * {square root over (ε x )}, 0]
11100
[−R2 * {square root over (ε x )} * sin(5.0 * π/12.0), −R2 * {square root over (ε x )} * sin(π/12.0)]
11101
[−R1 * {square root over (ε x )} * sin(π/4.0), −R1 * {square root over (ε x )} * sin(π/4.0)]
11110
[R2 * {square root over (ε x )} * sin(5.0 * π/12.0), −R2 * {square root over (ε x )} * sin(π/12.0)]
11111
[R1 * {square root over (ε x )} * sin(π/4.0), −R1 * {square root over (ε x )} * sin(π/4.0)]
where ε x represents average energy per symbol, 4*R1 2 +12*R2 2 +16*R3 2 =32, and R1 represents the radius of an inner ring of the constellation, R2 represents the radius of a middle ring of the constellation and R3 represents the radius of an outer ring of the constellation; and
TABLE 6
Bit Label
[x, y] Coordinates
000000
[R2 * {square root over (ε χ )}* cos(25.0 * π/16.0), R2 * {square root over (ε χ )}* sin(25.0 * π/16.0)]
000001
[R4 * {square root over (ε χ )}* cos(35.0 * π/20.0), R4 * {square root over (ε χ )}* sin(35.0 * π/20.0)]
000010
[R2 * {square root over (ε χ )}* cos(27.0 * π/16.0), R2 * {square root over (ε χ )}* sin(27.0 * π/16.0)]
000011
[R3 * {square root over (ε χ )}* cos(35.0 * π/20.0), R3 * {square root over (ε χ )}* sin(35.0 * π/20.0)]
000100
[R4 * {square root over (ε χ )}* cos(31.0 * π/20.0), R4 * {square root over (ε χ )}* sin(31.0 * π/20.0)]
000101
[R4 * {square root over (ε χ )}* cos(33.0 * π/20.0), R4 * {square root over (ε χ )}* sin(33.0 * π/20.0)]
000110
[R3 * {square root over (ε χ )}* cos(31.0 * π/20.0), R3 * {square root over (ε χ )}* sin(31.0 * π/20.0)]
000111
[R3 * {square root over (ε χ )}* cos(33.0 * π/20.0), R3 * {square root over (ε χ )}* sin(33.0 * π/20.0)]
001000
[R2 * {square root over (ε χ )}* cos(23.0 * π/16.0), R2 * {square root over (ε χ )}* sin(23.0 * π/16.0)]
001001
[R4 * {square root over (ε χ )}* cos(25.0 * π/20.0), R4 * {square root over (ε χ )}* sin(25.0 * π/20.0)]
001010
[R2 * {square root over (ε χ )}* cos(21.0 * π/16.0), R2 * {square root over (ε χ )}* sin(21.0 * π/16.0)]
001011
[R3 * {square root over (ε χ )}* cos(25.0 * π/20.0), R3 * {square root over (ε χ )}* sin(25.0 * π/20.0)]
001100
[R4 * {square root over (ε χ )}* cos(29.0 * π/20.0), R4 * {square root over (ε χ )}* sin(29.0 * π/20.0)]
001101
[R4 * {square root over (ε χ )}* cos(27.0 * π/20.0), R4 * {square root over (ε χ )}* sin(27.0 * π/20.0)]
001110
[R3 * {square root over (ε χ )}* cos(29.0 * π/20.0), R3 * {square root over (ε χ )}* sin(29.0 * π/20.0)]
001111
[R3 * {square root over (ε χ )}* cos(27.0 * π/20.0), R3 * {square root over (ε χ )}* sin(27.0 * π/20.0)]
010000
[R1 * {square root over (ε χ )}* cos(13.0 * π/8.0), R1 * {square root over (ε χ )}* sin(13.0 * π/8.0)]
010001
[R4 * {square root over (ε χ )}* cos(37.0 * π/20.0), R4 * {square root over (ε χ )}* sin(37.0 * π/20.0)]
010010
[R2 * {square root over (ε χ )}* cos(29.0 * π/16.0), R2 * {square root over (ε χ )}* sin(29.0 * π/16.0)]
010011
[R3 * {square root over (ε χ )}* cos(37.0 * π/20.0), R3 * {square root over (ε χ )}* sin(37.0 * π/20.0)]
010100
[R1 * {square root over (ε χ )}* cos(15.0 * π/8.0), R1 * {square root over (ε χ )}* sin(15.0 * π/8.0)]
010101
[R4 * {square root over (ε χ )}* cos(39.0 * π/20.0), R4 * {square root over (ε χ )}* sin(39.0 * π/20.0)]
010110
[R2 * {square root over (ε χ )}* cos(31.0 * π/16.0), R2 * {square root over (ε χ )}* sin(31.0 * π/16.0)]
010111
[R3 * {square root over (ε χ )}* cos(39.0 * π/20.0), R3 * {square root over (ε χ )}* sin(39.0 * π/20.0)]
011000
[R1 * {square root over (ε χ )}* cos(11.0 * π/8.0), R1 * {square root over (ε χ )}* sin(11.0 * π/8.0)]
011001
[R4 * {square root over (ε χ )}* cos(23.0 * π/20.0), R4 * {square root over (ε χ )}* sin(23.0 * π/20.0)]
011010
[R2 * {square root over (ε χ )}* cos(19.0 * π/16.0), R2 * {square root over (ε χ )}* sin(19.0 * π/16.0)]
011011
[R3 * {square root over (ε χ )}* cos(23.0 * π/20.0), R3 * {square root over (ε χ )}* sin(23.0 * π/20.0)]
011100
[R1 * {square root over (ε χ )}* cos(9.0 * π/8.0), R1 * {square root over (ε χ )}* sin(9.0 * π/8.0)]
011101
[R4 * {square root over (ε χ )}* cos(21.0 * π/20.0), R4 * {square root over (ε χ )}* sin(21.0 * π/20.0)]
011110
[R2 * {square root over (ε χ )}* cos(17.0 * π/16.0), R2 * {square root over (ε χ )}* sin(17.0 * π/16.0)]
011111
[R3 * {square root over (ε χ )}* cos(21.0 * π/20.0), R3 * {square root over (ε χ )}* sin(21.0 * π/20.0)]
100000
[R2 * {square root over (ε χ )}* cos(7.0 * π/16.0), R2 * {square root over (ε χ )}* sin(7.0 * π/16.0)]
100001
[R4 * {square root over (ε χ )}* cos(5.0 * π/20.0), R4 * {square root over (ε χ )}* sin(5.0 * π/20.0)]
100010
[R2 * {square root over (ε χ )}* cos(5.0 * π/16.0), R2 * {square root over (ε χ )}* sin(5.0 * π/16.0)]
100011
[R3 * {square root over (ε χ )}* cos(5.0 * π/20.0), R3 * {square root over (ε χ )}* sin(5.0 * π/20.0)]
100100
[R4 * {square root over (ε χ )}* cos(9.0 * π/20.0), R4 * {square root over (ε χ )}* sin(9.0 * π/20.0)]
100101
[R4 * {square root over (ε χ )}* cos(7.0 * π/20.0), R4 * {square root over (ε χ )}* sin(7.0 * π/20.0)]
100110
[R3 * {square root over (ε χ )}* cos(9.0 * π/20.0), R3 * {square root over (ε χ )}* sin(9.0 * π/20.0)]
100111
[R3 * {square root over (ε χ )}* cos(7.0 * π/20.0), R3 * {square root over (ε χ )}* sin(7.0 * π/20.0)]
101000
[R2 * {square root over (ε χ )}* cos(9.0 * π/16.0), R2 * {square root over (ε χ )}* sin(9.0 * π/16.0)]
101001
[R4 * {square root over (ε χ )}* cos(15.0 * π/20.0), R4 * {square root over (ε χ )}* sin(15.0 * π/20.0)]
101010
[R2 * {square root over (ε χ )}* cos(11.0 * π/16.0), R2 * {square root over (ε χ )}* sin(11.0 * π/16.0)]
101011
[R3 * {square root over (ε χ )}* cos(15.0 * π/20.0), R3 * {square root over (ε χ )}* sin(15.0 * π/20.0)]
101100
[R4 * {square root over (ε χ )}* cos(11.0 * π/20.0), R4 * {square root over (ε χ )}* sin(11.0 * π/20.0)]
101101
[R4 * {square root over (ε χ )}* cos(13.0 * π/20.0), R4 * {square root over (ε χ )}* sin(13.0 * π/20.0)]
101110
[R3 * {square root over (ε χ )}* cos(11.0 * π/20.0), R3 * {square root over (ε χ )}* sin(11.0 * π/20.0)]
101111
[R3 * {square root over (ε χ )}* cos(13.0 * π/20.0), R3 * {square root over (ε χ )}* sin(13.0 * π/20.0)]
110000
[R1 * {square root over (ε χ )}* cos(3.0 * π/8.0), R1 * {square root over (ε χ )}* sin(3.0 * π/8.0)]
110001
[R4 * {square root over (ε χ )}* cos(3.0 * π/20.0), R4 * {square root over (ε χ )}* sin(3.0 * π/20.0]
110010
[R2 * {square root over (ε χ )}* cos(3.0 * π/16.0), R2 * {square root over (ε χ )}* sin(3.0 * π/16.0)]
110011
[R3 * {square root over (ε χ )}* cos(3.0 * π/20.0), R3 * {square root over (ε χ )}* sin(3.0 * π/20.0)]
110100
[R1 * {square root over (ε χ )}* cos(π/8.0), R1 * {square root over (ε χ )}* sin(π/8.0)]
110101
[R4 * {square root over (ε χ )}* cos(π/20.0), R4 * {square root over (ε χ )}* sin(π/20.0)]
110110
[R2 * {square root over (ε χ )}* cos(π/16.0), R2 * {square root over (ε χ )}* sin(π/16.0)]
110111
[R3 * {square root over (ε χ )}* cos(π/20.0), R3 * {square root over (ε χ )}* sin(π/20.0)]
111000
[R1 * {square root over (ε χ )}* cos(5.0 * π/8.0), R1 * {square root over (ε χ )}* sin(5.0 * π/8.0)]
111001
[R4 * {square root over (ε χ )}* cos(17.0 * π/20.0), R4 * {square root over (ε χ )}* sin(17.0 * π/20.0)]
111010
[R2 * {square root over (ε χ )}* cos(13.0 * π/16.0), R2 * {square root over (ε χ )}* sin(13.0 * π/16.0)]
111011
[R3 * {square root over (ε χ )}* cos(17.0 * π/20.0), R3 * {square root over (ε χ )}* sin(17.0 * π/20.0)]
111100
[R1 * {square root over (ε χ )}* cos(7.0 * π/8.0), R1 * {square root over (ε χ )}* sin(7.0 * π/8.0)]
111101
[R4 * {square root over (ε χ )}* cos(19.0 * π/20.0), R4 * {square root over (ε χ )}* sin(19.0 * π/20.0)]
111110
[R2 * {square root over (ε χ )}* cos(15.0 * π/16.0), R2 * {square root over (ε χ )}* sin(15.0 * π/16.0)]
111111
[R3 * {square root over (ε χ )}* cos(19.0 * π/20.0), R3 * {square root over (ε)} χ * sin(19.0 * π/20.0)]
where ε x represents average energy per symbol, 8*R1 2 +16*R2 2 +20*R3 2 +20*R4 2 =64, and R1 represents the radius of an inner ring of the constellation, R2 represents the radius of a first middle ring of the constellation, R3 represents the radius of a second middle ring of the constellation and R4 represents the radius of an outer ring of the constellation.
42. The method according to claim 41 , wherein each of the [x, y] bit coordinate positions is rotated by a same rotation factor (from 0 to 359°, inclusive), and/or each bit label is altered by interchanging the 0's and 1's, and/or a uniform swapping of bit positions is applied within each bit label.
43. An apparatus, comprising:
a modulation device configured to modulate a signal based at least in part on a signal constellation having bit labeling and [x, y] bit coordinate positions in accordance with a one of the following tables:
TABLE 1
Bit Label
[x, y] Coordinates
000
[0.0, 0.0]
001
[{square root over ((8.0 * ε x /7.0,)} 0.0]
010
[{square root over (8.0 * ε x /7.0)} * cos(4.0 * π/7.0),
{square root over (8.0 * ε x /7.0 )} * sin(4.0 * π/7.0)]
011
[{square root over (8.0 * ε x /7.0)} * cos(2.0 * π/7.0),
{square root over (8.0 * ε x /7.0 )} * sin(2.0 * π/7.0)]
100
[{square root over (8.0 * ε x /7.0)} * cos(12.0 * π/7.0),
{square root over (8.0 * ε x /7.0 )} * sin(12.0 * π/7.0)]
101
[{square root over (8.0 * ε x /7.0)} * cos(10.0 * π/7.0),
{square root over (8.0 * ε x /7.0 )} * sin(10.0 * π/7.0)]
110
[{square root over (8.0 * ε x /7.0)} * cos(6.0 * π/7.0),
{square root over (8.0 * ε x /7.0 )} * sin(6.0 * π/7.0)]
111
[{square root over (8.0 * ε x /7.0)} * cos(8.0 * π/7.0),
{square root over (8.0 * ε x /7.0 )} * sin(8.0 * π/7.0)]
where ε x represents average energy per symbol;
TABLE 2
Bit
Label
[x, y] Coordinates
0000
[R1 * {square root over (ε x )}, 0.0]
0001
[R1 * {square root over (ε x )} * cos (5.0 * π/3.0), R1 * {square root over (ε x )} * sin (5.0 * π/3.0)]
0010
[R1 * {square root over (ε x )} * cos (π/3.0), R1 * {square root over (ε x )} * sin (π/3.0)]
0011
[R2 * {square root over (ε x )} * cos (13.0 * π/30.0), R2 * {square root over (ε x )} * sin (13.0 * π/30.0)]
0100
[R2 * {square root over (ε x )} * cos (55.0 * π/30.0), R2 * {square root over (ε x )} * sin (55.0 * π/30.0)]
0101
[R2 * {square root over (ε x )} * cos (49.0 * π/30.0), R2 * {square root over (ε x )} * sin (49.0 * π/30.0)]
0110
[R2 * {square root over (ε x )} * cos (π/30.0), R2 * {square root over (ε x )} * sin (π/30.0)]
0111
[R2 * {square root over (ε x )} * cos (7.0 * π/30.0), R2 * {square root over (ε x )} * sin (7.0 * π/30.0)]
1000
[−R1 * {square root over (ε x )}, 0.0]
1001
[R1 * {square root over (ε x )} * cos (4.0 * π/3.0), R1 * {square root over (ε x )} * sin (4.0 * π/3.0)]
1010
[R1 * {square root over (ε x )} * cos (2.0 * π/3.0), R1 * {square root over (ε x )} * sin (2.0 * π/3.0)]
1011
[R2 * {square root over (ε x )} * cos (19.0 * π/30.0), R2 * {square root over (ε x )} * sin (19.0 * π/30.0)]
1100
[R2 * {square root over (ε x )} * cos (37.0 * π/30.0), R2 * {square root over (ε x )} * sin (37.0 * π/30.0)]
1101
[R2 * {square root over (ε x )} * cos (43.0 * π/30.0), R2 * {square root over (ε x )} * sin (43.0 * π/30.0)]
1110
[R2 * {square root over (ε x )} * cos (31.0 * π/30.0), R2 * {square root over (ε x )} * sin (31.0 * π/30.0)]
1111
[R2 * {square root over (ε x )} * cos (25.0 * π/30.0), R2 * {square root over (ε x )} * sin (25.0 * π/30.0)]
where ε x represents average energy per symbol, 6*R1 2 +10*R2 2 =16, and R1 represents the radius of an inner ring of the constellation and R2 represents the radius of an outer ring of the constellation;
TABLE 3
Bit
Label
[x, y] Coordinates
00000
[R1 * {square root over (ε x )} * cos(π/16.0), R1 * {square root over (ε x )} * sin(π/16.0)]
00001
[R1 * {square root over (ε x )} * cos(3.0 * π/16.0), R1 * {square root over (ε x )} * sin(3.0 * π/16.0)]
00010
[R1 * {square root over (ε x )} * sin(π/16.0), R1 * {square root over (ε x )} * cos(π/16.0)]
00011
[R1 * {square root over (ε x )} * sin(3.0 * π/16.0), R1 * {square root over (ε x )} * cos(3.0 * π/16.0)]
00100
[R1 * {square root over (ε x )} * cos(π/16.0), −R1 * {square root over (ε x )} * sin(π/16.0)]
00101
[R1 * {square root over (ε x )} * cos(3.0 * π/16.0), −R1 * {square root over (ε x )} * sin(3.0 * π/16.0)]
00110
[R1 * {square root over (ε x )} * sin(π/16.0), −R1 * {square root over (ε x )} * cos(π/16.0)]
00111
[R1 * {square root over (ε x )} * sin(3.0 * π/16.0), −R1 * {square root over (ε x )} * cos(3.0 * π/16.0)]
01000
[−R1 * {square root over (ε x )} * cos(π/16.0), R1 * {square root over (ε x )} * sin(π/16.0)]
01001
[−R1 * {square root over (ε x )} * cos(3.0 * π/16.0), R1 * {square root over (ε x )} * sin(3.0 * π/16.0)]
01010
[−R1 * {square root over (ε x )} * sin(π/16.0), R1 * {square root over (ε x )} * cos(π/16.0)]
01011
[−R1 * {square root over (ε x )} * sin(3.0 * π/16.0), R1 * {square root over (ε x )} * cos(3.0 * π/16.0)]
01100
[−R1 * {square root over (ε x )} * cos(π/16.0), −R1 * {square root over (ε x )} * sin(π/16.0)]
01101
[−R1 * {square root over (ε x )} * cos(3.0 * π/16.0), −R1 * {square root over (ε x )} * sin(3.0 * π/16.0)]
01110
[−R1 * {square root over (ε x )} * sin(π/16.0), −R1 * {square root over (ε x )} * cos(π/16.0)]
01111
[−R1 * {square root over (ε x )} * sin(3.0 * π/16.0), −R1 * {square root over (ε x )} * cos(3.0 * π/16.0)]
10000
[R2 * {square root over (ε x )} * cos(π/16.0), R2 * {square root over (ε x )} * sin(π/16.0)]
10001
[R2 * {square root over (ε x )} * cos(3.0 * π/16.0), R2 * {square root over (ε x )} * sin(3.0 * π/16.0)]
10010
[R2 * {square root over (ε x )} * sin(π/16.0), R2 * {square root over (ε x )} * cos(π/16.0)]
10011
[R2 * {square root over (ε x )} * sin(3.0 * π/16.0), R2 * {square root over (ε x )} * cos(3.0 * π/16.0)]
10100
[R2 * {square root over (ε x )} * cos(π/16.0), −R2 * {square root over (ε x )} * sin(π/16.0)]
10101
[R2 * {square root over (ε x )} * cos(3.0 * π/16.0), −R2 * {square root over (ε x )} * sin(3.0 * π/16.0)]
10110
[R2 * {square root over (ε x )} * sin(π/16.0), −R2 * {square root over (ε x )} * cos(π/16.0)]
10111
[R2 * {square root over (ε x )} * sin(3.0 * π/16.0), −R2 * {square root over (ε x )} * cos(3.0 * π/16.0)]
11000
[−R2 * {square root over (ε x )} * cos(π/16.0), R2 * {square root over (ε x )} * sin(π/16.0)]
11001
[−R2 * {square root over (ε x )} * cos(3.0 * π/16.0), R2 * {square root over (ε x )} * sin(3.0 * π/16.0)]
11010
[−R2 * {square root over (ε x )} * sin(π/16.0), R2 * {square root over (ε x )} * cos(π/16.0)]
11011
[−R2 * {square root over (ε x )} * sin(3.0 * π/16.0), R2 * {square root over (ε x )} * cos(3.0 * π/16.0)]
11100
[−R2 * {square root over (ε x )} * cos(π/16.0), −R2 * {square root over (ε x )} * sin(π/16.0)]
11101
[−R2 * {square root over (ε x )} * cos(3.0 * π/16.0), −R2 * {square root over (ε x )} * sin(3.0 * π/16.0)]
11110
[−R2 * {square root over (ε x )} * sin(π/16.0), −R2 * {square root over (ε x )} * cos(π/16.0)]
11111
[−R2 * {square root over (ε x )} * sin(3.0 * π/16.0), −R2 * {square root over (ε x )} * cos(3.0 * π/16.0)]
where ε x represents average energy per symbol, R1 2 +R2 2 =2, and R1 represents the radius of an inner ring of the constellation and R2 represents the radius of an outer ring of the constellation;
TABLE 4
Bit
Label
[x, y] Coordinates
00000
[−R3 * {square root over (ε x )} * cos(5.0 * π/16.0), R3 * {square root over (ε x )} * cos(3.0 * π/16.0)]
00001
[−R3 * {square root over (ε x )} * cos(7.0 * π/16.0), R3 * {square root over (ε x )} * cos(π/16.0)]
00010
[R3 * {square root over (ε x )} * cos(5.0 * π/16.0), R3 * {square root over (ε x )} * cos(3.0 * π/16.0)]
00011
[R3 * {square root over (ε x )} * cos(7.0 * π/16.0), R3 * {square root over (ε x )} * cos(π/16.0)]
00100
[−R2 * {square root over (ε x )} * sin(π/4.0), R2 * {square root over (ε x )} * sin(π/4.0)]
00101
[−R2 * {square root over (ε x )} * sin(π/12.0), R2 * {square root over (ε)} x * sin(5.0 * π/12.0)]
00110
[R2 * {square root over (ε x )} * sin(π/4.0), R2 * {square root over (ε x )} * sin(π/4.0)]
00111
[R2 * {square root over (ε x )} * sin(π/12.0), R2 * {square root over (ε x )} * sin(5.0 * π/12.0)]
01000
[−R3 * {square root over (ε x )} * cos(3.0 * π/16.0), R3 * {square root over (ε x )} * cos(5.0 * π/16.0)]
01001
[−R3 * {square root over (ε x )}* cos(π/16.0), R3 * {square root over (ε x )} * cos(7.0 * π/16.0)]
01010
[R3 * {square root over (ε x )} * cos(3.0 * π/16.0), R3 * {square root over (ε x )} * cos(5.0 * π/16.0)]
01011
[R3 * {square root over (ε x )} * cos(π/16.0), R3 * {square root over (ε x )} * cos(7.0 * π/16.0)]
01100
[−R2 * {square root over (ε x )} * sin(5.0 * π/12.0), R2 * {square root over (ε x )} * sin(π/12.0)]
01101
[−R1 * {square root over (ε x )} * sin(π/4.0), R1 * {square root over (ε x )} * sin(π/4.0)]
01110
[R2 * {square root over (ε x )} * sin(5.0 * π/12.0), R2 * {square root over (ε x )} * sin(π/12.0)]
01111
[R1 * {square root over (ε x )} * sin(π/4.0), R1 * {square root over (ε x )}* sin(π/4.0)]
10000
[−R3 * {square root over (ε x )} * cos(5.0 * π/16.0), −R3 * {square root over (ε x )} * cos(3.0 * π/16.0)]
10001
[−R3 * {square root over (ε x )} * cos(7.0 * π/16.0), −R3 * {square root over (ε x )} * cos(π/16.0)]
10010
[R3 * {square root over (ε x )} * cos(5.0 * π/16.0), −R3 * {square root over (ε x )} * cos(3.0 * π/16.0)]
10011
[R3 * {square root over (ε x )} * cos(7.0 * π/16.0), −R3 * {square root over (ε x )} * cos(π/16.0)]
10100
[−R2 * {square root over (ε x )} * sin(π/4.0), −R2 * {square root over (ε x )} * sin(π/4.0)]
10101
[−R2 * {square root over (ε x )} * sin(π/12.0), −R2 * {square root over (ε x )} * sin(5.0 * π/12.0)]
10110
[R2 * {square root over (ε x )} * sin(π/4.0), −R2 * {square root over (ε x )} * sin(π/4.0)]
10111
[R2 * {square root over (ε x )} * sin(π/12.0), −R2 * {square root over (ε x )} * sin(5.0 * π/12.0)]
11000
[−R3 * {square root over (ε x )} * cos(3.0 * π/16.0), −R3 * {square root over (ε x )} * cos(5.0 * π/16.0)]
11001
[−R3 * {square root over (ε x )} * cos(π/16.0), −R3 * {square root over (ε x )} * cos(7.0 * π/16.0)]
11010
[R3 * {square root over (ε x )} * cos(3.0 * π/16.0), R3 * {square root over (ε x )} * cos(5.0 * π/16.0)]
11011
[R3 * {square root over (ε x )} * cos(π/16.0), −R3 * {square root over (ε x )} * cos(7.0 * π/16.0)]
11100
[−R2 * {square root over (ε x )} * sin(5.0 * π/12.0), −R2 * {square root over (ε x )} * sin(π/12.0)]
11101
[−R1 * {square root over (ε x )} * sin(π/4.0), −R1 * {square root over (ε x )} * sin(π/4.0)]
11110
[R2 * {square root over (ε x )} * sin(5.0 * π/12.0), −R2 * {square root over (ε x )} * sin(π/12.0)]
11111
[R1 * {square root over (ε x )} * sin(π/4.0), −R1 * {square root over (ε x )} * sin(π/4.0)]
where ε x represents average energy per symbol, 4*R1 2 +12*R2 2 +16*R3 2 =32, and R1 represents the radius of an inner ring of the constellation, R2 represents the radius of a middle ring of the constellation and R3 represents the radius of an outer ring of the constellation;
TABLE 5
Bit
Label
[x, y] Coordinates
00000
[−R3 * {square root over (ε x )} * sin(π/4.0), R3 * {square root over (ε x )} * sin(π/4.0)]
00001
[−R3 * {square root over (ε x )} * sin(π/8.0), R3 * {square root over (ε x )} * cos(π/8.0)]
00010
[R3 * {square root over (ε x )} * sin(π/8.0), R3 * {square root over (ε x )} * cos(π/8.0)]
00011
[0, R3 * {square root over (ε x )}]
00100
[−R2 * {square root over (ε x )} * sin(π/4.0), R2 * {square root over (ε x )} * sin(π/4.0)]
00101
[−R2 * {square root over (ε x )} * sin(π/12.0), R2 * {square root over (ε x )} * sin(5.0 * π/12.0)]
00110
[R2 * {square root over (ε x )} * sin(π/4.0), R2 * {square root over (ε x )} * sin(π/4.0)]
00111
[R2 * {square root over (ε x )} * sin(π/12.0), R2 * {square root over (ε x )} * sin(5.0 * π/12.0)]
01000
[−R3 * {square root over (ε x )} * cos(π/8.0), R3 * {square root over (ε x )} * sin(π/8.0)]
01001
[−R3 * {square root over (ε x )}, 0]
01010
[R3 * {square root over (ε x )} * sin(π/4.0), R3 * {square root over (ε x )} * sin(π/4.0)]
01011
[R3 * {square root over (ε x )} * cos(π/8.0), R3 {square root over (ε x )} * sin(π/8.0)]
01100
[−R2 * {square root over (ε x )} * sin(5.0 * π/12.0), R2 * {square root over (ε x )} * sin(π/12.0)]
01101
[−R1 * {square root over (ε x )} * sin(π/4.0), R1 * {square root over (ε x )} * sin(π/4.0)]
01110
[R2 * {square root over (ε x )} * sin(5.0 * π/12.0), R2 * {square root over (ε x )} * sin(π/12.0)]
01111
[R1 * {square root over (ε x )} * sin(π/4.0), R1 * {square root over (ε x )} * sin(π/4.0)]
10000
[−R3 * {square root over (ε x )} * sin(π/8.0), −R3 * {square root over (ε x )} * cos(π/8.0)]
10001
[0, −R3 * {square root over (ε x )}]
10010
[R3 * {square root over (ε x )} * sin(π/4.0), −R3 * {square root over (ε x )} * sin(π/4.0)]
10011
[R3 * {square root over (ε x )} * sin(π/8.0), −R3 * {square root over (ε x )} * cos(π/8.0)]
10100
[−R2 * {square root over (ε x )} * sin(π/4.0), −R2 * {square root over (ε x )} * sin(π/4.0)]
10101
[−R2 * {square root over (ε x )} * sin(π/12.0), −R2 * {square root over (ε x )} * sin(5.0 * π/12.0)]
10110
[R2 * {square root over (ε x )} * sin(π/4.0), −R2 * {square root over (ε x )} * sin(π/4.0)]
10111
[R2 * {square root over (ε x )} * sin(π/12.0), −R2 * {square root over (ε x )} * sin(5.0 * π/12.0)]
11000
[−R3 * {square root over (ε x )} * sin(π/4.0), −R3 * {square root over (ε x )} * sin(π/4.0)]
11001
[−R3 * {square root over (ε x )} * cos(π/8.0), −R3 * {square root over (ε x )} * sin(π/8.0)]
11010
[R3 * {square root over (ε x )} * cos(π/8.0), −R3 * {square root over (ε x )} * sin(π/8.0)]
11011
[R3 * {square root over (ε x )}, 0]
11100
[−R2 * {square root over (ε x )} * sin(5.0 * π/12.0), −R2 * {square root over (ε x )} * sin(π/12.0)]
11101
[−R1 * {square root over (ε x )} * sin(π/4.0), −R1 * {square root over (ε x )} * sin(π/4.0)]
11110
[R2 * {square root over (ε x )} * sin(5.0 * π/12.0), −R2 * {square root over (ε x )} * sin(π/12.0)]
11111
[R1 * {square root over (ε x )} * sin(π/4.0), −R1 * {square root over (ε x )} * sin(π/4.0)]
where ε x represents average energy per symbol, 4*R1 2 +12*R2 2 +16*R3 2 =32, and R1 represents the radius of an inner ring of the constellation, R2 represents the radius of a middle ring of the constellation and R3 represents the radius of an outer ring of the constellation; and
TABLE 6
Bit Label
[x, y] Coordinates
000000
[R2 * {square root over (ε χ )}* cos(25.0 * π/16.0), R2 * {square root over (ε χ )}* sin(25.0 * π/16.0)]
000001
[R4 * {square root over (ε χ )}* cos(35.0 * π/20.0), R4 * {square root over (ε χ )}* sin(35.0 * π/20.0)]
000010
[R2 * {square root over (ε χ )}* cos(27.0 * π/16.0), R2 * {square root over (ε χ )}* sin(27.0 * π/16.0)]
000011
[R3 * {square root over (ε χ )}* cos(35.0 * π/20.0), R3 * {square root over (ε χ )}* sin(35.0 * π/20.0)]
000100
[R4 * {square root over (ε χ )}* cos(31.0 * π/20.0), R4 * {square root over (ε χ )}* sin(31.0 * π/20.0)]
000101
[R4 * {square root over (ε χ )}* cos(33.0 * π/20.0), R4 * {square root over (ε χ )}* sin(33.0 * π/20.0)]
000110
[R3 * {square root over (ε χ )}* cos(31.0 * π/20.0), R3 * {square root over (ε χ )}* sin(31.0 * π/20.0)]
000111
[R3 * {square root over (ε χ )}* cos(33.0 * π/20.0), R3 * {square root over (ε χ )}* sin(33.0 * π/20.0)]
001000
[R2 * {square root over (ε χ )}* cos(23.0 * π/16.0), R2 * {square root over (ε χ )}* sin(23.0 * π/16.0)]
001001
[R4 * {square root over (ε χ )}* cos(25.0 * π/20.0), R4 * {square root over (ε χ )}* sin(25.0 * π/20.0)]
001010
[R2 * {square root over (ε χ )}* cos(21.0 * π/16.0), R2 * {square root over (ε χ )}* sin(21.0 * π/16.0)]
001011
[R3 * {square root over (ε χ )}* cos(25.0 * π/20.0), R3 * {square root over (ε χ )}* sin(25.0 * π/20.0)]
001100
[R4 * {square root over (ε χ )}* cos(29.0 * π/20.0), R4 * {square root over (ε χ )}* sin(29.0 * π/20.0)]
001101
[R4 * {square root over (ε χ )}* cos(27.0 * π/20.0), R4 * {square root over (ε χ )}* sin(27.0 * π/20.0)]
001110
[R3 * {square root over (ε χ )}* cos(29.0 * π/20.0), R3 * {square root over (ε χ )}* sin(29.0 * π/20.0)]
001111
[R3 * {square root over (ε χ )}* cos(27.0 * π/20.0), R3 * {square root over (ε χ )}* sin(27.0 * π/20.0)]
010000
[R1 * {square root over (ε χ )}* cos(13.0 * π/8.0), R1 * {square root over (ε χ )}* sin(13.0 * π/8.0)]
010001
[R4 * {square root over (ε χ )}* cos(37.0 * π/20.0), R4 * {square root over (ε χ )}* sin(37.0 * π/20.0)]
010010
[R2 * {square root over (ε χ )}* cos(29.0 * π/16.0), R2 * {square root over (ε χ )}* sin(29.0 * π/16.0)]
010011
[R3 * {square root over (ε χ )}* cos(37.0 * π/20.0), R3 * {square root over (ε χ )}* sin(37.0 * π/20.0)]
010100
[R1 * {square root over (ε χ )}* cos(15.0 * π/8.0), R1 * {square root over (ε χ )}* sin(15.0 * π/8.0)]
010101
[R4 * {square root over (ε χ )}* cos(39.0 * π/20.0), R4 * {square root over (ε χ )}* sin(39.0 * π/20.0)]
010110
[R2 * {square root over (ε χ )}* cos(31.0 * π/16.0), R2 * {square root over (ε χ )}* sin(31.0 * π/16.0)]
010111
[R3 * {square root over (ε χ )}* cos(39.0 * π/20.0), R3 * {square root over (ε χ )}* sin(39.0 * π/20.0)]
011000
[R1 * {square root over (ε χ )}* cos(11.0 * π/8.0), R1 * {square root over (ε χ )}* sin(11.0 * π/8.0)]
011001
[R4 * {square root over (ε χ )}* cos(23.0 * π/20.0), R4 * {square root over (ε χ )}* sin(23.0 * π/20.0)]
011010
[R2 * {square root over (ε χ )}* cos(19.0 * π/16.0), R2 * {square root over (ε χ )}* sin(19.0 * π/16.0)]
011011
[R3 * {square root over (ε χ )}* cos(23.0 * π/20.0), R3 * {square root over (ε χ )}* sin(23.0 * π/20.0)]
011100
[R1 * {square root over (ε χ )}* cos(9.0 * π/8.0), R1 * {square root over (ε χ )}* sin(9.0 * π/8.0)]
011101
[R4 * {square root over (ε χ )}* cos(21.0 * π/20.0), R4 * {square root over (ε χ )}* sin(21.0 * π/20.0)]
011110
[R2 * {square root over (ε χ )}* cos(17.0 * π/16.0), R2 * {square root over (ε χ )}* sin(17.0 * π/16.0)]
011111
[R3 * {square root over (ε χ )}* cos(21.0 * π/20.0), R3 * {square root over (ε χ )}* sin(21.0 * π/20.0)]
100000
[R2 * {square root over (ε χ )}* cos(7.0 * π/16.0), R2 * {square root over (ε χ )}* sin(7.0 * π/16.0)]
100001
[R4 * {square root over (ε χ )}* cos(5.0 * π/20.0), R4 * {square root over (ε χ )}* sin(5.0 * π/20.0)]
100010
[R2 * {square root over (ε χ )}* cos(5.0 * π/16.0), R2 * {square root over (ε χ )}* sin(5.0 * π/16.0)]
100011
[R3 * {square root over (ε χ )}* cos(5.0 * π/20.0), R3 * {square root over (ε χ )}* sin(5.0 * π/20.0)]
100100
[R4 * {square root over (ε χ )}* cos(9.0 * π/20.0), R4 * {square root over (ε χ )}* sin(9.0 * π/20.0)]
100101
[R4 * {square root over (ε χ )}* cos(7.0 * π/20.0), R4 * {square root over (ε χ )}* sin(7.0 * π/20.0)]
100110
[R3 * {square root over (ε χ )}* cos(9.0 * π/20.0), R3 * {square root over (ε χ )}* sin(9.0 * π/20.0)]
100111
[R3 * {square root over (ε χ )}* cos(7.0 * π/20.0), R3 * {square root over (ε χ )}* sin(7.0 * π/20.0)]
101000
[R2 * {square root over (ε χ )}* cos(9.0 * π/16.0), R2 * {square root over (ε χ )}* sin(9.0 * π/16.0)]
101001
[R4 * {square root over (ε χ )}* cos(15.0 * π/20.0), R4 * {square root over (ε χ )}* sin(15.0 * π/20.0)]
101010
[R2 * {square root over (ε χ )}* cos(11.0 * π/16.0), R2 * {square root over (ε χ )}* sin(11.0 * π/16.0)]
101011
[R3 * {square root over (ε χ )}* cos(15.0 * π/20.0), R3 * {square root over (ε χ )}* sin(15.0 * π/20.0)]
101100
[R4 * {square root over (ε χ )}* cos(11.0 * π/20.0), R4 * {square root over (ε χ )}* sin(11.0 * π/20.0)]
101101
[R4 * {square root over (ε χ )}* cos(13.0 * π/20.0), R4 * {square root over (ε χ )}* sin(13.0 * π/20.0)]
101110
[R3 * {square root over (ε χ )}* cos(11.0 * π/20.0), R3 * {square root over (ε χ )}* sin(11.0 * π/20.0)]
101111
[R3 * {square root over (ε χ )}* cos(13.0 * π/20.0), R3 * {square root over (ε χ )}* sin(13.0 * π/20.0)]
110000
[R1 * {square root over (ε χ )}* cos(3.0 * π/8.0), R1 * {square root over (ε χ )}* sin(3.0 * π/8.0)]
110001
[R4 * {square root over (ε χ )}* cos(3.0 * π/20.0), R4 * {square root over (ε χ )}* sin(3.0 * π/20.0]
110010
[R2 * {square root over (ε χ )}* cos(3.0 * π/16.0), R2 * {square root over (ε χ )}* sin(3.0 * π/16.0)]
110011
[R3 * {square root over (ε χ )}* cos(3.0 * π/20.0), R3 * {square root over (ε χ )}* sin(3.0 * π/20.0)]
110100
[R1 * {square root over (ε χ )}* cos(π/8.0), R1 * {square root over (ε χ )}* sin(π/8.0)]
110101
[R4 * {square root over (ε χ )}* cos(π/20.0), R4 * {square root over (ε χ )}* sin(π/20.0)]
110110
[R2 * {square root over (ε χ )}* cos(π/16.0), R2 * {square root over (ε χ )}* sin(π/16.0)]
110111
[R3 * {square root over (ε χ )}* cos(π/20.0), R3 * {square root over (ε χ )}* sin(π/20.0)]
111000
[R1 * {square root over (ε χ )}* cos(5.0 * π/8.0), R1 * {square root over (ε χ )}* sin(5.0 * π/8.0)]
111001
[R4 * {square root over (ε χ )}* cos(17.0 * π/20.0), R4 * {square root over (ε χ )}* sin(17.0 * π/20.0)]
111010
[R2 * {square root over (ε χ )}* cos(13.0 * π/16.0), R2 * {square root over (ε χ )}* sin(13.0 * π/16.0)]
111011
[R3 * {square root over (ε χ )}* cos(17.0 * π/20.0), R3 * {square root over (ε χ )}* sin(17.0 * π/20.0)]
111100
[R1 * {square root over (ε χ )}* cos(7.0 * π/8.0), R1 * {square root over (ε χ )}* sin(7.0 * π/8.0)]
111101
[R4 * {square root over (ε χ )}* cos(19.0 * π/20.0), R4 * {square root over (ε χ )}* sin(19.0 * π/20.0)]
111110
[R2 * {square root over (ε χ )}* cos(15.0 * π/16.0), R2 * {square root over (ε χ )}* sin(15.0 * π/16.0)]
111111
[R3 * {square root over (ε χ )}* cos(19.0 * π/20.0), R3 * {square root over (ε)} χ * sin(19.0 * π/20.0)]
where ε x represents average energy per symbol, 8*R1 2 +16*R2 2 +20*R3 2 +20*R4 2 =64, and R1 represents the radius of an inner ring of the constellation, R2 represents the radius of a first middle ring of the constellation, R3 represents the radius of a second middle ring of the constellation and R4 represents the radius of an outer ring of the constellation.
44. The apparatus according to claim 43 , wherein each of the [x, y] bit coordinate positions is rotated by a same rotation factor (from 0 to 359°, inclusive), and/or each bit label is altered by interchanging the 0's and 1's, and/or a uniform swapping of bit positions is applied within each bit label.