Octagonal quadrature amplitude modulation
Octagonal non-rectangular Quadrature Amplitude Modulation (QAM) is disclosed. Grid points from a uniform rectangular grid, which includes points that have equal horizontal and vertical spacing, are selected to form a non-rectangular octagonal grid that approximates an octagonal shape. QAM symbols are mapped to respective grid points in the non-rectangular octagonal grid to form a non-rectangular octagonal QAM constellation that also approximates the octagonal shape. Input signals can then be modulated using the non-rectangular octagonal QAM constellation.
1. A method comprising:
selecting, by a grid point selector, from a uniform rectangular grid comprising points that have equal horizontal and vertical spacing, a subset of the points to form a non-rectangular octagonal grid, the non-rectangular octagonal grid approximating an octagonal shape; and
mapping, by a grid point mapper, Quadrature Amplitude Modulation (QAM) symbols to respective grid points in the non-rectangular octagonal grid to form a non-rectangular octagonal QAM constellation that approximates the octagonal shape.
2. The method of claim 1 ,
the non-rectangular octagonal grid comprising N points, N=2 n , n≧1,
the rectangular grid comprising an M-by-M matrix of points, M a positive integer and M 2 >N.
3. The method of claim 1 ,
the non-rectangular octagonal QAM constellation comprising symbols in k cosets, k=2 K , K≧1,
the selecting comprising selecting points from the rectangular grid in groups of k adjacent points,
the mapping comprising mapping a QAM symbol from each of the k cosets to each group of k points.
4. The method of claim 1 ,
the non-rectangular octagonal grid comprising N points, N=2 n , n≧1,
the selecting comprising selecting points of the rectangular grid that fall within a circle centered at an origin of the rectangular grid and expanding the circle until N points fall within the circle.
5. The method of claim 3 ,
the non-rectangular octagonal grid comprising N points, N=2 n , n≧1,
the selecting comprising selecting points of the rectangular grid in groups of k adjacent points that fall within a circle centered at an origin of the rectangular grid and expanding the circle until N/k groups of k points fall within the circle.
6. The method of claim 1 , further comprising:
modulating input signals using the non-rectangular octagonal QAM constellation.
7. The method of claim 6 , the input signals comprising trellis coded input signals.
8. A non-transitory computer readable medium storing instructions which when executed cause the method of claim 1 to be performed.
9. An apparatus comprising:
a grid point selector that selects, from a uniform rectangular grid comprising points that have equal horizontal and vertical spacing, a subset of the points to form a non-rectangular octagonal grid, the non-rectangular octagonal grid approximating an octagonal shape; and
a grid point mapper that maps Quadrature Amplitude Modulation (QAM) symbols to respective grid points in the non-rectangular octagonal grid to form a non-rectangular octagonal QAM constellation.
10. The apparatus of claim 9 ,
the non-rectangular octagonal grid comprising N points, N=2 n , n≧1,
the rectangular grid comprising an M-by-M matrix of points, M a positive integer and M 2 >N.
11. The apparatus of claim 9 ,
the non-rectangular octagonal QAM constellation comprising symbols in k cosets, k=2 K , K≧1,
the grid point selector selecting points from the rectangular grid in groups of k adjacent points,
the grid point mapper mapping a QAM symbol from each of the k cosets to each group of k points.
12. The apparatus of claim 9 ,
the non-rectangular octagonal grid comprising N points, N=2 n , n≧1,
the grid point selector selecting points of the rectangular grid that fall within a circle centered at an origin of the rectangular grid and expanding the circle until N points fall within the circle.
13. The apparatus of claim 11 ,
the non-rectangular octagonal grid comprising N points, N=2 n , n≧1,
the grid point selector selecting points of the rectangular grid in groups of k adjacent points that fall within a circle centered at an origin of the rectangular grid and expanding the circle until N/k groups of k points fall within the circle.
14. The apparatus of claim 9 , further comprising:
a modulator, operatively coupled to the grid point mapper, that modulates input signals using the non-rectangular octagonal QAM constellation.
15. The apparatus of claim 14 , further comprising:
a trellis coder operatively coupled to the modulator, that generates trellis coded signals as the input signals.
16. A method comprising:
receiving, by an interface, input signals;
modulating the received input signals, by a Quadrature Amplitude Modulation (QAM) modulator operatively coupled to the interface, using a non-rectangular octagonal QAM constellation comprising QAM symbols mapped to points in a non-rectangular octagonal grid that approximates an octagonal shape, the points in the non-rectangular octagonal grid having been selected from points in a uniform rectangular grid that comprises more grid points than the non-rectangular octagonal grid.
17. An apparatus comprising:
an interface that receives input signals;
a Quadrature Amplitude Modulation (QAM) modulator, operatively coupled to the interface, that modulates the received input signals using a non-rectangular octagonal QAM constellation comprising QAM symbols mapped to points in a non-rectangular octagonal grid that approximates an octagonal shape, the points in the non-rectangular octagonal grid having been selected from points in a uniform rectangular grid that comprises more grid points than the non-rectangular octagonal grid.