Non-constant modulus codebook design
According to certain embodiments, a method for use in a wireless transmitter for simultaneously transmitting a plurality of wireless signals using a plurality of antenna elements comprises selecting a non-constant modulus (NCM) spatial precoder from a NCM codebook comprising a plurality of NCM spatial precoders. The plurality of the NCM spatial precoders are based on a unit-power beamforming vector optimized so that the wireless transmitter transmits up to the full power of each antenna element of the plurality of antenna elements while an overall transmitted power remains constant. The method further comprises applying the selected NCM spatial precoder to a data signal for generating a plurality of coded signals; and transmitting the plurality of coded signals as wireless signals via a power amplifier operating at full power.
1. A method for use in a wireless transmitter for simultaneously transmitting a plurality of wireless signals using a plurality of antenna elements, the method comprising:
selecting a non-constant modulus (NCM) spatial precoder from a NCM codebook comprising a plurality of NCM spatial precoders, wherein the plurality of the NCM spatial precoders are based on a unit-power beamforming vector optimized so that the wireless transmitter transmits up to the full power of each antenna element of the plurality of antenna elements while an overall transmitted power remains constant, wherein the NCM codebook comprises a codebook of size S constructed with a quantization table
M
=
S
4
as follows:
CB
S
2
=
{
P
1
2
,
P
2
2
,
…
,
P
S
2
}
=
{
[
cos
(
m
π
2
(
M
+
1
)
)
j
b
sin
(
m
π
2
(
M
+
1
)
)
]
❘
b
∈
{
0
,
1
}
,
m
=
{
±
1
,
±
2
,
…
,
±
M
}
with
M
=
S
4
}
where P k p denotes the k-th precoder of port-p codebook CB S p ;
applying the selected NCM spatial precoder to a data signal for generating a plurality of coded signals; and
transmitting the plurality of coded signals as wireless signals via a power amplifier operating at full power.
2. The method of claim 1 , wherein the unit-power beamforming vector is for transmission over two ports and comprises
W
b
,
θ
=
[
cos
θ
exp
(
j
π
b
2
)
sin
θ
]
,
b
∈
{
0
,
1
}
and
-
π
2
≤
θ
≤
π
2
optimized by values b o and θ o for the channel gain maximization problem
[
b
o
θ
o
]
=
max
b
∈
{
0
,
1
}
,
-
π
2
≤
θ
≤
π
2
HW
b
,
θ
2
where θ o indicates a maximal angle for achieving maximum beamforming gain and the N r -by-two channel matrix H is given by
H
=
[
h
¯
1
h
¯
2
]
=
[
h
1
,
1
h
1
,
2
⋮
⋮
h
N
r
,
1
h
N
r
,
2
]
.
3. The method of claim 2 , wherein a set of quantized angles are given by
θ
m
=
m
π
2
(
M
+
1
)
for m=±1, ±2, . . . , ±M.
4. The method of claim 1 , wherein a phase quantization of the NCM codebook comprises B discrete co-phasing hypotheses, wherein the beamforming vector is defined as
W
~
b
,
θ
=
1
2
[
cos
θ
exp
(
j
2
π
b
B
)
sin
θ
]
,
b
∈
{
0
,
1
,
…
,
B
-
1
}
and
-
π
2
≤
θ
≤
π
2
,
and the corresponding NCM codebook with size S=2 MB is represented by
CB
S
2
=
{
[
cos
m
π
2
(
M
+
1
)
exp
(
j
π
b
B
)
sin
m
π
2
(
M
+
1
)
]
❘
b
∈
{
0
,
1
,
…
,
B
-
1
}
,
m
=
{
±
1
,
±
2
,
…
,
±
M
}
with
M
=
S
4
}
.
5. The method of claim 1 , wherein the NCM codebook comprises a NCM codebook for a first number of ports, and the method further comprises obtaining a NCM codebook for a second number of ports based on the NCM codebook for the first number of ports.
6. The method of claim 1 , further comprising obtaining a NCM codebook for a number of ports 2p where
CB
S
2
p
=
{
[
P
k
1
p
0
p
0
p
P
k
2
p
]
P
k
3
2
❘
P
k
i
p
∈
gCB
S
i
p
for
i
=
1
,
2
,
P
k
3
2
∈
CB
s
3
2
}
.
7. The method of claim 1 , wherein the elements of the NCM codebook comprise complex numbers with a finite set of magnitudes.
8. The method of claim 7 , wherein the complex number is either purely real or purely imaginary.
9. The method of claim 8 , wherein the real and imaginary parts of the complex numbers are chosen from a finite set of values.
10. The method of claim 9 , wherein the finite set of values is scaled by a common factor.
11. The method of claim 10 , wherein the common factor is a function of a transmit power of the power amplifier.
12. A wireless transmitter operable to simultaneously transmit a plurality of wireless signals using a plurality of antenna elements, the wireless transmitter comprising processing circuitry operable to:
select a non-constant modulus (NCM) spatial precoder from a NCM codebook comprising a plurality of NCM spatial precoders, wherein the plurality of NCM spatial precoders are based on a unit-power beamforming vector optimized so that the wireless transmitter transmits up to the full power of each antenna element of the plurality of antenna elements while an overall transmitted power remains constant, wherein the NCM codebook comprises a codebook of size S constructed with a quantization table
M
=
S
4
as follows:
CB
S
2
=
{
P
1
2
,
P
2
2
,
…
,
P
S
2
}
=
{
[
cos
(
m
π
2
(
M
+
1
)
)
j
b
sin
(
m
π
2
(
M
+
1
)
)
]
❘
b
∈
{
0
,
1
}
,
m
=
{
±
1
,
±
2
,
…
,
±
M
}
with
M
=
S
4
}
where P k p denotes the k-th precoder of port-p codebook CB S p ;
apply the selected NCM spatial precoder to a data signal for generating a plurality of coded signals; and
transmit the plurality of coded signals as wireless signals via a power amplifier operating at full power.
13. The wireless transmitter of claim 12 , wherein the unit-power beamforming vector is for transmission over two ports and comprises
W
b
,
θ
=
[
cos
θ
exp
(
j
π
b
B
)
sin
θ
]
,
b
∈
{
0
,
1
}
and
-
π
2
≤
θ
≤
π
2
optimized by values b o and θ o for the channel gain maximization problem
[
b
o
θ
o
]
=
max
b
∈
{
0
,
1
}
,
-
π
2
≤
θ
≤
π
2
HW
b
,
θ
2
where θ o indicates a maximal angle for achieving maximum beamforming gain and the N r -by-two channel matrix H is given by
H
=
[
h
¯
1
h
¯
2
]
=
[
h
1
,
1
h
1
,
2
⋮
⋮
h
N
r
,
l
h
N
r
,
2
]
.
14. The wireless transmitter of claim 13 , wherein a set of quantized angles are given by
θ
m
=
m
π
2
(
M
+
1
)
for m=±1, ±2, . . . , ±M.
15. The wireless transmitter of claim 12 , wherein a phase quantization of the NCM codebook comprises B discrete co-phasing hypotheses, wherein the beamforming vector is defined as
W
~
b
,
θ
=
1
2
[
cos
θ
exp
(
j
2
π
b
B
)
sin
θ
]
,
b
∈
{
0
,
1
,
…
,
B
-
1
}
and
-
π
2
≤
θ
≤
π
2
,
and the corresponding NCM codebook with size S=2 MB is represented by
CB
S
2
=
{
[
cos
m
π
2
(
M
+
1
)
exp
(
j
π
b
B
)
sin
m
π
2
(
M
+
1
)
]
❘
b
∈
{
0
,
1
,
…
,
B
-
1
}
,
m
=
{
±
1
,
±
2
,
…
,
±
M
}
with
M
=
S
4
}
.
16. The wireless transmitter of claim 12 , wherein the NCM codebook comprises a NCM codebook for a first number of ports, and the processing circuitry is further operable to obtain a NCM codebook for a second number of ports based on the NCM codebook for the first number of ports.
17. The wireless transmitter of claim 12 , the processing circuitry further operable to obtain a NCM codebook for a number of ports 2p where
CB
s
2
p
=
{
[
P
k
1
p
0
p
0
p
P
k
2
p
]
P
k
3
2
❘
P
k
i
p
∈
gCB
S
i
p
for
i
=
1
,
2
,
P
k
3
2
∈
CB
S
3
2
}
.
18. The wireless transmitter of claim 12 , wherein the elements of the NCM codebook comprise complex numbers with a finite set of magnitudes, wherein the complex number is either purely real or purely imaginary.
19. The wireless transmitter of claim 18 , wherein the real and imaginary parts of the complex numbers are chosen from a finite set of values, wherein the finite set of values is scaled by a common factor, which is a function of a transmit power of the power amplifier.
20. A wireless transmitter operable to simultaneously transmit a plurality of wireless signals using a plurality of antenna elements, the wireless transmitter comprising a selecting module, an applying module, and a transmitting module;
the selecting module operable to select a non-constant modulus (NCM) spatial precoder from a NCM codebook comprising a plurality of NCM spatial precoders, wherein the plurality of NCM spatial precoders are based on a unit-power beamforming vector optimized so that the wireless transmitter transmits up to the full power of each antenna element of the plurality of antenna elements while an overall transmitted power remains constant, wherein the NCM codebook comprises a codebook of size S constructed with a quantization table
M
=
S
4
as follows:
CB
S
2
=
{
P
1
2
,
P
2
2
,
…
,
P
S
2
}
=
{
[
cos
(
m
π
2
(
M
+
1
)
)
j
b
sin
(
m
π
2
(
M
+
1
)
)
]
❘
b
∈
{
0
,
1
}
,
m
=
{
±
1
,
±
2
,
…
,
±
M
}
with
M
=
S
4
}
where P k p denotes the k-th precoder of port-p codebook CB S p ;
the applying module operable to apply the selected NCM spatial precoder to a data signal for generating a plurality of coded signals; and
the transmitting module operable to transmit the plurality of coded signals as wireless signals via a power amplifier operating at full power.