Peak-to-average power ratio control
A method of a wireless communication transmitter is disclosed for peak-to-average power ratio (PAPR) control of communication symbols with N time-domain signal samples for transmission via each of M antenna elements. The method comprises: applying a PAPR cost function f(x) which has a proximal operator with closed form and is differentiable in an interval, and the proximal operator comprises a parameter lambda for tuning; selecting a value for lambda to perform a trade-off between PAPR and at least one other characteristic of the wireless communication transmitter; selecting a precoding for the collection of samples as a solution to an optimization problem for the selected value for lambda, wherein the optimization problem comprises minimization of an overall cost function comprising at least the PAPR cost function, and wherein solving the optimization problem comprises using the proximal operator of the PAPR cost function. Corresponding apparatus, wireless communication transmitter, radio base station, and computer program product are also disclosed.
1. A method of a wireless communication transmitter for peak-to-average power ratio—PAPR—control of communication symbols with N time-domain signal samples for transmission via each of M antenna elements, the method comprising:
applying a PAPR cost function ƒ(x) which has a proximal operator with closed form and is differentiable in the interval [0, a[, wherein x denotes a collection of samples for transmission, wherein a denotes a threshold which corresponds to a maximum allowable amplitude for each time-domain signal sample, and wherein the proximal operator comprises a parameter λ for tuning;
selecting a value for the parameter λ, wherein the selection comprises performing a trade-off between PAPR and at least one other characteristic of the wireless communication transmitter; and
selecting a precoding for the collection of samples as a solution to an optimization problem for the selected value for the parameter λ, wherein the optimization problem comprises minimization of an overall cost function comprising at least the PAPR cost function, and wherein solving the optimization problem comprises using the proximal operator of the PAPR cost function.
2. The method of claim 1 , wherein the PAPR cost function has an infinite value in the interval [a, ∞).
3. The method of claim 1 , wherein the PAPR cost function is a log-barrier function or a Huber function.
4. The method of claim 3 , wherein the log-barrier function is ƒ(x)=Σ i=1 L −log(a−[Ax] i ), wherein A denotes a transfer function.
5. The method of claim 1 , wherein the proximal operator of the PAPR cost function is defined as
pro
x
λ
f
(
v
)
=
arg
min
x
(
f
(
x
)
+
1
2
λ
x
-
v
2
2
)
.
6. The method of claim 1 , wherein the optimization problem is
arg
min
x
(
f
(
x
)
+
g
(
x
)
)
,
wherein g(x) is a channel transfer penalty function.
7. The method of claim 6 , wherein
g
(
x
)
=
{
0
for
error
free
channel
transfer
∞
otherwise
.
8. The method of claim 1 , wherein solving the optimization problem comprises applying an iterative optimization algorithm, wherein each iteration uses the proximal operator.
9. The method of claim 8 , wherein the iterative optimization algorithm is a Douglas-Rachford operator splitting algorithm and/or an alternating direction method of multipliers—ADMM.
10. The method of claim 1 , wherein the at least one other characteristic of the wireless communication transmitter comprises an error vector magnitude—EVM.
11. The method of claim 1 , wherein performing the trade-off comprises increasing PAPR to improve the at least one other characteristic.
12. The method of claim 1 , wherein selecting the value for the parameter λ comprises addressing a look-up table of values for the parameter λ based on the number of antenna elements M, the number of time-domain signal samples N, and use case requirements for PAPR and the at least one other characteristic of the wireless communication transmitter.
13. The method of claim 12 , further comprising solving the optimization problem for a plurality of values of the parameter λ, and populating the look-up table accordingly.
14. The method of claim 1 , further comprising transmitting the N time-domain signal samples via the M antenna elements using the selected precoding.
15. A computer program product comprising a non-transitory computer readable medium, having thereon a computer program comprising program instructions, the computer program being loadable into a data processing unit and configured to cause execution of the method according to claim 1 when the computer program is run by the data processing unit.
16. An apparatus for a wireless communication transmitter and for peak-to-average power ratio—PAPR—control of communication symbols with N time-domain signal samples for transmission via each of M antenna elements, the apparatus comprising controlling circuitry configured to cause:
application of a PAPR cost function ƒ(x) which has a proximal operator with closed form and is differentiable in the interval [0, a[, wherein x denotes a collection of samples for transmission, wherein denotes a threshold which corresponds to a maximum allowable amplitude for each time-domain signal sample, and wherein the proximal operator comprises a parameter λ for tuning; selection of a value for the parameter λ, wherein the selection comprises performance of a trade-off between PAPR and at least one other characteristic of the wireless communication transmitter; and
selection of a precoding for the collection of samples as a solution to an optimization problem for the selected value for the parameter A, wherein the optimization problem comprises minimization of an overall cost function comprising at least the PAPR cost function, and wherein solving the optimization problem comprises using the proximal operator of the PAPR cost function.
17. The apparatus of claim 16 , wherein the controlling circuitry is configured to:
apply a PAPR cost function ƒ(x) which has a proximal operator with closed form and is differentiable in the interval [0, a[, wherein x denotes a collection of samples for transmission, wherein a denotes a threshold which corresponds to a maximum allowable amplitude for each time-domain signal sample, and wherein the proximal operator comprises a parameter λ for tuning;
select a value for the parameter λ, wherein the selection comprises performing a trade-off between PAPR and at least one other characteristic of the wireless communication transmitter; and
select a precoding for the collection of samples as a solution to an optimization problem for the selected value for the parameter λ, wherein the optimization problem comprises minimization of an overall cost function comprising at least the PAPR cost function, and wherein solving the optimization problem comprises using the proximal operator of the PAPR cost function.
18. A wireless communication transmitter comprising the apparatus of claim 16 .
19. A radio base station comprising the wireless communication transmitter of claim 18 .