Optimized high rate space-time codes for wireless communication
A space-time coding arrangement for wireless communications is disclosed where the codes are generated through stochastic approximation. The codes can be optimized over a wide range of performance metrics, receiver structures, and channel characteristics.
1. A method of generating space-time codes for a transmission system comprising the steps of:
(i) selecting a set of initial coding parameters for the space-time code;
(ii) simulating a series of observations based on a model of known communication channel characteristics and decoding the simulated series of observations using a selected receiver structure so as to compute a performance metric for the coding parameters;
(iii) estimating a gradient for the performance metric as a function of the coding parameters;
(iv) updating the coding parameters for the space-time code using the estimated gradient;
(v) repeating steps (ii) through (iv) until an optimized set of coding parameters is obtained for the space-time code.
2. The method of claim 1 wherein the performance metric is the bit error probability.
3. The method of claim 1 wherein the performance metric is the frame error probability.
4. The method of claim 1 wherein the gradient is estimated using a score function method.
5. The method of claim 1 wherein the gradient is estimated by
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where y i are the simulated observations based on coded symbols x i , M is the number of simulated observations, θ are the coding parameters, and γ is the computed performance metric.
6. The method of claim 1 wherein the coding parameters are updated at step (iv) in accordance with
θ k −a k ĝ(θ k ),
where θ k represents the coding parameters, ĝ(θ k ) is the estimated gradient, and a k is a positive constant that varies with k.
7. The method of claim 6 wherein the coding parameters are updated by projecting results on a nearest point in a constraint space.
8. The method of claim 1 wherein the selected receiver structure is a suboptimal detector.
9. The method of claim 1 wherein the coding parameters are dispersion matrices for a linear dispersion code.
10. A transmission system which utilizes the space-time codes generated by the method of claim 1 .
11. A transmitter comprising:
a plurality of antennas; and
an encoder responsive to incoming symbols and which delivers coded symbols to said antennas in a series of time intervals, the coded symbols arranged in accordance with a space-time code where the space-time code is generated by
(i) selecting a set of initial coding parameters for the space-time code;
(ii) simulating a series of observations based on a model of known communication channel characteristics and decoding the simulated series of observations using a selected receiver structure so as to compute a performance metric for the coding parameters;
(iii) estimating a gradient for the performance metric as a function of the coding parameters;
(iv) updating the coding parameters for the space-time code using the estimated gradient;
(v) repeating steps (ii) through (iv) until an optimized set of coding parameters is obtained for the space-time code.
12. The transmitter of claim 11 wherein the performance metric is the bit error probability.
13. The transmitter of claim 11 wherein the performance metric is the frame error probability.
14. The transmitter of claim 11 wherein the gradient is estimated using a score function method.
15. The transmitter of claim 11 wherein the gradient is estimated by
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where y i are the simulated observations based on coded symbols x i , M is the number of simulated observations, θ are the coding parameters, and γ is the computed performance metric.
16. The transmitter of claim 11 wherein the coding parameters are updated at step (iv) in accordance with
θ k −a k ĝ(θ k ),
where θ k represents the coding parameters, ĝ(θ k ) is the estimated gradient, and a k is a positive constant that varies with k.
17. The transmitter of claim 16 wherein the coding parameters are updated by projecting results on a nearest point in a constraint space.
18. The transmitter of claim 11 wherein the selected receiver structure is a suboptimal detector.
19. The transmitter of claim 11 wherein the coding parameters are dispersion matrices for a linear dispersion code.
20. A receiver comprising:
a plurality of antennas; and
a decoder which receives incoming symbols from said antennas in a series of time intervals and which interprets the incoming symbols using a pre-specified detector structure and which delivers decoded symbols arranged in accordance with a space-time code where the space-time code is generated by
(i) selecting a set of initial coding parameters for the space-time code;
(ii) simulating a series of observations based on a model of known communication channel characteristics and decoding the simulated series of observations using the pre-specified detector structure so as to compute a performance metric for the coding parameters;
(iii) estimating a gradient for the performance metric as a function of the coding parameters;
(iv) updating the coding parameters for the space-time code using the estimated gradient;
(v) repeating steps (ii) through (iv) until an optimized set of coding parameters is obtained for the space-time code.
21. The receiver of claim 20 wherein the performance metric is the bit error probability.
22. The receiver of claim 20 wherein the performance metric is the frame error probability.
23. The receiver of claim 20 wherein the gradient is estimated using a score function method.
24. The receiver of claim 20 wherein the gradient is estimated by
g
^
(
θ
k
)
=
1
M
∑
i
=
1
M
γ
(
y
i
,
x
i
,
θ
k
)
[
∇
q
log
p
(
y
i
❘
x
i
,
θ
)
❘
θ
=
θ
k
]
where y i are the simulated observations based on coded symbols x i , M is the number of simulated observations, θ are the coding parameters, and γ is the computed performance metric.
25. The receiver of claim 20 wherein the coding parameters are updated at step (iv) in accordance with
θ k −a k ĝ(θ k ),
where θ k represents the coding parameters, ĝ(θ k ) is the estimated gradient, and a k is a positive constant that varies with k.
26. The receiver of claim 25 wherein the coding parameters are updated by projecting results on a nearest point in a constraint space.
27. The receiver of claim 20 wherein the selected receiver structure is a suboptimal detector.
28. The receiver of claim 20 wherein the coding parameters are dispersion matrices for a linear dispersion code.