Method and device for multiple input/multiple output transmit and receive weights for equal-rate data streams

1. A method of operating a communication system, the method comprising the steps of:

providing a channel matrix of a gain and phase between each transmit antenna and each receive antenna of the communication system;

computing at least one receive weight vector as a function of the channel matrix and at least one transmit weight vector;

computing a gradient matrix as a function of the transmit weight vector, the channel matrix, the receive weight vector and a constraint weight; and

computing an updated transmit weight vector as a function of the transmit weight vector, the receive weight vector, the gradient matrix, and the channel matrix.

2. The method of claim 1 wherein the transmit weight vector is computed as a function of a step size.

3. The method of claim 1 wherein the updated transmit weight vector is computed according to:

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where r u is the u th element of r and x u is u th element of x.

4. The method of claim 1 wherein each column of the gradient matrix is computed according to:

G= ( H H WW H H +2γ(trace( V H V )−1) I M T ) V−H H W.

5. The method of claim 1 wherein the updated transmit weight vector is computed according to:

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where r u is the u th element of r and x u is u th element of x.

6. The method of claim 1 wherein each column of the gradient matrix is computed according to:

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u

=

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∑

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=

1

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H

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w

l

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l

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trace

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M

T

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u

-

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H

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w

u

,

where u designates a column of the gradient vector.

7. A system for operating a communication system comprising:

means for providing a channel matrix of a gain and phase between each transmit antenna and each receive antenna of the communication system;

means for computing at least one receive weight vector as a function of the channel matrix and at least one of transmit weight vectors; and

means for computing a gradient matrix as a function of the channel matrix, the receive weight vector, the transmit weight vector and a constraint weight; and

means for computing an updated transmit weight vector as a function of the transmit weight vector, the channel matrix, the gradient matrix, and the receive weight vector.

8. The system of claim 7 further comprising means for computing the transmit weight vector as a function of a step size.

9. A computer readable medium storing a computer program comprising:

computer readable code for providing a channel matrix of a gain and phase between each transmit antenna end each receive antenna of the communication system;

computer readable code for computing at least one receive weight vector as a function of the channel matrix and at least one of transmit weight vectors;

computer readable code for computing a gradient matrix as a function of the channel matrix, the receive weight vector and the transmit weight vector; and

computer readable code for computing an updated transmit weight vector as a function of the transmit weight vector and the gradient matrix.

10. The program of claim 9 further comprising computer readable code for computing a gradient matrix as a function of the transmit weight vector, the channel matrix, the receive weight vector and a constraint weight, computing the updated transmit weight vector as a function of the gradient matrix and the transmit weight vector.

11. The program of claim 9 further comprising computer readable code for computing the transmit weight vector as a function of a step size.

12. The method of claim 9 wherein the updated transmit weight vector is computed according to:

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=

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l

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l

+

n

)

-

x

u



2

,

where r u is the u th element of r and x u is u th element of x.

13. The method of claim 9 wherein each column of the gradient matrix is computed according to:

G =( H H WW H H +2γ(trace( V H V )−1) I M T ) V−H H W.

14. The method of claim 9 wherein the updated transmit weight vector is computed according to:

min

w

u

,

v

u

⁢

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u

=

1

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s

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=

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∑

l

=

u

N

s

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Hv

l

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x

l

+

n

)

-

x

u



2

,

where r u is the u th element of r and x u is u th element of x.

15. The method of claim 9 wherein each column of the gradient matrix is computed according to:

∇

v

u

=

(

∑

l

=

1

u

⁢

H

H

⁢

w

l

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l

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+

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trace

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v

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u

,

where u designates a column of the gradient vector.

16. A method of operating a communication system, the method comprising the steps of:

computing a plurality of transmit weight vectors and a plurality of receive weight vectors that minimizes an expected mean squared error between analytical successive cancellation symbol estimates and transmitted symbols, wherein each analytical successive cancellation symbol estimate is computed according to

r

u

=

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y

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=

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,

where {circumflex over (x)} t =slice(r l ); and

utilizing the transmit and receive weight vectors in transmitting and receiving signals.

17. The method of claim 16 wherein the transmit weight vector is normalized according to;

trace(V H V)=1.

18. A method of operating a communication system, the method comprising the steps of:

computing a plurality of transmit weight vectors wherein the transmit weight vectors are computed according to:

V=U V S V Z V H

where U V =Z H and Z V is chosen according to:

Z V,l H {tilde over (D)}Z V,l= 1−{overscore (MSE)}=trace({tilde over (D)})/N s ; and

subject to Z V Z V H =Z V H Z V =I N s

utilizing the plurality of transmit weight vectors to transmit signals.

19. The method of claim 18 wherein the right singular vectors of the transmit weight matrix are the columns of the normalized DFT matrix.

20. The method of claim 18 wherein the right singular vectors of the transmit weight matrix are the columns of the normalized Hadamard matrix.