Coordinated multi-point transmission and reception schemes for cellular downlink

1. A method for generating transmit precoders for a communication system having a plurality of transmitters and a plurality of receivers forming a plurality of transmitter-receiver pairs, each of the plurality of transmitters and the plurality of receivers having a respective plurality of antennas, the method comprising:

initializing the transmit precoders;

updating a plurality of receiver filters and a plurality of slack variables using closed form expressions and updating the transmit precoders responsive to said updated receiver filters and slack variables; and

iteratively repeating the updating steps until convergence is reached to obtain a final set of transmit precoders,

wherein the transmit precoders are updated to perform precoding for multiple stream data transmission for each of the plurality of transmitter-receiver pairs on each of a plurality of slots under a per-antenna power constraint imposed on each of the plurality of antennas;

wherein said step of updating the transmit precoders comprises:

computing, using a bi-section search method, a dual function for a set of Lagrange variables corresponding to the per-antenna power constraint imposed on each of the plurality of transmitters; and

optimizing the dual function using a sub-gradient method.

2. The method of claim 1 , wherein said initializing step initializes the transmit precoders to a set of non-zero values satisfying the per-antenna power constraint imposed on each of the plurality of transmitters.

3. The method of claim 1 , wherein said step of updating the transmit precoders comprises reformulating a weighted sum rate objective maximization problem as a semi-definite programming problem that considers all of the plurality of transmitters.

4. The method of claim 3 , wherein the semi-definite programming problem is a convex problem solvable using interior-point methods.

5. The method of claim 1 , wherein said step of updating the transmit precoders comprises:

computing a dual function for a set of Lagrange variables corresponding to the per-antenna power constraint imposed on each of the plurality of transmitters and setting up an optimization problem based on the dual function;

reformulating the optimization problem in an alternate and equivalent form that comprises an outer maximization over a set of scaling factors and an inner minimization over the set of Lagrange variables; and

solving the optimization problem in the alternate and equivalent form using an iterative method.

6. The method of claim 1 , wherein said step of updating the transmit precoders comprises:

computing a dual function for a set of Lagrange variables corresponding to the per-antenna power constraint imposed on each of the plurality of transmitters and setting up an optimization problem based on the dual function;

reformulating the optimization problem in an alternate and equivalent form that comprises a joint maximization over two sets of variables; and

solving the optimization problem in the alternate and equivalent form using an alternating maximization approach that maximizes the two sets of variables in an alternating manner.

7. The method of claim 1 , wherein said step of updating the transmit precoders comprises:

computing a dual function for a set of Lagrange variables corresponding to a per-antenna power constraint imposed on each of the plurality of transmitters and setting up an optimization problem based on the dual function; and

reformulating the optimization problem as a semi-definite programming problem; and

solving the semi-definite programming problem.

8. A method for generating transmit precoders for a communication system having a plurality of transmitters and a plurality of receivers forming a plurality of transmitter-receiver pairs, each of the plurality of transmitters and the plurality of receivers having a respective plurality of antennas, the method comprising:

initializing the transmit precoders;

updating a plurality of receiver filters and a plurality of slack variables using closed form expressions and updating the transmit precoders responsive to said updated receiver filters and slack variables; and

iteratively repeating the updating steps until convergence is reached to obtain a final set of transmit precoders,

wherein the transmit precoders are updated to perform precoding for multiple stream data transmission for each of the plurality of transmitter-receiver pairs on each of a plurality of slots under a per-antenna power constraint imposed on each of the plurality of antennas

wherein said step of updating the transmit precoders comprises:

optimizing the transmit precoders under a total power constraint imposed on each of the plurality of transmitters; and

scaling the optimized transmit precoders to enforce the per-antenna power constraint imposed on each of the plurality of transmitters,

wherein scaling factors used to scale the optimized transmit precoders are determined using a geometric program.

9. An apparatus for generating transmit precoders for a communication system having a plurality of transmitters and a plurality of receivers forming a plurality of transistor-receiver pairs, each of the plurality of transmitters and the plurality of receivers having a respective plurality of antennas, the apparatus comprising:

a transmit precoder initializer for initializing the transmit precoders;

an updater for updating a plurality of receiver filters and a plurality of slack variables, as a first part of an iteration;

a transmit precoder updater for updating the transmit precoders responsive to updated receiver filters and slack variables, as a second part of the iteration; and

an iteration controller for iteratively repeating the first part of the iteration that updates of the receiver filters and the slack variables and the second part of the iteration that updates the transmit precoders until convergence is reached to obtain a final set of transmit precoders,

wherein the transmit precoders are updated to perform precoding for multiple stream data transmission for each of a plurality of transmitter-receiver pairs on each of a plurality of slots under a per-antenna power constraint imposed on each of the plurality of transmitters, the receiver filters and the slack variables being updated using closed form expressions;

wherein said transmit precoder updater updates the transmit precoders by computing a dual function for a set of Lagrange variables corresponding to the per-antenna power constraint imposed on each of the plurality of transmitters and setting up an optimization problem based on the dual function, reformulating the optimization problem as a semi-definite programming problem and solving the semi-definite programming problem.

10. The apparatus of claim 9 , wherein said transmit precoder initializer initializes the transmit precoders to a set of non-zero values satisfying the per-antenna power constraint imposed on each of the plurality of transmitters.

11. The apparatus of claim 9 , wherein said transmit precoder updater updates the transmit precoders by reformulating a weighted sum rate objective maximization problem as a semi-definite programming problem that considers all of the plurality of transmitters.

12. The apparatus of claim 11 , wherein the semi-definite programming problem is a convex problem solvable using interior-point methods.

13. The apparatus of claim 9 , wherein said transmit precoder updater updates the transmit precoders by computing, using a bi-section search method, a dual function for a set of Lagrange variables corresponding to the per-antenna power constraint imposed on each of the plurality of transmitters, and optimizing the dual function using a sub-gradient method.

14. The apparatus of claim 9 , wherein said transmit precoder updater updates the transmit precoders by computing a dual function for a set of Lagrange variables corresponding to the per-antenna power constraint imposed on each of the plurality of transmitters and setting up an optimization problem based on the dual function, reformulating the optimization problem in an alternate and equivalent form that comprises an outer maximization over a set of scaling factors and an inner minimization over the set of Lagrange variables, and solving the optimization problem in the alternate and equivalent form using an iterative method.

15. The apparatus of claim 9 , wherein said transmit precoder updater updates the transmit precoders by computing a dual function for a set of Lagrange variables corresponding to the per-antenna power constraint imposed on each of the plurality of transmitters and setting up an optimization problem based on the dual function, reformulating the optimization problem in an alternate and equivalent form that comprises a joint maximization over two sets of variables, solving the optimization problem in the alternate and equivalent form using an alternating maximization approach that maximizes the two sets of variables in an alternating manner.

16. The apparatus of claim 9 , wherein said transmit precoder updater updates the transmit precoders by optimizing the transmit precoders under a total power constraint imposed on each of the plurality of transmitters, and scaling the optimized transmit precoders to enforce the per-antenna power constraint imposed on each of the plurality of transmitters, wherein scaling factors used to scale the optimized transmit precoders are determined using a geometric program.