Beamforming with partial channel knowledge

1. A method, in a transmitter, for selecting steering vectors for simultaneously transmitting one or more streams between the transmitter and a receiver, wherein the receiver has N R receive antennas, wherein the transmitter knows respective channels associated with M receive antennas of the receiver, wherein M is less than N R , and wherein N S is the number of the one or more streams, the method comprising:

constructing a partial channel matrix that describes a multiple input, multiple output (MIMO) channel between the transmitter and the M receive antennas;

generating L independent vectors using the partial channel matrix, wherein L is a rank of the partial channel matrix; and

when N S is greater than L,

(i) selecting the L independent vectors as steering vectors to steer L streams of the one or more of streams;

(ii) selecting N S −L orthogonal vectors in a null space of the L independent vectors as steering vectors to steer a remainder of the streams in the one or more streams; and

(iii) respectively utilizing the steering vectors for transmitting (a) the L streams of the one or more of streams (N S ), and (b) the remainder of the streams in the one or more streams (N S ).

2. The method of claim 1 , wherein:

the transmitter has N T transmit antennas, and

a dimensionality of the null space is N T −L.

3. The method of claim 2 , further comprising, varying the N S −L orthogonal vectors over time when i) N S is greater than L, and ii) N T is greater than or equal to N S .

4. The method of claim 2 , further comprising, varying the N S −L orthogonal vectors over frequency when i) N S is greater than L, and ii) N T is greater than or equal to N S .

5. The method of claim 1 , wherein generating L independent vectors using the partial channel matrix includes performing singular value decomposition (SVD) of the partial channel matrix.

6. The method of claim 1 , wherein the number N S of streams to be transmitted to the receiver is less than or equal to a minimum of N R and a number N T of the transmit antennas of the transmitter.

7. The method of claim 1 , wherein constructing the partial channel matrix comprises:

determining an additional partial channel matrix corresponding to a backward channel; and

determining the partial channel matrix from the additional partial channel matrix.

8. The method of claim 1 , wherein when i) N S =2 and ii) M=1:

selecting the L independent vectors as steering vectors to steer L of the one or more streams comprises selecting one independent vector to steer a first stream to a single receive antenna of the receiver; and

selecting N S −L orthogonal vectors in the null space of the L independent vectors comprises selecting a vector to steer a second stream in a null space of a row vector in the partial channel matrix.

9. The method of claim 1 , further comprising, when N S is less than or equal to L, selecting N S of the L independent vectors as steering vectors.

10. The method of claim 9 , wherein when i) N S =1 and ii) M=1:

selecting N S of the L independent vectors as steering vectors comprises selecting one independent vector to steer the one stream to a single receive antenna of the receiver.

11. The method of claim 9 , wherein when i) N S =1 and ii) M=2:

generating L independent vectors using the partial channel matrix comprises generating a single independent vector using the partial channel matrix, and

selecting N S of the L independent vectors as steering vectors comprises selecting the single independent vector to steer the one stream.

12. An apparatus for use in transmit beamforming to a beamformee, wherein the beamformee has N R receive antennas, the apparatus comprising:

a controller configured to

construct a partial channel matrix that describes a multiple input, multiple output (MIMO) channel between a beamformer and M receive antennas, wherein M is less than N R ,

generate L independent vectors using the partial channel matrix, wherein L is a rank of the partial channel matrix, and

when a number N S of one or more streams is greater than L, i) select the L independent vectors as steering vectors to steer L streams of the plurality of streams, and ii) select N S −L orthogonal vectors in a null space of the L independent vectors as steering vectors to steer a remainder of the streams in the plurality of streams.

13. The apparatus of claim 12 , wherein

the beamformer has N T transmit antennas, and

a dimensionality of the null space is N T −L.

14. The apparatus of claim 13 , wherein the controller is configured to vary the N S −L orthogonal vectors over time when i) N S is greater than L, and ii) N T is greater than or equal to N S .

15. The apparatus of claim 13 , wherein the controller is configured to vary the N S −L orthogonal vectors over frequency when i) N S is greater than L, and ii) N T is greater than or equal to N S .

16. The apparatus of claim 12 , further comprising one or more radio interfaces coupled to the controller, wherein the one or more radio interfaces are configured to couple to N T beamformer antennas.

17. The apparatus of claim 12 , wherein the controller is configured to generate L independent vectors based on performing a singular value decomposition (SVD) of the partial channel matrix.

18. The apparatus of claim 12 , wherein the number N S of streams to be transmitted to the receiver is less than or equal to a minimum of N R and a number N T of the transmit antennas of a beamformer.

19. The apparatus of claim 12 , wherein the controller is configured to:

determine an additional partial channel matrix corresponding to a backward channel, and

determine the partial channel matrix from the additional partial channel matrix.

20. The apparatus of claim 12 , wherein the controller is configured to, when N S is less than or equal to L, select N S of the L independent vectors as steering vectors.