Interference alignment for transmitter/receiver pairs in wireless communication systems

1. A method comprising:

selecting second transmitter-receiver pairs proximate to a first transmitter-receiver pair, wherein the first transmitter-receiver pair is in a first cell and the second transmitter-receiver pairs are not in the first cell, and wherein the first and second transmitter-receiver pairs form a first group;

canceling interference caused by signals in one direction between the first transmitter-receiver pair and the second transmitter-receiver pairs,

in response to canceling the interference caused by the signals in one direction, aligning beamforming vectors of signals for transmission by the second transmitter-receiver pairs to be received by the first transmitter-receiver pair in a first subspace of channels defined by channel matrices between the first transmitter-receiver pair and the second transmitter-receiver pairs, wherein a second subspace of the channels is free of the signals transmitted by the second transmitter-receiver pairs; and

aligning beamforming vectors of signals in a second group of transmitter-receiver pairs relative to at least one beamforming vector associated with at least one transmitter-receiver pair that is a member of the first group and the second group.

2. The method of claim 1 , wherein canceling the interference comprises:

decoding messages in the signals transmitted by the first transmitter-receiver pair at a first receiver and the second transmitter-receiver pairs at a second receiver; and

providing the decoded messages for canceling interference caused by the signals in one direction between the first transmitter-receiver pair and the second transmitter-receiver pairs.

3. The method of claim 2 , further comprising:

assigning a decoding order to the first transmitter-receiver pair and the second transmitter-receiver pairs, wherein providing the decoded messages comprises providing the decoded messages to the first transmitter-receiver pair or the second transmitter-receiver pairs based on the decoding order.

4. The method of claim 3 , wherein aligning signals transmitted by the second transmitter-receiver pairs comprises precoding the signals transmitted by the second transmitter-receiver pairs using estimates of channels between the first and second transmitter-receiver pairs so that the precoded signals are elements of the first subspace.

5. The method of claim 4 , wherein precoding the signals comprises precoding the signals to form the beamforming vectors for the signals, wherein the beamforming vectors are defined relative to a direction of a predetermined beamforming vector used by one of the second transmitter-receiver pairs.

6. The method of claim 5 , further comprising:

jointly decoding messages in signals received by the first transmitter-receiver pair and at least one third transmitter-receiver pair, wherein said at least one third transmitter-receiver pair is in the first cell.

7. The method of claim 6 , wherein jointly decoding the messages comprises exchanging scalar observations of signals received by the first transmitter-receiver pair and said at least one third transmitter-receiver pair.

8. The method of claim 7 , wherein jointly decoding the messages comprises combining the scalar observations received at the first transmitter-receiver pair and said at least one third transmitter-receiver pair with vector observations of signals received by the first transmitter-receiver pair and said at least one third transmitter-receiver pair.

9. An apparatus comprising:

a memory coupled to at least one processor;

the at least one processor to:

select second transmitter-receiver pairs proximate to a first transmitter-receiver pair, wherein the first transmitter-receiver pair is in a first cell and the second transmitter-receiver pairs are not in the first cell, and wherein the first and second transmitter-receiver pairs form a first group;

cancel interference caused by signals in one direction between the first transmitter-receiver pair and the second transmitter-receiver pairs,

in response to cancelling the interference caused by the signals in one direction, align beamforming vectors of signals for transmission by the second transmitter-receiver pairs to be received by the first transmitter-receiver pair in a first subspace of channels defined by channel matrices between the first transmitter-receiver pair and the second transmitter-receiver pairs, wherein a second subspace of the channels is free of the signals transmitted by the second transmitter-receiver pairs, and

align beamforming vectors of signals n a second group of transmitter-receiver pairs relative to at least one beamforming vector associated with at least one transmitter-receiver pair that is a member of the first group and the second group.

10. The apparatus of claim 9 , wherein the processor is to:

decode messages in the signals transmitted by the first transmitter-receiver pair and the second transmitter-receiver pairs; and

provide the decoded messages for canceling interference caused by the signals in one direction between the first transmitter-receiver pair and the second transmitter-receiver pairs.

11. The apparatus of claim 10 , wherein the processor is to assign a decoding order to the first transmitter-receiver pair and the second transmitter-receiver pairs, and wherein the processor is to provide the decoded messages to the first transmitter-receiver pair or the second transmitter-receiver pairs based on the decoding order.

12. The apparatus of claim 11 , wherein the processor is to precode the signals transmitted by the second transmitter-receiver pairs using estimates of channels between the first and second transmitter-receiver pairs so that the precoded signals are elements of the first subspace.

13. The apparatus of claim 12 , wherein the processor is to precode the signals to form beamforming vectors for the signals, wherein the beamforming vectors are defined relative to a direction of a predetermined beamforming vector used by one of the second transmitter-receiver pairs.

14. The apparatus of claim 13 , wherein the processor is to jointly decode messages in signals received by the first transmitter-receiver pair and at least one third transmitter-receiver pair, wherein said at least one third transmitter-receiver pair is in the first cell.

15. The apparatus of claim 14 , wherein the processor is to jointly decode the messages using scalar observations of signals received by the first transmitter-receiver pair and said at least one third transmitter-receiver pair.

16. The apparatus of claim 15 , wherein the processor is to combine the scalar observations received at the first transmitter-receiver pair and said at least one third transmitter-receiver pair with vector observations of signals received by the first transmitter-receiver pair and said at least one third transmitter-receiver pair.

17. A non-transitory computer readable medium embodying a set of executable instructions, the set of executable instructions to manipulate at least one processor to:

select second transmitter-receiver pairs proximate to a first transmitter-receiver pair, wherein the first transmitter-receiver pair is in a first cell and the second transmitter-receiver pairs are not in the first cell, and wherein the first and second transmitter-receiver pairs form a first group;

cancel interference caused by signals in one direction between the first transmitter-receiver pair and the second transmitter-receiver pairs;

in response to canceling the interference caused by the signals in one direction, align beamforming vectors of signals for transmission by the second transmitter-receiver pairs to be received by the first transmitter-receiver pair in a first subspace of channels defined by channel matrices between the first transmitter-receiver pair and the second transmitter-receiver pairs, wherein a second subspace of the channels is free of the signals transmitted by the second transmitter-receiver pairs, and

align beamforming vectors of signals in a second group of transmitter-receiver pairs relative to at least one beamforming vector associated with at least one transmitter-receiver pair that is a member of the first group and the second group.

18. The non-transitory computer readable medium set forth in claim 17 , comprising a set of executable instructions to manipulate said at least one processor to jointly decode messages in signals received by the first transmitter-receiver pair and at least one third transmitter-receiver pair, wherein said at least one third transmitter-receiver pair is in the first cell.