Beamforming calibration

1. A method of wireless communication, comprising:

in a wireless communication device, the device comprising an array of transceiver chains, each transceiver chain i) characterized by a bandwidth, and ii) comprising a transmit chain and a receive chain:

first determining, at each of one or more center frequencies and sub-bandwidths sufficient to cover the bandwidth: i) a first set of inter-chain transmit gain and phase/delay differences across transmit chains, and ii) a first set of inter-chain receive gain and phase/delay differences across the receive chains;

second determining, after the first determining and in a same manner as the first determining: i) a second set of inter-chain transmit gain and phase/delay differences across the transmit chains, and ii) a second set of inter-chain receive gain and phase/delay differences across the receive chains; and

first adjusting each transmit chain by the difference between the second set of inter-chain transmit gain and phase/delay differences and the first set of inter-chain transmit gain and phase/delay differences, and each receive chain by the difference between the second set of inter-chain receive gain and phase/delay differences and the first set of inter-chain receive gain and phase/delay differences.

2. The method of claim 1 , wherein:

the array comprises M≥3 transceiver chains;

determining a set of inter-chain transmit gain and phase/delay differences across transmit chains comprises, for one or more times sufficient to cover all chains compared to a transmit reference chain k 1 :

first transmitting, from each of a plurality of N 1 ≤M−1 chains of the M chains including chain k 1 and not including a receive chain p R×1 of the M chains, a chain-specific signal;

first receiving, by the receive chain p R×1 , the transmitted chain-specific signals; and

third determining a gain and phase/delay difference between each first received chain-specific signal and the received signal specific to chain k 1 ; and

determining a set of inter-chain receive gain and phase/delay differences across receive chains comprises, for one or more times sufficient to cover all chains compared to a receive reference chain k 2 :

second transmitting, from a reference transmit chain p T×1 of the M chains, a reference signal;

second receiving, by each of a plurality of N 2 ≤M−1 chains of the M chains including chain k 2 and not including reference transmit chain p T×1 , each second transmitted reference signal; and

fourth determining a gain and phase/delay difference between each second received reference signal and the second received reference signal at chain k 2 .

3. The method of claim 2 , wherein the set of chain-specific signals across the plurality of N 1 ≤M−1 chains is a set of orthogonal signals.

4. The method of claim 3 , wherein each orthogonal chain-specific signal is a Hadamard signal.

5. The method of claim 3 , wherein transmitting the set of chain-specific signals comprises transmitting the set of chain specific signals at a same time.

6. The method of claim 1 , wherein:

the array is characterized by a beamforming codebook; and

further comprising, prior to the first determining:

third transmitting a beam from the device to a test receiver, the test receiver at a far field distance from the device along a first transmit direction, the beam determined by a first beamforming codebook of the device to transmit the beam in the first transmit direction;

second adjusting a gain and phase of the transmit chains to produce maximum received power at the test receiver;

fifth determining, for each transmit chain of the device, a transmit gain difference and a transmit phase difference between the beam producing the maximum received power at the test receiver and the beam determined by the first beamforming codebook of the device to transmit at the first transmit direction;

first modifying each codebook entry for each transmit direction with the determined transmit gain difference and the determined transmit phase difference;

third receiving, by the device, a beam from a test transmitter at a far field distance along a first receive direction using a receive beam determined by the first beamforming codebook of the device to receive at the first receive direction;

third adjusting a gain and phase of the receive chains to produce the maximum received combined power at the device from the test transmitter;

sixth determining, for each receive chain, a receive gain difference and a receive phase difference between the beam producing the maximum received power at the device and the beam determined by the first beamforming codebook of the device to receive at the first receive direction; and

second modifying each codebook entry for each receive direction with the second determined receive gain difference and the second determined receive phase difference.

7. The method of claim 6 , wherein the first transmit direction and the first receive direction are each a boresight direction of the device.

8. A wireless communication device, comprising:

a memory;

an array of transceiver chains, each transceiver chain i) characterized by a bandwidth, and ii) comprising a transmit chain and a receive chain; and

at least one processor coupled to the memory, the memory including instructions executable by the at least one processor to cause the device to:

first determine, at each of one or more center frequencies and sub-bandwidths sufficient to cover the bandwidth: i) a first set of inter-chain transmit gain and phase/delay differences across transmit chains, and ii) a first set of inter-chain receive gain and phase/delay differences across the receive chains;

second determine, after the first determining and in a same manner as the first determining: i) a second set of inter-chain transmit gain and phase/delay differences across the transmit chains, and ii) a second set of inter-chain receive gain and phase/delay differences across the receive chains; and

first adjust each transmit chain by the difference between the second set of inter-chain transmit gain and phase/delay differences and the first set of inter-chain transmit gain and phase/delay differences, and each receive chain by the difference between the second set of inter-chain receive gain and phase/delay differences and the first set of inter-chain receive gain and phase/delay differences.

9. The device of claim 8 , wherein:

the array comprises M≥3 transceiver chains;

determining a set of inter-chain transmit gain and phase/delay differences across transmit chains comprises, for one or more times sufficient to cover all chains compared to a transmit reference chain k 1 :

first transmitting, from each of a plurality of N 1 ≤M−1 chains of the M chains including chain k 1 and not including a receive chain p R×1 of the M chains, a chain-specific signal;

first receiving, by the receive chain p R×1 , the transmitted chain-specific signals; and

third determining a gain and phase/delay difference between each first received chain-specific signal and the received signal specific to chain k 1 ; and

determining a set of inter-chain receive gain and phase/delay differences across receive chains comprises, for one or more times sufficient to cover all chains compared to a receive reference chain k 2 :

second transmitting, from a reference transmit chain p T×1 of the M chains, a reference signal;

second receiving, by each of a plurality of N 2 ≤M−1 chains of the M chains including chain k 2 and not including reference transmit chain p T×1 , each second transmitted reference signal; and

fourth determining a gain and phase/delay difference between each second received reference signal and the second received reference signal at chain k 2 .

10. The device of claim 9 , wherein the set of chain-specific signals across the plurality of N 1 ≤M−1 chains is a set of orthogonal signals.

11. The device of claim 10 , wherein each orthogonal chain-specific signal is a Hadamard signal.

12. The device of claim 10 , wherein transmitting the set of chain-specific signals comprises transmitting the set of chain specific signals at a same time.

13. The device of claim 8 , wherein:

the array is characterized by a beamforming codebook; and

the memory includes further instructions executable by the at least one processor to cause the device to, prior to the first determining:

third transmit a beam from the device to a test receiver, the test receiver at a far field distance from the device along a first transmit direction, the beam determined by a first beamforming codebook of the device to transmit the beam in the first transmit direction;

second adjust a gain and phase of the transmit chains to produce maximum received power at the test receiver;

fifth determine, for each transmit chain of the device, a transmit gain difference and a transmit phase difference between the beam producing the maximum received power at the test receiver and the beam determined by the first beamforming codebook of the device to transmit at the first transmit direction;

first modify each codebook entry for each transmit direction with the determined transmit gain difference and the determined transmit phase difference;

third receive, by the device, a beam from a test transmitter at a far field distance along a first receive direction using a receive beam determined by the first beamforming codebook of the device to receive at the first receive direction;

third adjust a gain and phase of the receive chains to produce the maximum received combined power at the device from the test transmitter;

sixth determine, for each receive chain, a receive gain difference and a receive phase difference between the beam producing the maximum received power at the device and the beam determined by the first beamforming codebook of the device to receive at the first receive direction; and

second modify each codebook entry for each receive direction with the second determined receive gain difference and the second determined receive phase difference.

14. The device of claim 13 , wherein the first transmit direction and the first receive direction are each a boresight direction of the device.

15. A non-transitory computer-readable medium storing processor-executable code, the code when read and executed by at least one processor of a wireless communication device, the device comprising an array of transceiver chains, each transceiver chain i) characterized by a bandwidth, and ii) comprising a transmit chain and a receive chain, causes the device to:

first determine, at each of one or more center frequencies and sub-bandwidths sufficient to cover the bandwidth: i) a first set of inter-chain transmit gain and phase/delay differences across transmit chains, and ii) a first set of inter-chain receive gain and phase/delay differences across the receive chains;

second determine, after the first determining and in a same manner as the first determining: i) a second set of inter-chain transmit gain and phase/delay differences across the transmit chains, and ii) a second set of inter-chain receive gain and phase/delay differences across the receive chains; and

first adjust each transmit chain by the difference between the second set of inter-chain transmit gain and phase/delay differences and the first set of inter-chain transmit gain and phase/delay differences, and each receive chain by the difference between the second set of inter-chain receive gain and phase/delay differences and the first set of inter-chain receive gain and phase/delay differences.

16. The non-transitory computer-readable medium of claim 15 , wherein:

the array comprises M≥3 transceiver chains;

determining a set of inter-chain transmit gain and phase/delay differences across transmit chains comprises, for one or more times sufficient to cover all chains compared to a transmit reference chain k 1 :

first transmitting, from each of a plurality of N 1 ≤M−1 chains of the M chains including chain k 1 and not including a receive chain p R×1 of the M chains, a chain-specific signal;

first receiving, by the receive chain p R×1 , the transmitted chain-specific signals; and

third determining a gain and phase/delay difference between each first received chain-specific signal and the received signal specific to chain k 1 ; and

determining a set of inter-chain receive gain and phase/delay differences across receive chains comprises, for one or more times sufficient to cover all chains compared to a receive reference chain k 2 :

second transmitting, from a reference transmit chain p T×1 of the M chains, a reference signal;

second receiving, by each of a plurality of N 2 ≤M−1 chains of the M chains including chain k 2 and not including reference transmit chain p T×1 , each second transmitted reference signal; and

fourth determining a gain and phase/delay difference between each second received reference signal and the second received reference signal at chain k 2 .

17. The non-transitory computer-readable medium of claim 16 , wherein the set of chain-specific signals across the plurality of N 1 ≤M−1 chains is a set of orthogonal signals.

18. The non-transitory computer-readable medium of claim 17 , wherein each orthogonal chain-specific signal is a Hadamard signal.

19. The non-transitory computer-readable medium of claim 17 , wherein transmitting the set of chain-specific signals comprises transmitting the set of chain specific signals at a same time.

20. The non-transitory computer-readable medium of claim 15 , wherein:

the array is characterized by a beamforming codebook; and

the code when read and executed by at least one processor of the device, further causes the device to:

third transmit a beam from the device to a test receiver, the test receiver at a far field distance from the device along a first transmit direction, the beam determined by a first beamforming codebook of the device to transmit the beam in the first transmit direction;

second adjust a gain and phase of the transmit chains to produce maximum received power at the test receiver;

fifth determine, for each transmit chain of the device, a transmit gain difference and a transmit phase difference between the beam producing the maximum received power at the test receiver and the beam determined by the first beamforming codebook of the device to transmit at the first transmit direction;

first modify each codebook entry for each transmit direction with the determined transmit gain difference and the determined transmit phase difference;

third receive, by the device, a beam from a test transmitter at a far field distance along a first receive direction using a receive beam determined by the first beamforming codebook of the device to receive at the first receive direction;

third adjust a gain and phase of the receive chains to produce the maximum received combined power at the device from the test transmitter;

sixth determine, for each receive chain, a receive gain difference and a receive phase difference between the beam producing the maximum received power at the device and the beam determined by the first beamforming codebook of the device to receive at the first receive direction; and

second modify each codebook entry for each receive direction with the second determined receive gain difference and the second determined receive phase difference.

21. The non-transitory computer-readable medium of claim 20 , wherein the first transmit direction and the first receive direction are each a boresight direction of the device.

22. An apparatus for wireless communications, comprising:

an array of transceiver chains, each transceiver chain i) characterized by a bandwidth, and ii) comprising a transmit chain and a receive chain:

means for first determining, at each of one or more center frequencies and sub-bandwidths sufficient to cover the bandwidth: i) a first set of inter-chain transmit gain and phase/delay differences across transmit chains, and ii) a first set of inter-chain receive gain and phase/delay differences across the receive chains;

means for second determining, after the first determining and in a same manner as the first determining: i) a second set of inter-chain transmit gain and phase/delay differences across the transmit chains, and ii) a second set of inter-chain receive gain and phase/delay differences across the receive chains; and

means for first adjusting each transmit chain by the difference between the second set of inter-chain transmit gain and phase/delay differences and the first set of inter-chain transmit gain and phase/delay differences, and each receive chain by the difference between the second set of inter-chain receive gain and phase/delay differences and the first set of inter-chain receive gain and phase/delay differences.

23. The apparatus of claim 22 , wherein:

the array comprises M≥3 transceiver chains;

means for determining a set of inter-chain transmit gain and phase/delay differences across transmit chains comprises, for one or more times sufficient to cover all chains compared to a transmit reference chain k 1 :

means for first transmitting, from each of a plurality of N 1 ≤M−1 chains of the M chains including chain k 1 and not including a receive chain p R×1 of the M chains, a chain-specific signal;

means for first receiving, by the receive chain p R×1 , the transmitted chain-specific signals; and

means for third determining a gain and phase/delay difference between each first received chain-specific signal and the received signal specific to chain k 1 ; and

means for determining a set of inter-chain receive gain and phase/delay differences across receive chains comprises, for one or more times sufficient to cover all chains compared to a receive reference chain k 2 :

means for second transmitting, from a reference transmit chain p T×1 of the M chains, a reference signal;

means for second receiving, by each of a plurality of N 2 ≤M−1 chains of the M chains including chain k 2 and not including reference transmit chain p T×1 , each second transmitted reference signal; and

means for fourth determining a gain and phase/delay difference between each second received reference signal and the second received reference signal at chain k 2 .

24. The apparatus of claim 23 , wherein the set of chain-specific signals across the plurality of N 1 ≤M−1 chains is a set of orthogonal signals.

25. The apparatus of claim 24 , wherein each orthogonal chain-specific signal is a Hadamard signal.

26. The apparatus of claim 24 , wherein means for transmitting the set of chain-specific signals comprises means for transmitting the set of chain specific signals at a same time.

27. The apparatus of claim 22 , wherein:

the array is characterized by a beamforming codebook; and

the apparatus further comprises:

means for third transmitting, prior to the first determining, a beam from the apparatus to a test receiver, the test receiver at a far field distance from the apparatus along a first transmit direction, the beam determined by a first beamforming codebook of the apparatus to transmit the beam in the first transmit direction;

means for second adjusting a gain and phase of the transmit chains to produce maximum received power at the test receiver;

means for fifth determining, for each transmit chain of the apparatus, a transmit gain difference and a transmit phase difference between the beam producing the maximum received power at the test receiver and the beam determined by the first beamforming codebook of the apparatus to transmit at the first transmit direction;

means for first modifying each codebook entry for each transmit direction with the determined transmit gain difference and the determined transmit phase difference;

means for third receiving, by the apparatus, a beam from a test transmitter at a far field distance along a first receive direction using a receive beam determined by the first beamforming codebook of the apparatus to receive at the first receive direction;

means for third adjusting a gain and phase of the receive chains to produce the maximum received combined power at the apparatus from the test transmitter;

means for sixth determining, for each receive chain, a receive gain difference and a receive phase difference between the beam producing the maximum received power at the apparatus and the beam determined by the first beamforming codebook of the apparatus to receive at the first receive direction; and

means for second modifying each codebook entry for each receive direction with the second determined receive gain difference and the second determined receive phase difference.

28. The apparatus of claim 27 , wherein the first transmit direction and the first receive direction are each a boresight direction of the apparatus.