Beamforming scheme for phased-array antennas

A first communication device, comprising:

• an integrated circuit device configured to generate a transmitter antenna weight vector based on a mathematical combination of at least i) a plurality of received signals, ii) antenna weight vectors applied by a second communication device when transmitting the at least one training signal a plurality of times, and iii) at least one training signal;
• wherein:
• the plurality of received signals have been received by the first communication device,
• the plurality of received signals correspond to the at least one training signal having been transmitted by the second communication device the plurality of times via a plurality of antennas by the second communication device applying a respective antenna weight vector from a plurality of different antenna weight vectors each time the at least one training signal is transmitted, and wherein each of the plurality of antenna weight vectors is a respective base vector of a unitary matrix,
• (i) the antenna weight vectors applied by the second communication device when transmitting the at least one training signal the plurality of times have been received by the first communication device, or (ii) indicators of the antenna weight vectors that were applied by the second communication device when transmitting the at least one training signal the plurality of times have been received by the first communication device, and
• the first communication device is configured to transmit the transmitter antenna weight vector to the second communication device.