Feedback assisted stochastic gradient adaptation of multiantenna transmission

This paper describes a feedback assisted stochastic gradient algorithm for adapting the weights of a multiantenna transmitter in a multiuser multiple-input single-output per user (MISO) communication system, which yields both a power delivery (aperture) gain and a fading channel diversity gain from the multiple transmit antennas. Feedback from the receiver is used to attain partial channel state information at the transmitter, which attempts to maximize the power delivered to the receiver. The system utilizes a perturbation probing and update formulation: a vector perturbation probe is transmitted and perturbation sign feedback from the receiver defines the transmitter weight vector additive update. This feedback provides a coarse estimate of the gradient of the delivered power and is used to adapt the multiantenna baseband weights of the transmitter. The second moment update of the algorithm is derived, and the tracking performance of the algorithm applied to a dynamic AR1 fading channel is analyzed, with simulations confirming the analysis. Bit-error rate simulations in a dynamic fading channel show that the algorithm can perform as well or better than previously proposed vector selection feedback, and in slower fading the algorithm substantially outperforms diversity space time coding.