A simple gradient sign algorithm for transmit antenna weight adaptation with feedback

In this paper, a simple algorithm for adaptation of the complex baseband weights of a transmit antenna array using feedback from the receiver is proposed and analyzed. The system utilizes stochastic gradient adaptation to maximize the power delivered to the receiver for a constrained transmission power, which provides both fading diversity and beam steering gain. Dual perturbed transmission weight vectors are time multiplexed onto the pilot signal, and the receiver generates feedback selecting the perturbed weight vector which delivers greater power. This feedback is used to provide weight adaptation at the transmitter, and this adaptation is shown to be an update by a coarse estimate of the gradient of the delivered power. The performance of the algorithm is analyzed in terms of convergence and tracking of an AR1 fading channel, with simulations confirming the analysis. Bit error rate (BER) simulations in a dynamic fading channel show that the algorithm outperforms previously proposed vector selection feedback, and in slower fading, the algorithm substantially outperforms diversity space time coding.