This paper describes a feedback assisted stochastic gradient algorithm for transmission tracking of the dominant channel subspaces for multiple-input-multiple-output (MIMO) communications systems. Subspace tracking is introduced as a means of tracking multiple transmission weights, being the MIMO generalization of beam steering in the familiar multiple-input-single-output case. The subspace solution approximates that of water filling (WF) in some cases, without the complete rate/power allocation required by WE The gain of subspace tracking in low rank systems is demonstrated, particularly, in the case where the number of transmit antennas exceeds the number of receive antennas. Simulations of ergodic capacity show the utility of both subspace tracking in general and of the specific adaptation algorithm, and simulations of frame-error rates show the utility in a specific coding example.

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.