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.

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 WF. 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.

This paper describes the benefits of transmission subspace tracking for multiple input multiple output communications systems, and applies the concepts of previous work on adaptive transmit antenna algorithms to this problem. A specific stochastic gradient technique of subspace or "multi-mode" tracking of the independent modes of the MIMO transfer function and the application to space time coding is considered. The technique provides gains by tracking the active modes when there are more transmit than receive antennas. With the proposed algorithm, the receiver generates binary feedback selecting preferred perturbed weights, which gives the transmitter a gradient estimate useful for subspace tracking. The capacity resulting from this approach is shown by simulation.

The tracking performance of a transmit antenna weight adaptation algorithm applied in a fading channel is considered. The system uses a stochastic gradient algorithm incorporating gradient sign feedback from a receiving unit to adjust the transmit weights. The feedback is simply a bit indicating which of two normalized perturbed transmission weights delivers greater power to the receiver. A reasonable performance measure is defined and an analytic estimate of the performance in an AR1 vector fading channel is derived and compared to simulations.