FEEDBACK OF DIFFERENTIAL PRECODER FOR GEOMETRICAL MEAN DECOMPOSITION SYSTEMS

Abstract

For a time-correlated channel, we consider the differential feedback of the geometrical mean decomposition (GMD) precoder, which is known to be optimal for a number of criteria. When the channel varies slowly, we can expect the optimal GMD precoders of consecutive channel uses to be close. We consider the feedback of the so-called differential precoder and show that it lies in a neighborhood of the identity matrix using matrix perturbation theory. Furthermore the radius of the neighborhood is proportional to a time-correlation parameter. Such a characterization is crucial for efficient quantization of the differential precoder. Simulations are given to demonstrate that, with a small feedback rate, the performance of the proposed differential GMD comes close to the case when perfect channel state information is available to the transmitter.