Bi-Directional Training for FDD Systems

We study distributed algorithms for joint adaptation of precoding and combining filters in frequency-division duplex (FDD) multiple-input multiple-output (MIMO) cellular systems. Neither the base stations nor the mobiles have a priori channel state information, and the transmit/receive filters are directly adapted through training. We propose extensions of bi- directional training (BiT), designed for time- division duplex (TDD) systems, to FDD systems where uplink-downlink reciprocity may not apply. A direct application of BiT can give mismatched precoders with substantial performance degradation. Our approach assumes angular reciprocity, that is, the channel multipath, which causes the frequency selectivity, is characterized by angles of arrival/departure that vary predictably with frequency. Hence spatial beams corresponding to angles of arrival can be turned around to point towards the corresponding angles of departure in the paired band. We present three methods based on this general approach with different complexity for angular estimation and selection. Simulation results indicate that when the multipath is sufficiently sparse, most of the achievable gain with channel reciprocity and TDD can be recovered.