Bi-Directional Training Methods with Frequency-Division Duplexing

We study distributed algorithms for joint adaptation of precoding and combining filters in frequency division duplex (FDD) multiple-input multiple-output (MIMO) cellular systems. Our approach extends bi-directional training (BiT), designed for time division duplex (TDD) systems, to FDD systems where uplink/downlink reciprocity may not apply. An analysis of the performance loss due to different uplink-downlink frequencies in a point-to-point scenario, shows that a direct application of BiT gives mismatched precoders with substantial performance degradation. We first propose an algorithm assuming each base transceiver station (BTS) knows the uplink and downlink channels of mobiles within the cell. We then consider the scenario where neither the BTSs nor the mobiles have a priori channel state information. Our proposed approaches assume angular reciprocity characterized by angles of arrival/departure that vary predictably with frequency. Hence spatial beams corresponding to angles of arrival can be turned around to the corresponding angles of departure in the paired band. We present three methods, differing in how the angular decomposition is applied and used, namely, to reconstruct the combiner directly, or to reconstruct the received signal. Simulation results indicate that when the multipath is sufficiently sparse, most of achievable gain with channel reciprocity and TDD can be recovered.