Progressive Hybrid Precoding and Combining for Massive MIMO ARQ Systems

In this paper, we consider a progressive transceiver design for point-to-point massive multiple input multiple output (MIMO) with automatic repeat request (ARQ). As an alternative to address the difficulties such as prohibitive hardware complexity, cost, and power consumption encountered by a fully digital implementation of massive MIMO, a hybrid architecture, which introduces RF analog processing together with baseband digital processing, is employed. Based on the perfect channel state information, the hybrid RF-baseband transceiver is derived, aiming at increasing the achievable rate through exploiting the time diversity inherent in ARQ packet retransmissions. Due to the intractability of joint optimization of the hybrid precoder and combiner, we heuristically assume that the fully digital linear minimum-mean-square-error (MMSE) filter is perfectly realizable by its hybrid counterpart at the receiver, and decouple the precoding from the combining design, where the previous failed retransmissions are sequentially incorporated into the joint RF-baseband precoding/combining optimization. Specifically, for each ARQ round, we construct the RF precoder either from the transmit array response vectors or from a discrete Fourier transform-based codebook. In consideration of the RF precoding effect, the optimal baseband precoder is analytically derived. To minimize the performance loss incurred by the decoupled precoder/combiner optimization, the proposed two-step design technique is further applied to derive the hybrid combiner as an approximation of the optimal linear MMSE solution in terms of error performance. The efficacy of the proposed progressive hybrid solutions is numerically evaluated by performance comparison with various baselines. The effect of RF precoding/combining with finite-resolution elements is also examined.