Active Channel Sparsification and Precoding for Dual-Polarized FDD Massive MIMO

We study the problem of common Downlink (DL) channel training and Uplink (UL) closed-loop feedback for dual-polarized FDD massive MIMO systems. As is well-known, due to the lack of instantaneous channel reciprocity in FDD systems, the process of DL training and UL feedback is absolutely crucial. In a massive MIMO system, the number of antennas employed at the base station (BS) and therefore the channel dimension is very high (M » 1). Given the limited time-frequency resources dedicated to pilot submission, this poses a challenge for reliable channel training, resulting in poor channel state information (CSI) quality and low system throughput. This challenge is even more pronounced, when one considers dual-polarized arrays, in which each antenna element is associated with two (vertical and horizontal) polarizations, scaling the channel dimension to 2M. A natural question is raised: given limited pilot dimension, how can the BS efficiently train DL channel vectors of all users in the system, such that stable estimation of the channels is feasible? In this paper we propose an answer to this question. We first characterize the set of common virtual beams for a generic dual-polarized channel covariance as a necessary step for common DL training. Then, we use a user-beam bipartite graph model to perform active channel sparsification, the idea of which is to reduce the support size of the channel coefficients vector for all users to a value less than the available pilot dimension, while at the same time, maximizing the effective channel matrix rank.We show that this problem translates to a mixed integer linear program (MILP) which can be efficiently solved in a wide range of practical scenarios.