Uplink-Downlink Channel Covariance Transformations and Precoding Design\n for FDD Massive MIMO

Abstract

A large majority of cellular networks deployed today make use of Frequency\nDivision Duplexing (FDD) where, in contrast with Time Division Duplexing (TDD),\nthe channel reciprocity does not hold and explicit downlink (DL) probing and\nuplink (UL) feedback are needed in order to achieve spatial multiplexing gain.\nTo support massive MIMO, the overhead incurred by conventional DL probing and\nUL feedback schemes scales linearly with the number of BS antennas and,\ntherefore, may be very large. In this paper, we present a new approach to\nachieve a very competitive trade-off between spatial multiplexing gain and\nprobing-feedback overhead in such systems. Our approach is based on two novel\nmethods: (i) an efficient regularization technique based on Deep Neural\nNetworks (DNN) that learns the Angular Spread Function (ASF) of users channels\nand permits to estimate the DL covariance matrix from the noisy i.i.d. channel\nobservations obtained freely via UL pilots (UL-DL covariance transformation),\n(ii) a novel "sparsifying precoding" technique that uses the estimated DL\ncovariance matrix from (i) and imposes a controlled sparsity on the DL channel\nsuch that given any assigned DL pilot dimension, it is able to find an optimal\nsparsity level and a corresponding sparsifying precoder for which the\n"effective" channel vectors after sparsification can be estimated at the BS\nwith a low mean-square error. We compare our proposed DNN-based method in (i)\nwith other methods in the literature via numerical simulations and show that it\nyields a very competitive performance. We also compare our sparsifying precoder\nin (ii) with the state-of-the-art statistical beamforming methods under the\nassumption that those methods also have access to the covariance knowledge in\nthe DL and show that our method yields higher spectral efficiency since it uses\nin addition the instantaneous channel information after sparsification.\n