FDD Massive MIMO via UL/DL Channel Covariance Extrapolation and Active\n Channel Sparsification

Abstract

We propose a novel method for massive Multiple-Input Multiple-Output (massive\nMIMO) in Frequency Division Duplexing (FDD) systems. Due to the large frequency\nseparation between Uplink (UL) and Downlink (DL), in FDD systems channel\nreciprocity does not hold. Hence, in order to provide DL channel state\ninformation to the Base Station (BS), closed-loop DL channel probing and\nChannel State Information (CSI) feedback is needed. In massive MIMO this incurs\ntypically a large training overhead. For example, in a typical configuration\nwith M = 200 BS antennas and fading coherence block of T = 200 symbols, the\nresulting rate penalty factor due to the DL training overhead, given by max{0,\n1 - M/T}, is close to 0. To reduce this overhead, we build upon the well-known\nfact that the Angular Scattering Function (ASF) of the user channels is\ninvariant over frequency intervals whose size is small with respect to the\ncarrier frequency (as in current FDD cellular standards). This allows to\nestimate the users' DL channel covariance matrix from UL pilots without\nadditional overhead. Based on this covariance information, we propose a novel\nsparsifying precoder in order to maximize the rank of the effective sparsified\nchannel matrix subject to the condition that each effective user channel has\nsparsity not larger than some desired DL pilot dimension T_{dl}, resulting in\nthe DL training overhead factor max{0, 1 - T_{dl} / T} and CSI feedback cost of\nT_{dl} pilot measurements. The optimization of the sparsifying precoder is\nformulated as a Mixed Integer Linear Program, that can be efficiently solved.\nExtensive simulation results demonstrate the superiority of the proposed\napproach with respect to concurrent state-of-the-art schemes based on\ncompressed sensing or UL/DL dictionary learning.\n