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

Abstract

We propose a novel method for massive multiple-input multiple-output (massive MIMO) in frequency division duplexing (FDD) systems. Due to the large frequency separation between uplink (UL) and downlink (DL) in FDD systems, channel reciprocity does not hold. Hence, in order to provide DL channel state information to the base station (BS), closed-loop DL channel probing, and <italic>channel state information</italic> (CSI) feedback is needed. In massive MIMO, this typically incurs a large training overhead. For example, in a typical configuration with <inline-formula> <tex-math notation="LaTeX">$M \simeq 200$ </tex-math></inline-formula> BS antennas and fading coherence block of <inline-formula> <tex-math notation="LaTeX">$T \simeq 200$ </tex-math></inline-formula> symbols, the resulting rate penalty factor due to the DL training overhead, given by <inline-formula> <tex-math notation="LaTeX">$\max \{0, 1 - M/T\}$ </tex-math></inline-formula>, is close to 0. To reduce this overhead, we build upon the well-known fact that the <italic>angular scattering function</italic> of the user channels is <italic>invariant</italic> over frequency intervals whose size is small with respect to the carrier frequency (as in current FDD cellular standards). This allows us to estimate the users’ DL channel covariance matrix from UL pilots without additional overhead. Based on this covariance information, we propose a novel <italic>sparsifying precoder</italic> in order to maximize the rank of the effective sparsified channel matrix subject to the condition that each effective user channel has sparsity not larger than some desired DL pilot dimension <inline-formula> <tex-math notation="LaTeX">${\sf T_{dl}}$ </tex-math></inline-formula>, resulting in the DL training overhead factor <inline-formula> <tex-math notation="LaTeX">$\max \{0, 1 - {\sf T_{dl}}/ T\}$ </tex-math></inline-formula> and CSI feedback cost of <inline-formula> <tex-math notation="LaTeX">${\sf T_{dl}}$ </tex-math></inline-formula> pilot measurements. The optimization of the sparsifying precoder is formulated as a <italic>mixed integer linear program</italic>, that can be efficiently solved. Extensive simulation results demonstrate the superiority of the proposed approach with respect to the concurrent state-of-the-art schemes based on compressed sensing or UL/DL dictionary learning.