Large System Analysis of Linear Precoding in Correlated MISO Broadcast Channels under Limited Feedback

TL;DR

This paper analyzes the sum rate performance of linear precoding in large MISO broadcast channels with imperfect CSI and correlated channels, providing deterministic approximations that facilitate optimization of system parameters.

Contribution

It introduces novel deterministic equivalents for SINR in large correlated MISO systems, enabling practical optimization of precoding and feedback strategies.

Findings

Deterministic SINR approximations are accurate for large systems.

Optimal regularization and user number are derived for sum rate maximization.

Feedback and power allocation schemes are optimized based on the analysis.

Abstract

In this paper, we study the sum rate performance of zero-forcing (ZF) and regularized ZF (RZF) precoding in large MISO broadcast systems under the assumptions of imperfect channel state information at the transmitter and per-user channel transmit correlation. Our analysis assumes that the number of transmit antennas $M$ and the number of single-antenna users $K$ are large while their ratio remains bounded. We derive deterministic approximations of the empirical signal-to-interference plus noise ratio (SINR) at the receivers, which are tight as $M,K\to\infty$. In the course of this derivation, the per-user channel correlation model requires the development of a novel deterministic equivalent of the empirical Stieltjes transform of large dimensional random matrices with generalized variance profile. The deterministic SINR approximations enable us to solve various practical optimization problems. Under sum rate maximization, we derive (i) for RZF the optimal regularization parameter, (ii) for ZF the optimal number of users, (iii) for ZF and RZF the optimal power allocation scheme and (iv) the optimal amount of feedback in large FDD/TDD multi-user systems. Numerical simulations suggest that the deterministic approximations are accurate even for small $M,K$.