On the Optimal Feedback Rate in Interference-Limited Multi-Antenna Cellular Systems

TL;DR

This paper analyzes the optimal number of feedback bits in multi-antenna cellular systems with limited feedback, deriving how it scales with system parameters for MRT and ZF precoding methods.

Contribution

It provides a tight lower bound on the optimal feedback bits that maximize net spectral efficiency, considering both uplink and downlink performance.

Findings

Optimal feedback scales linearly with the number of antennas.

Feedback scales logarithmically with channel coherence time.

Feedback scales linearly with the pathloss exponent for ZF.

Abstract

We consider a downlink cellular network where multi-antenna base stations (BSs) transmit data to single-antenna users by using one of two linear precoding methods with limited feedback: (i) maximum ratio transmission (MRT) for serving a single user or (ii) zero forcing (ZF) for serving multiple users. The BS and user locations are drawn from a Poisson point process, allowing expressions for the signal- to-interference coverage probability and the ergodic spectral efficiency to be derived as a function of system parameters such as the number of BS antennas and feedback bits, and the pathloss exponent. We find a tight lower bound on the optimum number of feedback bits to maximize the net spectral efficiency, which captures the overall system gain by considering both of downlink and uplink spectral efficiency using limited feedback. Our main finding is that, when using MRT, the optimum number of feedback bits scales linearly with the number of antennas, and logarithmically with the channel coherence time. When using ZF, the feedback scales in the same ways as MRT, but also linearly with the pathloss exponent. The derived results provide system-level insights into the preferred channel codebook size by averaging the effects of short-term fading and long-term pathloss.