Unified Derivation of Optimal Feedback Rate in Downlink Cellular Systems With Multi-Antenna Base Stations

A downlink cellular network in which base stations (BSs) are distributed according to a homogeneous Poisson point process is considered. Each BS simultaneously serves multiple single-antenna users for downlink transmission; zero-forcing beamforming (ZFBF) is used for spatial division multiplexing. Each user quantizes and feeds back the channel state information (CSI) to the transmitter to ensure that at least partial CSI is available at the transmitter. The net spectral efficiency is introduced as a main performance metric; it measures the net profit achieved by using limited-feedback-based ZFBF. This paper mainly analyzes the optimal number of feedback bits that maximizes the net spectral efficiency. The optimal number is analyzed with respect to various important system parameters by extending and generalizing previous studies. Specifically, this paper analyzes the asymptotic behaviors of the optimal number with respect to the signal-to-noise ratio (SNR) and the channel coherence time; it does so by providing close approximations to the optimal number that is generally satisfied regardless of the values of the SNR, number of users, path loss exponent, and channel coherence time. It is demonstrated by simulation that the proposed approximations are extremely close to the optimal number on the region of interest of the system parameters.