Bounds on the optimal feedback rate for multi-antenna systems in interference-limited cellular networks

A cellular system in which multi-antenna base stations (BSs) communicate with single-antenna users is considered. BSs are distributed according to a Poisson point process, and each BS uses zero-forcing beamforming (ZFBF) to simultaneously transmit multiple data streams prepared for multiple users. Single-user transmission, which is equivalent to maximum ratio transmission, is also considered as a special case of ZFBF. Net spectral efficiency is the main performance metric used in this paper and is analyzed theoretically to obtain the optimal number of feedback bits required to maximize it. Specifically, tight upper and lower bounds for the derivative of spectral efficiency are newly determined, and the bounds are further used to estimate the optimal number of feedback bits. Consequently, a close estimate of the optimal number is proposed, and the estimate accurately shows the scaling rate of the optimal number. The analytical results of this paper can provide more accurate insights into the required number of feedback bits and achievable system-level performance in interference-limited cellular networks.