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

Abstract

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. INDEX TERMS Multiple-input multiple-output (MIMO), cellular network, zero-forcing beamforming (ZFBF), limited feedback, spectral efficiency.

A Study on Determining the Optimal Feedback Rate in Distributed Block Diagonalization with Limited Feedback for Dense Cellular Networks

“…In addition, the first term in ( 8) is an increasing function of B. Nevertheless, the rate of increase in relation to B diminishes, as demonstrated in earlier studies, such as [16]. Consequently, the derivative of the first term with respect to B is generally a decreasing function of B, approaching zero as B increases, as evidenced in previous works [9,10].…”

“…Define CW m (a, Ω) as the complex Wishart distribution, and CB m (a, b) as the complex matrix variate beta distribution. According to [14,[16][17][18], we have…”

“…In the domain of limited-feedback-based precoding, which involves the quantization of vector or matrix channels, the quantization-cell upper bound (QUB) model has been utilized [9,16]. Simplifying both analytical investigations and simulations, this model offers a closely modeled upper bound regarding the distribution of errors in quantization during the quantization process.…”

“…Simplifying both analytical investigations and simulations, this model offers a closely modeled upper bound regarding the distribution of errors in quantization during the quantization process. Assuming d(W j , H) = λ 1,j , the QUB model yields the following result [12,16]:…”

Spherical-Cap Approximation of Vector Quantization for Quantization-Based Combining in MIMO Broadcast Channels with Limited Feedback

“…Based on SCVQ, the capacity was analyzed when a multiantenna transmission was used in a random ad hoc network in which the locations of access points were distributed based on the Poisson point process (PPP) [ 19 ]. The performance of a MIMO system with limited feedback in a random cellular network was analyzed in [ 16 , 20 , 21 ]. The ergodic secrecy rate was analyzed in multiantenna cellular systems with limited feedback in [ 22 ].…”