On the Accuracy of Quantization Cell Approximation in MIMO Broadcast Systems Based on Limited Feedback

This study investigates the accuracy of quantization cell approximation (QCA) in a multiple-input multiple-output (MIMO) broadcast channel. QCA is an analytical quantization model used to approximate the quantized channel state information (CSI) in limited-feedback-based MIMO systems. It has been widely used in important studies for analytical tractability because it approximates the quantized CSI as a simple beta random variable multiplied by a deterministic value. Moreover, the effect of quantization is solely concentrated on the deterministic value such that the corresponding performance analysis is stochastically independent of the quantization process. Nevertheless, the accuracy of QCA has not been carefully demonstrated in previous studies. In this study, a generalized version of QCA is proposed with a complete analysis. Because the proposed QCA requires the use of a specific distance measure, the validity of the distance measure is first investigated. Based on the proposed distance measure, the accuracy of QCA is estimated by analyzing the difference between the spectral efficiencies achieved using QCA and random matrix quantization (RMQ). The corresponding results show that the difference gradually decreases and converges to zero as the number of feedback bits increases. As QCA and RMQ provide performance upper and lower bounds, respectively, in terms of codebook construction, these results prove the asymptotic validity of QCA with respect to the number of feedback bits. Both analysis and simulation results demonstrate that the difference in spectral efficiencies is also small for a moderate number of feedback bits. In addition, this study also demonstrates an asymptotic difference in spectral efficiencies with respect to the signal-to-noise-ratio (SNR). The difference increases with the SNR, but it is bounded by a finite value. Thus, the difference in the worst case SNR can also be suppressed by increasing the number of feedback bits.