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

The spherical-cap approximation of vector quantization (SCVQ) is an analytical model used for the mathematical analysis of multiple-input multiple-output (MIMO) systems with limited feedback. SCVQ closely emulates the distribution of the quantization error induced by the finite-rate quantization of a channel using a simple and analytically tractable approach. However, the conventional SCVQ model is not applicable when antenna-combining schemes such as quantization-based combining (QBC) are considered. Because QBC is an effective antenna-combining method that minimizes channel quantization errors, it can be adopted for various practical MIMO broadcast systems. Nevertheless, evaluating the performance of QBC-based MIMO systems with an explicit codebook can be extremely difficult, depending on the system complexity. To resolve this, this study generalizes the conventional SCVQ to be compatible with the QBC. The proposed generalized version of the SCVQ effectively emulates the quantization error obtained using QBC, while enabling a simple simulation independent of the number of feedback bits and mathematically tractable analysis. We validate the effectiveness of the proposed model by presenting a wireless communication application based on a dense cellular network.