Optimal Shape-Gain Quantization for Multiuser MIMO Systems with Linear Precoding

TL;DR

This paper proposes an optimal bit allocation method for shape-gain vector quantization in multiuser MIMO systems, reducing quantization error and interference by balancing shape and gain quantization bits.

Contribution

It derives the distortion for gain quantization, relates shape quantization distortion to system parameters, and establishes the optimal ratio of direction to magnitude bits.

Findings

Quantization distortion is proportional to 2^{-2Bs}/(2M-1).

Optimal direction bits are approximately (2M - 1) times the magnitude bits.

Significant reduction in quantization error and MU interference.

Abstract

This paper studies the optimal bit allocation for shape-gain vector quantization of wireless channels in multiuser (MU) multiple-input multiple-output (MIMO) downlink systems based on linear precoding. Our design minimizes the mean squared-error between the original and quantized channels through optimal bit allocation across shape (direction) and gain (magnitude) for a fixed feedback overhead per user. This is shown to significantly reduce the quantization error, which in turn, decreases the MU interference. This paper makes three main contributions: first, we focus on channel gain quantization and derive the quantization distortion, based on a Euclidean distance measure, corresponding to singular values of a MIMO channel. Second, we show that the Euclidean distance-based distortion of a unit norm complex channel, due to shape quantization, is proportional to \frac{2^{-2Bs}}{2M-1}, where, Bs is the number of shape quantization bits and M is the number of transmit antennas. Finally, we show that for channels in complex space and allowing for a large feedback overhead, the number of direction quantization bits should be approximately (2M - 1) times the number of channel magnitude quantization bits.