Near-Optimal Quantization for LoS MIMO with QPSK Modulation

Abstract

As signaling bandwidths increase, analog-to-digital conversion becomes a fundamental bottleneck for modern all-digital baseband signal processing architectures. Motivated by emerging millimeter (mm) wave communication systems, we investigate the impact of severe quantization for 2 × 2 and 4×4 line-of-sight (LoS) multi-input and multi-output (MIMO) systems employing QPSK. Unlike prior work on MIMO with low-precision quantization, channel state information is utilized only at the receiver (i.e., transmit precoding is not employed). Rather than designing an optimal quantizer, we focus on quantizers with regular structure, and ask whether high-SNR performance approaches that of an unquantized system. First, we prove for a 2×2 MIMO system that phase-only quantization (attractive because it does not require automatic gain control) is unable to achieve this, but that 2-level amplitude and 8-level phase quantization can achieve the maximum data rate of 4 bits per channel use as SNR gets large. We then show that quantizer design based on conventional minimum mean squared quantization error (MMSQE) criterion performs worse than a quantizer based on equal-probability regions. We show that I/Q quantization with 16 regions per antenna using the equal probability criterion achieves the unquantized benchmark at high SNR, which is a maximum data rate of 8 bits per channel use. We illustrate our investigations via numerical examples.