Asymmetric Quantizers Are Better at Low SNR

TL;DR

This paper demonstrates that using asymmetric one-bit quantizers with asymmetric signal constellations in low SNR Gaussian channels fully recovers the capacity loss caused by symmetric quantization, improving spectral efficiency.

Contribution

It introduces the use of asymmetric quantizers and constellations to eliminate capacity loss at low SNR in Gaussian channels.

Findings

Asymmetric quantizers recover the 2/pi capacity loss at low SNR.

Symmetric quantization causes about two decibels of power loss.

Asymmetric schemes restore capacity to the unquantized channel level.

Abstract

We study the behavior of channel capacity when a one-bit quantizer is employed at the output of the discrete-time average-power-limited Gaussian channel. We focus on the low signal-to-noise ratio regime, where communication at very low spectral efficiencies takes place, as in Spread-Spectrum and Ultra-Wideband communications. It is well know that, in this regime, a symmetric one-bit quantizer reduces capacity by 2/pi, which translates to a power loss of approximately two decibels. Here we show that if an asymmetric one-bit quantizer is employed, and if asymmetric signal constellations are used, then these two decibels can be recovered in full.