Analysis of 1-bit Output Noncoherent Fading Channels in the Low SNR Regime

TL;DR

This paper analyzes the capacity of multi-antenna fading channels with 1-bit quantization in low SNR regimes, revealing a near 2 dB power penalty compared to infinite resolution systems, relevant for energy-efficient sensor networks.

Contribution

It derives the second-order asymptotics of mutual information for 1-bit quantized fading channels, extending previous coherent case results to noncoherent scenarios.

Findings

Mutual information incurs about 1.96 dB power penalty with 1-bit ADCs.

Asymptotic analysis applies to practical low-power, low-cost sensor networks.

Results generalize recent coherent case findings to noncoherent channels.

Abstract

We consider general multi-antenna fading channels with coarsely quantized outputs, where the channel is unknown to the transmitter and receiver. This analysis is of interest in the context of sensor network communication where low power and low cost are key requirements (e.g. standard IEEE 802.15.4 applications). This is also motivated by highly energy constrained communications devices where sampling the signal may be more energy consuming than processing or transmitting it. Therefore the analog-to-digital converters (ADCs) for such applications should be low-resolution, in order to reduce their cost and power consumption. In this paper, we consider the extreme case of only 1-bit ADC for each receive signal component. We derive asymptotics of the mutual information up to the second order in the signal-to-noise ratio (SNR) under average and peak power constraints and study the impact of quantization. We show that up to second order in SNR, the mutual information of a system with two-level (sign) output signals incorporates only a power penalty factor of almost 1.96 dB compared to the system with infinite resolution for all channels of practical interest. This generalizes a recent result for the coherent case.