Asymptotic Capacity of 1-Bit MIMO Fading Channels

TL;DR

This paper analyzes the asymptotic capacity of multi-antenna MIMO fading channels with 1-bit quantization, providing exact characterizations in various regimes and proposing bounds and schemes for both coherent and non-coherent cases.

Contribution

It offers a comprehensive asymptotic capacity analysis of 1-bit MIMO channels, including new bounds, schemes, and exact results for different CSI scenarios and block lengths.

Findings

Exact asymptotic capacity in coherent case

Capacity bounds for non-coherent case with T<=3

Capacity matches in low SNR regime

Abstract

In this work, we investigate the capacity of multi-antenna fading channels with 1-bit quantized output per receive antenna. Specifically, leveraging Bayesian statistical tools, we analyze the asymptotic regime with a large number of receive antennas. In the coherent case, where the channel state information (CSI) is known at the receiver's side, we completely characterize the asymptotic capacity and provide the exact scaling in the extreme regimes of signal-to-noise ratio (SNR) and the number of transmit antennas. In the non-coherent case, where the CSI is unknown but remains constant during T symbol periods, we first obtain the exact asymptotic capacity for T<=3. Then, we propose a scheme involving uniform signaling in the covariance space and derive a non-asymptotic lower bound on the capacity for an arbitrary block size T. Furthermore, we propose a genie-aided upper bound where the channel is revealed to the receiver. We show that the upper and lower bounds coincide when T is large. In the low SNR regime, we derive the asymptotic capacity up to a vanishing term, which, remarkably, matches our capacity lower bound.