Sum-Capacity Achieving Schemes of a 2-User Gaussian Multiple-Access Channel with 1-bit ADC

Abstract

In this paper, we investigate the fundamentals of a static 2-user Gaussian multiple-access channel (MAC) with 1-bit analog-to-digital-converter (ADC) being equipped at the base station. To shed new light on the characteristics of sum-capacity achieving schemes, we first consider the 1-bit MAC as a single-user channel that is affected by additive white Gaussian noise (AWGN) and a fixed yet unknown interference from the other user. By examining the Kuhn-Tucker condition (KTC) for an input signal to be optimal, we demonstrate that the capacity-achieving signal of this single-user channel must have a bounded amplitude. Based on this characteristic, Dubin's theorem on extreme points of convex sets is exploited to show that the sum-capacity achieving signals of the considered MAC are discrete, with each signal having at most five mass points. In the case of equal power allocation between the two users, we establish an upper bound on the total sum-rate. We then show that the upper bound is achievable by a simple scheme in which the first user employs binary phase shift keying (BPSK) while the second user uses π/2-BPSK. Therefore, this scheme achieves one of the optimal points in the capacity region of the static 2-user 1-bit MAC. Our results show that the proposed simple scheme greatly outperforms PSK-based signaling schemes that are sum-capacity achieving in the fading 2-user 1-bit MAC.