Optimal Signaling Schemes and Sum-Capacity of 1-bit ADC Fading 2-User MACs under Gaussian-Mixture Interference

In this work, we establish the sum-capacity-achieving signaling schemes and the sum-capacity of a 2-user multiple access Rayleigh fading channel with 1-bit output quantization in the presence of Gaussian-mixture co-channel interference. The considered Gaussian mixture channel is an accurate model to capture non-Gaussian co-channel interference plus noise in practical wireless networks under coexistence regimes, especially for those having heterogeneous structures and high frequency reuse factor. By first examining the phases of the optimal input signals, we demonstrate that these phases must be π/2 circularly symmetric. As a result, the problem of optimizing the sum-rate is equivalent to minimizing the conditional output entropy. By establishing the Kuhn-Tucker condition on the optimal amplitude input distributions, we then show that the optimal input amplitudes are bounded. Our proof relies on the convexity of the log of sum of Q functions. Then, given the linearity of the conditional entropy over the feasible set of bounded amplitude distributions, it is concluded that the optimal input signals must have constant amplitudes. Therefore, the use of any π/2 circularly symmetric signaling schemes with constant amplitudes and full power are sum-capacity-achieving. Using these optimal input signals, the sum-capacity can finally be calculated.