On Orthogonal signalling in Gaussian Multiple Access Channel with peak constraints

This paper is a follow up to [1] on the two-user Gaussian Multiple Access Channel (MAC) with peak constraints at the transmitters. It is shown that there exist an infinite number of sum-rate-optimal points on the boundary of the capacity region. In contrast to the Gaussian MAC with power constraints, we verify that Time Division (TD) can not achieve any of the sum-rate-optimal points in the Gaussian MAC with peak constraints. Using the so-called I-MMSE identity of Guo et.al, the largest achievable sum-rate by Orthogonal Code Division (OCD) is characterized where it is shown that Walsh-Hadamard spreading codes of length 2 are optimal. In the symmetric case where the peak constraints at both transmitters are similar, we verify that OCD can achieve a sum-rate that is strictly larger than the highest sum-rate achieved by TD. Finally, it is demonstrated that there are values for the maximum peak at the transmitters such that OCD can not achieve any of the sum-rate-optimal points on the boundary of the capacity region.