Sum Capacity (Sub)Optimality of Orthogonal Transmissions in Vector Gaussian Multiple Access Channels

We study in this paper the sum capacity achievability of orthogonal transmissions in vector Gaussian multiple access channels (MAC). Specifically, we derive the sufficient and necessary conditions, in terms of channel matrices and transmitter power constraints, for orthogonal transmission to achieve the sum capacity of a vector Gaussian MAC. The obtained conditions provide a unified framework in explaining many of the results that are intuitively true. They also enable us to explore cases that have not been addressed to determine the (sub)optimality of orthogonal transmissions compared with the overlay transmission.