Sum capacity 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 sufficient and necessary conditions, in terms of channel matrices and transmitter power constraints, for orthogonal transmissions to achieve the sum capacity of a vector Gaussian MAC. The obtained conditions provide a unified framework that helps explain many intuitive and known results as well as explore cases that have not been addressed. In the cases when these conditions are violated, our results enable us to quantify the suboptimality of orthogonal transmission when the sum capacity can only be achieved by overlay transmission.