Copulas and Multi-User Channel Orders

We investigate the application of copulas for characterizing channel orders, e.g., degradedness or strong/very strong interference, of Gaussian multiuser channels with statistical channel state information at the transmitter (CSIT). When there is solely statistical CSIT, identifying such channel orders is much more involved and, thus, the capacity remains unknown in general. We use the maximum copula to construct equivalent channels by modifying the joint distributions such that these newly constructed channels possess certain channel orders. We also derive sufficient conditions to attain these equivalent channels. We further discuss the meaning of achieving the maximum copula with respect to the concordance between the fading channels. We illustrate the theoretical results by numerical simulations, which visualize the joint probability distributions.