The Jacobi MIMO Channel

Abstract

This paper presents a new fading model for multi-input multi-output channels: the Jacobi fading model. It asserts that ${\bf H}$ , the transfer matrix which couples the $m_{t}$ inputs into $m_{r}$ outputs, is a submatrix of an $m\times m$ random (Haar-distributed) unitary matrix. The (squared) singular values of ${\bf H}$ follow the law of the classical Jacobi ensemble of random matrices, hence the name of the channel. One motivation to define such a channel comes from multimode/multicore optical fiber communication. It turns out that this model can be qualitatively different from the Rayleigh model, leading to interesting practical and theoretical results. This paper first evaluates the ergodic capacity of the channel. Then, it considers the nonergodic case, where it analyzes the outage probability and the diversity-multiplexing tradeoff. In the case where $k=m_{t}+m_{r}-m>0$ , it is shown that at least $k$ degrees of freedom are guaranteed not to fade for any channel realization, enabling a zero-outage probability or infinite diversity order at the corresponding rates. A simple scheme utilizing (a possibly outdated) channel state feedback is provided, attaining the no-outage guarantee. Finally, noting that as $m$ increases, the Jacobi model approaches the Rayleigh model, the paper discusses the applicability of the model in other communication scenarios.