The Jacobi MIMO channel

Abstract

In the Jacobi MIMO channel the transfer matrix H which couples the m <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">t</sub> inputs into m <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">r</sub> outputs is a sub-matrix of an m×m random (Haar-distributed) unitary matrix. The (squared) singular values of H follow the law of the classical Jacobi ensemble of random matrices; hence the name of the channel. A motivation to define such a channel comes from multimode/multicore optical fiber communication. It turns out that this model is qualitatively different than the Rayleigh model, leading to interesting practical and theoretical results. This work first evaluates the ergodic capacity of the channel. In the non-ergodic case, it analyzes the outage probability and the diversity-multiplexing tradeoff. In the case where k = m <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">t</sub> +m <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">r</sub> -m >; 0 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. Finally, we note that the Jacobi channel may provide a new fading model to other applications.