On the Outage Probability Conjecture for MIMO Channels

Multiple-Input-Multiple-Output (MIMO) communication systems have seen wide application due to its performance benefits such as multiplexing gain. For MIMO systems with non-ergodic Gaussian channel, a conjecture regarding its outage probability has been proposed by Telatar in [1]. This conjecture has been proved for the special single-output case, and is in general assumed to be true. In this work, we analyze the special Two-Input-Multiple-Output (TIMO) case theoretically, and provide a counterexample to the conjecture. The counter-example is verified both theoretically and by numerical experiments. We also present a theoretical analysis for general MIMO case, including a method for calculation. This result rejects the decades-long conjecture and provides interesting insight into the symmetry of MIMO systems.