Outage Probability Conjecture Does Not Hold for Two-Input-Multiple-Output (TIMO) System

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] and long considered true. A special single-output case of this conjecture has been proved theoretically. In this work, we address the special Two-Input-Multiple-Output (TIMO) case, and show that the conjecture is untrue. A concrete counter-example is proposed and verified both theoretically and by numerical experiments. This result rejects the decades-long conjecture and provides interesting insight into the symmetry of MIMO systems.