On the Outage Probability Conjecture for MIMO Channels

TL;DR

This paper challenges a longstanding conjecture on outage probability in MIMO channels by providing a counter-example in the TIMO case and offering new theoretical insights into MIMO system symmetry.

Contribution

It presents the first counter-example to the outage probability conjecture for TIMO systems and introduces a new analytical method for general MIMO cases.

Findings

Counter-example disproves the conjecture for TIMO systems

Theoretical and numerical verification of the counter-example

Provides a new analytical approach for MIMO outage probability calculation

Abstract

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 counter-example 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.