Proof of the outage probability conjecture for MISO channels

TL;DR

This paper proves a longstanding conjecture that the covariance matrices minimizing outage probability in MISO channels are diagonal with specific entries, confirming the optimal structure for Gaussian quadratic forms in this context.

Contribution

It provides a proof of the outage probability conjecture for MISO channels, establishing the optimal covariance matrix structure in this setting.

Findings

Confirmed the conjecture for MISO channels.

Identified the structure of covariance matrices minimizing outage probability.

Enhanced understanding of Gaussian quadratic forms in wireless communication.

Abstract

In Telatar 1999, it is conjectured that the covariance matrices minimizing the outage probability for MIMO channels with Gaussian fading are diagonal with either zeros or constant values on the diagonal. In the MISO setting, this is equivalent to conjecture that the Gaussian quadratic forms having largest tale probability correspond to such diagonal matrices. We prove here the conjecture in the MISO setting.