Proof of the outage probability conjecture for MISO channels

It is conjectured in [6] that the covariance matrices minimizing the outage probability under a power constraint 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 tail probability correspond to such diagonal matrices. This paper provides a proof of the conjecture in this MISO setting.