Monotonicity results for coherent single-user and multiple-access MIMO Rician channels

We introduce a preorder on the line-of-sight (LOS) matrices in coherent multiple-input multiple-output (MIMO) Rician fading channels. We demonstrate that under this preorder, the information rate and the rate-R outage probability corresponding to zero-mean multivariate circularly symmetric Gaussian inputs of arbitrary but fixed covariance matrices are monotonic in the LOS matrix. This result extends previous results obtained by Kim & Lapidoth, ISIT, 2003, and Hosli & Lapidoth, ITG Conference on SCC, 2004, i.e., our result implies the monotonicity of the information rates corresponding to isotropic Gaussian inputs and of channel capacity in the singular values of the LOS matrix. It is particularly useful in scenarios such as MIMO Rician multiple-access channels, where the achievable rates depend on the LOS matrices of the different users and cannot be determined based on their corresponding singular values alone. We also prove a converse to the main result. That is, given two different LOS matrices, we show that if for all zero-mean multivariate circularly symmetric Gaussian inputs the induced mutual information over one channel is at least as large as over the other channel, then the two LOS matrices can be ordered