Monotonicity Results for Coherent MIMO Ricean Channels

A preorder on the line-of-sight (LOS) matrices in coherent multipleinput multiple-output (MIMO) Ricean fading channels is introduced. It is demonstrated that under this preorder, the information rate corresponding to zero-mean multivariate circularly symmetric Gaussian inputs of arbitrary covariance matrices is monotonic in the LOS matrix. This 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 Ricean multi-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.