Monotonicity results for coherent MIMO Ricean channels
Daniel Hoesli, Young-Han Kim, and Amos Lapidoth
IEEE Transactions on Information Theory, vol. 51, no. 12, pp. 4334–4339, December 2005.
Preliminary results appeared in Proceedings of IEEE International Symposium on Information Theory, p. 54, Yokohama, Japan, June/July 2003.
The dependence of the Gaussian input information rate on the
line-of-sight (LOS) matrix in multiple-input multiple-output (MIMO)
coherent Rician fading channels is explored. It is proved that the
outage probability and the mutual information induced by a
multivariate circularly symmetric Gaussian input with any covariance
matrix are monotonic in the LOS matrix 
, or more precisely,
monotonic in 
in the sense of the Loewner partial
order. Conversely, it is also demonstrated that this ordering on the
LOS matrices is a necessary condition for the uniform monotonicity
over all input covariance matrices. This result is subsequently
applied to prove the monotonicity of the isotropic Gaussian input
information rate and channel capacity in the singular values of the
LOS matrix. Extensions to multiple-access channels (MAC) are also
provided.