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This paper extends the "single crossing point" property of the scalar MMSEfunction, derived by Guo, Shamai and Verd\'u (first presented in ISIT 2008), tothe parallel degraded MIMO scenario. It is shown that the matrix Q(t), which isthe difference between the MMSE assuming a Gaussian input and the MMSE assumingan arbitrary input, has, at most, a single crossing point for each of itseigenvalues. Together with the I-MMSE relationship, a fundamental connectionbetween Information Theory and Estimation Theory, this new property is employedto derive results in Information Theory. As a simple application of thisproperty we provide an alternative converse proof for the broadcast channel(BC) capacity region under covariance constraint in this specific setting.

On MMSE Properties and I-MMSE Implications in Parallel MIMO Gaussian Channels