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[itex]\mathcal{E}\left\{\textbf{N}\textbf{N}^H\right\} = \textbf{I}[/itex]

where [itex]\mathcal{E}\left\{\right\}[/itex] denotes expectation, [itex]\{\}^H[/itex] is conjugate transpose and [itex]\textbf{I}[/itex] is the identity matrix.

Basically, I want to know exactly what this tells me about the second order statistics of the elements of [itex]\textbf{N}[/itex]. For example, I know that if instead I just had an [itex](m \times 1)[/itex] vector, [itex]\textbf{n}[/itex], then an identity covariance matrix would imply that all the elements of [itex]\textbf{n}[/itex] have unit variance and are uncorrelated.

Can I make any similar deductions from the matrix equation, above? Many thanks for any help!