A Expectation operation for covariance calculation

[nikozm]

Hi,

If E[ww^H]=T, where w is a zero-mean row-vector and ^H is the Hermitian transpose then assuming that H is another random matrix, it holds that
E[H w (H w)^H] = T H H^H or T E[H H^H] ??

In other words, the expectation operation still holds as in the latter expression or vanishes as in the second equality above ??

Thank you in advance.

 

[andrewkirk]

It cannot be the case that $E[Hw(Hw)^H]=THH^H$ because the LHS is not a random variable, whereas the RHS is.

We can write $E[Hw(Hw)^H]=E[Hww^HH^H]$ but what, if anything, can be done from there depends on what we know about $w$. Is $w$ a random variable? If so, do we know anything about its distribution other than that each of its components has zero mean?