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A Expectation operation for covariance calculation

  1. Sep 6, 2016 #1

    If E[wwH]=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 HH or T E[H HH] ??

    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.
  2. jcsd
  3. Sep 6, 2016 #2


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    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?
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