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Let $M$ an $n \times p$ matrix with complex Gaussian elements with mean $= \mu$ and variance $= \sigma^2$. Also le define matrix $W$ as an $p \times m$ matrix for which the columns are of unit norm. We finally define vector $V=[v_1,\ldots,v_m]^T$ of dimension $m \times 1$, where $\mathbb{E}\{ |v_i|^2 \}=a$, $\forall i$. We assume that $M$, $W$ and $V$ are independent. We denote by $(\cdot)^H$ the conjugate transpose of $(\cdot)$.

Using the avobe definitions and assumptions, can we calculate $\mathbb{E}\{M W V V^H W^H M^H \}$? if so, how to do it?

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