Consider a (2;N) MIMO channel (with N > 1), where the MIMO channel is orthonor-

Question

Consider a (2;N) MIMO channel (with N > 1), where the MIMO channel is orthonor-
mal. In other words, the channel can be written as a N x 2 matrix H = [h1h2], where
h1 and h2 are Nx1 vectors such that II h1II2 = II h2 II2 = 1 and hH1 h2 = 0. Suppose that
the received signal is given by x = Hs + n, where the transmit power is E(II s II2)= 2P
and where n is a zero-mean AWGN vector with covariance E(nnH)= IN. Show that
the open-loop capacity of this orthonormal MIMO channel (open loop means that the
transmitter does not have the knowledge of the channel state information and performsuniform power allocation across the antennas) is twice that of the SIMO channel in part

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