1. A MIMO channel has a single cluster with the directional cosine ranges as E>t = E>r = [0, 1]. Compute the number of degrees of freedom of an n × n channel as a function of the antenna separation Llt = Llr = Ll.
2. Show that the capacity of a time-invariant MIMO channel with nt transmit, nr receive antennas and channel matrix H is the same as that of the channel with nr transmit, nt receive antennas, matrix H∗, and same total power constraint.