6.(20%) Consider a simple communication system that contains a single antenna at the transmitter and
M antennas at the receiver. The received signal at the mth antenna with a binary transmitted signal
can thus be expressed as
ym =uhm +wm,
where u = ±a is the transmitted signal, hm is the gain of antenna m, and wm is the associated AWGN
with zero mean and variance σ2 . Herein, u, w1,..., wM are mutually independent. Collecting Y1,....
YM into a vector, we have