Consider a flat fading channel in which, for a fixed transmit power P¯, the received SNR is one of four values: γ1 = 30dB, γ2 = 20dB, γ3 = 10dB, and γ4 = 0dB. The probabilities associated with each state are p1 = 0.1, p2 = 0.2, p3 = 0.3, and p4 = 0.4. Assume that both transmitter and receiver have CSI. (a) Find the optimal power allocation P[i] for this channel for average transmit power P¯ = 10mW. (b) Find the corresponding Shannon capacity per unit hertz.