Problem
Assume a Rayleigh fading channel, where the transmitter and receiver have CSI and the distribution of the fading SNR p(? ) is exponential with mean Y^ = 10 dB. Assume a channel bandwidth of 10 MHz.
(a) Find the cutoff value ?0 and the corresponding power adaptation that achieves Shannon capacity on this channel.
(b) Compute the Shannon capacity of this channel.
(c) Compare your answer in part (b) with the channel capacity in AWGN with the same average SNR.
(d) Compare your answer in part (b) with the Shannon capacity when only the receiver knows ? [i].
(e) Compare your answer in part (b) with the zero-outage capacity and outage capacity when the outage probability is .05.
(f ) Repeat parts (b), (c), and (d) - that is, obtain the Shannon capacity with perfect transmitter and receiver side information, in AWGN for the same average power, and with just receiver side information - for the same fading distribution but with mean Y^= -5 dB. Describe the circumstances under which a fading channel has higher capacity than an AWGN channel with the same average SNR and explain why this behavior occurs.
The response should include a reference list. Double-space, using Times New Roman 12 pnt font, one-inch margins, and APA style of writing and citations.