(a) Average over gain in the noncoherent detection result in (9.59) to rederive the Rayleigh fading error probability.
(b) Assume narrow-band fading with a single tap Gm. Assume that the sample value of the tap magnitude, gm, is measured perfectly and fed back to the transmitter. Suppose that the transmitter, using pulse-position modulation, chooses the input magnitude dynamically so as to maintain a constant received signal to noise ratio. That is, the transmitter sends a/gm/ instead of a. Find the expected transmitted energy per binary digit.