A binary sequence is transmitted via binary antipodal signaling over a Rayleigh fading channel…

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A binary sequence is transmitted via binary antipodal signaling over a Rayleigh fading channel with Lth-order diversity. When sl(t) is transmitted, the received equivalent lowpass signals are

The fading among the L subchannels is statistically independent. The additive noise terms {zk(t)} are zero-mean, statistically independent, and identically distributed white Gaussian noise processes with autocorrelation function Rzz(τ ) = 2N0δ(τ ). Each of the L signals is passed through a filter matched to s1(t) and the output is phase-corrected to yield

a. Determine the PDF of U conditional on fixed values for the {ak}.

b. Determine the expression for the probability of error when the {ak} are statistically independent and identically distributed Rayleigh random variables.