A time-dispersive channel having an impulse response h(t) is used to transmit four-phase PSK at a...

A time-dispersive channel having an impulse response h(t) is used to transmit four-phase PSK at a rate R = 1/T symbols/s. The equivalent discrete-time channel is shown in Figure P9.54. The sequence {ηk} is a white noise sequence having zero-mean and variance σ2 = N0.

a. What is the sampled autocorrelation function sequence {xk} defined by

for this channel?

b. The minimum MSE performance of a linear equalizer and a decision-feedback equalizer having an infinite number of taps depends on the folded-spectrum of the channel

where H(ω) is the Fourier transform of h(t). Determine the folded spectrum of the channel given above. c. Use your answer in (b) to express the minimum MSE of a linear equalizer in terms of the folded spectrum of the channel. (You may leave your answer in integral form.)

d. Repeat (c) for an infinite-tap decision-feedback equalizer.