Reference no: EM131452459

Communication Systems Project -

Project Details:

Suppose in a digital communication system, when a bit is a zero -δ(t) is transmitted and when a bit is a one, + δ(t) is transmitted, where δ(0) = 1 and δ(t ≠ 0) = 0. Note that a random sequence of m > 0 independent bits are transmitted. Note that the probability of a zero is the same as that of a one and the bit rate is 1/T, i.e., T is the bit duration. Assume a raised-cosine pulse, with the roll-off factor 1, is employed, i.e., the overall system impulse response-in the absence of the channel or in the presence of an ideal channel-is the raised cosine pulse with a = 1.

a) Assuming the channel is ideal (H_C(f) = 1), sketch the received ideal waveform as a function of time form = 10. Suppose the channel is not ideal and its transfer function is as follows: H_C(f) = 0.9, if 0 ≤ |f| ≤  0.7/T and H_C(f) = 0, elsewhere, where T is the bit duration: Sketch the received distorted waveform as a function of time for m = 10.

b) Suppose the received distorted waveform is synchronously sampled at multiples of T and sent to an adaptive linear equalizer with 21 taps, employing Least-Mean-Square (LMS) algorithm. Note that in LMS, the error signal for every transmitted bit is used to update the taps. Sketch the square of the error signal for m = 1000,if a) Δ = 0.1, b) Δ = 0.01, and c) Δ = 0.001. Comment about the results and discuss the role of the step size Δ on the square of the error signal.

Attachment:- Communication Systems Project.rar