Part 1
Problem 1
The result of transmitting a single pulse through a channel is a received sequence of pulses at the sampling instants given by {0.1, 0.3, -0.2, 0.96, 0.4, -0.1, 0.1} where the leftmost sample is the earliest. The value 0.96 corresponds to the mainlobe of the pulse, and the other entries are adjacent pulse samples.
(a) Design a 3-tap equalizer based on the zero-forcing approach.
(b) Determine the values of the equalized output pulses at time instants k = -3, -2, ...,0, 1, ..., 3.
(c) After equalization, what is the largest magnitude sample contributing to ISI?
(d) What is the sum of the magnitudes of the ISI?
Problem 2
The channel impulse response at the sampling instants given by {0.01, 0.02, -0.03, 0.1, 0.98, 0.2, -0.1, 0.05, 0.02} where the leftmost sample is the earliest. The value 0.98 corresponds to the mainlobe of the pulse, and the other entries are adjacent pulse samples.
(a) Design a 9-tap equalizer based on the MMSE approach.
(b) Determine the values of the equalized output pulses at time instants k = -8, -7, ...,0, 1, ..., 8.
(c) After equalization, what is the largest magnitude sample contributing to ISI?
(d) What is the sum of the magnitudes of the ISI?
Problem 3
A multipath transmission occurs when a transmitted signal arrives at the receiver by two or more paths of different delays. A simple model of a multipath communication channel is shown below in Figure.
(a) Determine H(ω), the frequency response for this channel.
(b) Plot |H(V)| versus ω over [(-3Π/Τ)(3Π/Τ)] for α = 0.5 and α = 1.
Part 2
Problem 1
Consider a linear system model for a channel with input and output as shown in
Determine:
(a) H(f), the frequency response of this system
(b) | H(f)|, its magnitude
(c) ?(f), its phase
Problem 2
Figure shows a receiver based on sampling the matched-filter output at t = T.
Obtain expressions for v(t) and v(T) and relate these to the response of the correlator sampler shown in Figure.
