In this programming assignment you will try out and test diﬀerent equalizers for intersymbol interference
(ISI) channels and check their performance in terms of the probability of symbol error.
Consider a discrete-time baseband-equivalent channel model with input-output (I/O) relationship given by
fkInk + n, where the symbols In are drawn from a binary PAM constellation and n denotes
additive white Gaussian noise (AWGN) with variance N0. We will test two ISI channels with corresponding
taps [0:227;0:45;0:7;0:45;0:227] (channel 1) and [0:41;0:815;0:41] (channel 2). Since for both channels ∑
2 = 1, the received signal-to-noise-ratio (SNR) is
= 1=N0. Unless speciﬁed otherwise, the linear and
decision-feedback (DF) equalizers to be tested will have 41 taps.
Test Scenario 1: Implement the zero-forcing (ZF) linear equalizer for channel 2. Plot the symbol error rate
(SER) curve versus SNR (use semilog) for the SNR values
= 0 : 2 : 18dB, by generating 108
In addition to the simulated SER, plot the theoretical SER performance of the linear ZF equalizer (use the
corresponding formulas from the book or the notes). In a diﬀerent ﬁgure, compare the theoretical SER
curves for equalizer lengths 13, 23 and 33. Comment brieﬂy on their relative performance.
Test Scenario 2: Implement the linear minimum mean-square error (LMMSE) equalizer for channels 1 and
2. Plot the two simulated SER semi-log curves as in Test Scenario 1 along with the (approximate) theoretical
SER for each channel (use formula [url removed, login to view]). Comment on the diﬀerence in performance between the two
Test Scenario 3: Implement the MMSE-DF equalizer for channel 2 and plot the simulated SER versus
SNR semi-log curve along with its (approximate) theoretical SER [Find Jmin, then calculate SNR
(1 Jmin)=(Jmin) and ﬁnally ﬁnd Pe Q(
)]. Compare in a diﬀerent plot, the theoretical BER vs. SNR
curves of the linear ZF, LMMSE, and MMSE-DF for the same channel 2.
Test Scenario 4: Implement the Viterbi Algorithm (VA) for maximum likelihood sequence estimation
(MLSE). In addition to the simulated BER versus SNR curve, plot the matched-ﬁlter (MF) lower bound
for both channels 1 and 2, and comment on the MLSE-MF gap. Finally, compare on a separate graph the
performance of MMSE-DF and MLSE equalization schemes for channel 1 only.
Your report should explain what the code does step-by-step