Adaptive Channel Equalization using NLMS Algorithm

An adaptive linear equalizer operating in two modes: training mode and decision-direction mode

We consider the channel:
C(z)=0.5 + 1.2z-1 + 1.5z-2 + z-3
The equalizer structure shown in "READ ME" file; Symbols {s(i)} are transmitted through the channel and
corrupted by additive complex-valued white noise {v(i)}. The received signal {u(i)} is processed by the FIR
equalizer to generate estimates {s(i-Δ)}, which are fed into a decision device. The equalizer possesses two
modes of operation: a training mode during which a delayed replica of the input sequence is used as
reference sequence, and a decision-directed mode during which the output of the decision-device
replaces the reference sequence. The input sequence {s(i)} is chosen from a QAM constellation.
1) Write a program that trains the adaptive filter with 500 symbols from a QPSK constellation,
followed by decision-directed operation during 5000 symbols from a 64 QAM constellation.
Choose the noise variance in order to enforce an SNR level of 30 dB at the input of the
equalizer. Choose Δ = 15 and equalizer length L = 35. Use ε-NLMS to train the equalizer with step
size μ = 0.4 and ε = 10-6. Plot the scatter diagrams of {s(i), u(i), s(i-Δ)}. (*Program
adaptive_channel_e_NLMS.m)
2) Generate symbol-error-rate (SER) curves versus SNR at the input of the equalizer for (4, 16, 64,
256) - QAM data. Let the SNR vary between 5 dB and 30 dB in increments of 1 dB.