Adaptive equalizer adjusts its parameters based on the characteristics of the communication channel. It uses adaptive algorithms to continuously estimate and correct for channel distortion, aiming to minimize errors in the received signal. Adaptive equalizers are versatile and effective in varying channel conditions.
MATLAB Code
clc;
clear;
close all;
% Parameters
N = 100000; % Number of samples
filter_order = 10; % Order of the adaptive filter
lambda = 0.99; % Forgetting factor for RLS algorithm
delta = 1; % Initial value for the inverse correlation matrix
SNR_range = -20:1:20; % SNR range in dB
ber = zeros(length(SNR_range), 1); % Initialize BER array
% Generate a random signal
original_signal = randi([0, 1], N, 1) * 2 - 1; % Bipolar signal (-1, 1)
% Channel impulse response
h = [0.8, 0.5, 0.2];
% Loop over SNR values
for snr_idx = 1:length(SNR_range)
SNR = SNR_range(snr_idx); % Current SNR value
% Pass the signal through the channel
received_signal = filter(h, 1, original_signal);
% Add some noise
received_signal = awgn(received_signal, SNR, 'measured');
% Initialize the adaptive filter coefficients
w = zeros(filter_order, 1);
% Initialize buffer for the input to the adaptive filter
x_buf = zeros(filter_order, 1);
% Initialize output
equalized_signal = zeros(N, 1);
% Initialize the inverse correlation matrix
P = delta * eye(filter_order);
% Adaptive equalization using RLS
for n = 1:N
% Update the input buffer
x_buf = [received_signal(n); x_buf(1:end-1)];
% Calculate the gain vector
k = (P * x_buf) / (lambda + x_buf' * P * x_buf);
% Calculate the error signal
e = original_signal(n) - w' * x_buf;
% Update the filter coefficients
w = w + k * e;
% Update the inverse correlation matrix
P = (P - k * x_buf' * P) / lambda;
% Store the equalized output
equalized_signal(n) = w' * x_buf;
end
% Decode the equalized signal using threshold 0
decoded_signal = equalized_signal > 0;
decoded_signal = decoded_signal * 2 - 1; % Convert from (0, 1) to (-1, 1)
% Calculate BER
num_errors = sum(original_signal ~= decoded_signal);
ber(snr_idx) = num_errors / N;
end
% Plot BER vs SNR
figure;
semilogy(SNR_range, ber, 'b-o');
xlabel('SNR (dB)');
ylabel('Bit Error Rate (BER)');
title('BER vs SNR');
grid on;
Output
Fig 1: BER vs SNR for Adaptive Equalizer (to mitigate the channel distortion)