Adaptive Equalizer to mitigate Channel Distortion - in MATLAB

 

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)

Copy the Code from here

% The code is written by SalimWireless.Com 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;