Steps
1. Convert Bit Stream to Bipolar Format. Converts the bit stream from binary (0, 1) to bipolar format (-1, 1).
2. Define Channel Impulse Response
3. Pass Signal Through the Channel. Convolves the bipolar signal with the channel impulse response to simulate the channel effect.
4. Adds Gaussian noise to the received signal based on the specified SNR.
5. Initialize Adaptive Filter Parameters.
w: Initializes the adaptive filter coefficients.x_buf: Initializes the buffer for the input to the adaptive filter.equalized_signal: Initializes the array to store the equalized signal.P: Initializes the inverse correlation matrix.6. Adaptive Equalization Using RLS Algorithm
Loops through each sample to perform adaptive equalization:
- Update Input Buffer: Adds the current sample to the input buffer.
- Calculate Gain Vector: Computes the gain vector
kfor the adaptive filter. - Calculate Error Signal: Computes the error between the original signal and the filter output.
- Update Filter Coefficients: Updates the adaptive filter coefficients based on the error signal.
- Update Inverse Correlation Matrix: Updates the inverse correlation matrix for the RLS algorithm.
- Store Equalized Output: Stores the equalized signal in the output array.
7. Plot Original and Equalized Signals
MATLAB Script
clc;
clear;
close all;
% Parameters
bit_stream = [1, 1, 0, 0, 1, 0, 1, 1, 1, 0]; % Original bit stream
N = length(bit_stream); % 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 = 15; % SNR value in dB
% Convert bit stream to bipolar format (-1, 1)
original_signal = bit_stream * 2 - 1;
% Channel impulse response
h = [0.75, 0.05, 0.02];
% Pass the signal through the channel
received_signal = filter(h, 1, original_signal);
% Add some noise
received_signal_noisy = 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_noisy(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
% Plot original and equalized signals
figure;
subplot(2, 1, 1);
stem(original_signal, 'filled');
title('Original Signal');
xlabel('Sample Index');
ylabel('Amplitude');
grid on;
subplot(2, 1, 2);
stem(equalized_signal, 'filled');
title('Equalized Signal');
xlabel('Sample Index');
ylabel('Amplitude');
grid on;
Output
