Skip to main content

Equalizer to reduce Multi-path Effects using MATLAB

 

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 k for 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


     

    Copy the MATLAB Code from here

     

    Further Reading

    People are good at skipping over material they already know!

    View Related Topics to







    Contact Us

    Name

    Email *

    Message *

    Popular Posts

    BER vs SNR for M-ary QAM, M-ary PSK, QPSK, BPSK, ...(MATLAB Code + Simulator)

    📘 Overview of BER and SNR 🧮 Online Simulator for BER calculation of m-ary QAM and m-ary PSK 🧮 MATLAB Code for BER calculation of M-ary QAM, M-ary PSK, QPSK, BPSK, ... 📚 Further Reading 📂 View Other Topics on M-ary QAM, M-ary PSK, QPSK ... 🧮 Online Simulator for Constellation Diagram of m-ary QAM 🧮 Online Simulator for Constellation Diagram of m-ary PSK 🧮 MATLAB Code for BER calculation of ASK, FSK, and PSK 🧮 MATLAB Code for BER calculation of Alamouti Scheme 🧮 Different approaches to calculate BER vs SNR What is Bit Error Rate (BER)? The abbreviation BER stands for Bit Error Rate, which indicates how many corrupted bits are received (after the demodulation process) compared to the total number of bits sent in a communication process. BER = (number of bits received in error) / (total number of tran...
    Read more

    Theoretical BER vs SNR for binary ASK, FSK, and PSK with MATLAB Code + Simulator

    📘 Overview & Theory 🧮 MATLAB Codes 📚 Further Reading Theoretical BER vs SNR for Amplitude Shift Keying (ASK) The theoretical Bit Error Rate (BER) for binary ASK depends on how binary bits are mapped to signal amplitudes. For typical cases: If bits are mapped to 1 and -1, the BER is: BER = Q(√(2 × SNR)) If bits are mapped to 0 and 1, the BER becomes: BER = Q(√(SNR / 2)) Where: Q(x) is the Q-function: Q(x) = 0.5 × erfc(x / √2) SNR : Signal-to-Noise Ratio N₀ : Noise Power Spectral Density Understanding the Q-Function and BER for ASK Bit '0' transmits noise only Bit '1' transmits signal (1 + noise) Receiver decision threshold is 0.5 BER is given by: P b = Q(0.5 / σ) , where σ = √(N₀ / 2) Using SNR = (0.5)² / N₀, we get: BER = Q(√(SNR / 2)) Theoretical BER vs ...
    Read more

    Online Simulator for ASK, FSK, and PSK

    Try our new Digital Signal Processing Simulator!   Start Simulator for binary ASK Modulation Message Bits (e.g. 1,0,1,0) Carrier Frequency (Hz) Sampling Frequency (Hz) Run Simulation Simulator for binary FSK Modulation Input Bits (e.g. 1,0,1,0) Freq for '1' (Hz) Freq for '0' (Hz) Sampling Rate (Hz) Visualize FSK Signal Simulator for BPSK Modulation ...
    Read more

    How Windowing Affects Your Periodogram

    The windowed periodogram is a widely used technique for estimating the Power Spectral Density (PSD) of a signal. It enhances the classical periodogram by mitigating spectral leakage through the application of a windowing function. This technique is essential in signal processing for accurate frequency-domain analysis.   Power Spectral Density (PSD) The PSD characterizes how the power of a signal is distributed across different frequency components. For a discrete-time signal, the PSD is defined as the Fourier Transform of the signal’s autocorrelation function: S x (f) = FT{R x (Ï„)} Here, R x (Ï„)}is the autocorrelation function. FT : Fourier Transform   Classical Periodogram The periodogram is a non-parametric PSD estimation method based on the Discrete Fourier Transform (DFT): P x (f) = \(\frac{1}{N}\) X(f) 2 Here: X(f): DFT of the signal x(n) N: Signal length However, the classical periodogram suffers from spectral leakage due to abrupt truncation of the ...
    Read more

    MATLAB Code for QPSK Modulation and Demodulation

    📘 Overview 🧮 MATLAB Codes 🧮 Theory 🧮 BER performance of QPSK with BPSK, 4-QAM, 16-QAM, 64-QAM, 256-QAM, etc 📚 Further Reading   Quadrature Phase Shift Keying (QPSK) is a digital modulation scheme that conveys two bits per symbol by changing the phase of the carrier signal. Each pair of bits is mapped to one of four possible phase shifts: 0°, 90°, 180°, or 270° 00  ===> 0 degree phase shift of carrier signal 01  ===> 90 degree 11  ===> 180 degree 10  ===> 270 degree   MATLAB Script clc; clear all; close all; clc; M = 4; data = randi([0 (M-1)], 1000, 1); Phase = 0; modData=pskmod(data,M,Phase); figure(1); scatterplot(modData); channelAWGN = 15; rxData2 = awgn(modData, channelAWGN); figure(2); scatterplot(rxData2); demodData = pskdemod(rxData2,M,Phase);   Result data 1 0 2 2 0 2 1 . . . modData -1.00000000000000 + 1.22464679914735e-16i -1.83697019872103e-16 - 1.000000000000...
    Read more

    MATLAB code for BER vs SNR for M-QAM, M-PSK, QPSk, BPSK, ...(with Online Simulator)

    🧮 MATLAB Code for BPSK, M-ary PSK, and M-ary QAM Together 🧮 MATLAB Code for M-ary QAM 🧮 MATLAB Code for M-ary PSK 📚 Further Reading MATLAB Script for BER vs. SNR for M-QAM, M-PSK, QPSK, BPSK % Written by Salim Wireless clc; clear; close all; num_symbols = 1e5; snr_db = -20:2:20; psk_orders = [2, 4, 8, 16, 32]; qam_orders = [4, 16, 64, 256]; ber_psk_results = zeros(length(psk_orders), length(snr_db)); ber_qam_results = zeros(length(qam_orders), length(snr_db)); for i = 1:length(psk_orders) psk_order = psk_orders(i); for j = 1:length(snr_db) data_symbols = randi([0, psk_order-1], 1, num_symbols); modulated_signal = pskmod(data_symbols, psk_order, pi/psk_order); received_signal = awgn(modulated_signal, snr_db(j), 'measured'); demodulated_symbols = pskdemod(received_signal, psk_order, pi/psk_order); ber_psk_results(i, j) = sum(data_symbols ~= demodulated_symbols) / num_symbols; end end for i...
    Read more

    MATLAB code for Pulse Code Modulation (PCM) and Demodulation

    📘 Overview & Theory 🧮 Quantization in Pulse Code Modulation (PCM) 🧮 MATLAB Code for Pulse Code Modulation (PCM) 🧮 MATLAB Code for Pulse Amplitude Modulation and Demodulation of Digital data 🧮 Other Pulse Modulation Techniques (e.g., PWM, PPM, DM, and PCM) 📚 Further Reading MATLAB Code for Pulse Code Modulation clc; close all; clear all; fm=input('Enter the message frequency (in Hz): '); fs=input('Enter the sampling frequency (in Hz): '); L=input('Enter the number of the quantization levels: '); n = log2(L); t=0:1/fs:1; % fs nuber of samples have tobe selected s=8*sin(2*pi*fm*t); subplot(3,1,1); t=0:1/(length(s)-1):1; plot(t,s); title('Analog Signal'); ylabel('Amplitude--->'); xlabel('Time--->'); subplot(3,1,2); stem(t,s);grid on; title('Sampled Sinal'); ylabel('Amplitude--->'); xlabel('Time--->'); % Quantization Process vmax=8; vmin=-vmax; %to quanti...
    Read more

    MATLAB Code for ASK, FSK, and PSK (with Online Simulator)

    📘 Overview & Theory 🧮 MATLAB Code for ASK 🧮 MATLAB Code for FSK 🧮 MATLAB Code for PSK 🧮 Simulator for binary ASK, FSK, and PSK Modulations 📚 Further Reading ASK, FSK & PSK HomePage MATLAB Code MATLAB Code for ASK Modulation and Demodulation % The code is written by SalimWireless.Com % Clear previous data and plots clc; clear all; close all; % Parameters Tb = 1; % Bit duration (s) fc = 10; % Carrier frequency (Hz) N_bits = 10; % Number of bits Fs = 100 * fc; % Sampling frequency (ensure at least 2*fc, more for better representation) Ts = 1/Fs; % Sampling interval samples_per_bit = Fs * Tb; % Number of samples per bit duration % Generate random binary data rng(10); % Set random seed for reproducibility binary_data = randi([0, 1], 1, N_bits); % Generate random binary data (0 or 1) % Initialize arrays for continuous signals t_overall = 0:Ts:(N_bits...
    Read more