Simulator for BPSK Constellation Diagram SNR (dB): 15 Add AWGN Noise Run Simulation

  MATLAB code for channel impulse response estimation using FFT-based channel estimation method % The code is developed by SalimWireless.com clc; clear all; close all; % Parameters N = 128; % Signal length epsilon = 1e-3; % Regularization term useWhiteNoise = true; % Set false to use delta function probe SNR_dB = 100; % Signal-to-Noise Ratio in dB % True channel (FIR with 3 taps) true_h = [0.8, 0.5+0.3j, 0.2, 0.1]; L = length(true_h); % Generate probe signal if useWhiteNoise x = randn(1, N); % White noise else x = zeros(1, N); % Delta function x(1) = 1; end % Pass through the channel (linear convolution) y_clean = conv(x, true_h, 'same'); % Add AWGN signal_power = mean(abs(y_clean).^2); noise_power = signal_power / (10^(SNR_dB/10)); noise = sqrt(noise_power/2) * (randn(1, N) + 1j * randn(1, N)); y_noisy = y_clean + noise; % FFTs Xf = fft(x); Yf = fft(y_noisy); % Estimate channel frequency response with regula...

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Impulse Response h[n] of an ARMA System Step-by-Step Solution 1. Start with the Transfer Function: Given: H(z) = (1 + 0.3z⁻¹) / (1 - 0.75z⁻¹ + 0.5z⁻²) This is an ARMA(2,1) system where: MA (numerator) coefficients: [1, 0.3] AR (denominator) coefficients: [1, -0.75, 0.5] 2. Find the Impulse Response h[n]: We want the inverse Z-transform of H(z). Instead of doing partial fraction decomposition, we use the system's difference equation. 3. Recursive Computation Using the Difference Equation: From the system equation: y[n] + 0.75y[n−1] − 0.5y[n−2] = x[n] + 0.3x[n−1] Assume x[n] = δ[n] (unit impulse): x[0] = 1 , others are 0. Then y[n] = h[n] 4. Compute h[n] values: n = 0: y[0] + 0 = 1 → h[0] = 1 n = 1: y[1] + 0.75*1 = 0.3 → h[1] = -0.45 n = 2: y[2] - 0.3375 - 0.5 = 0 → h[2] = 0.8375 n = 3: y[3] + 0.628125 + 0.225 = 0 → h[3] = -0.853125 5. Table of Fi...

  MATLAB Code clc; clear all; close all; % Number of samples to generate n = 100000; % Generate Uniform distribution between 0 and 1 r = rand(1, n);  % rand generates numbers in the range [0, 1] % Transform to the range [-1, 1] a = -1; b = 1; uniform_values = a + (b - a) * r; % Plot the histogram of the generated uniform distribution figure; histogram(uniform_values, 30, 'Normalization', 'pdf');  % Normalized to show probability density title('Uniform Distribution between -1 and 1'); xlabel('Value'); ylabel('Probability Density'); % Generate Gaussian distribution (Standard Normal Distribution) gaussian_values = randn(1, n);  % Standard normal distribution (mean = 0, std = 1) % Plotting the Gaussian distribution figure; histogram(gaussian_values, 30, 'Normalization', 'pdf');  % Normalized to show probability density title('Gaussian Distribution (Standard Normal)'); xlabel('Value'); ylabel('Probability Density...

Singular Value Decomposition (SVD) SVD can be performed on any rectangular or square matrix. In SVD, U and V are unitary matrices (orthogonal if the matrix is real), satisfying the conditions UU H = I and VV H = I. Computing the condition number is often important—it is defined as the ratio of the largest singular value to the smallest non-zero singular value in the diagonal matrix of singular values. A high condition number indicates a nearly singular or ill-conditioned matrix.   For a Matrix,   Step 1: W e normalize each column We get,  H = We divided the elements of the first column by √(2² + 3²) = √13 , and proceeded similarly for the other columns. Here singular values are not in decreasing order. Step 2: Now we arrange the singular values in decreasing order H =   That implies, H =  U Σ V H Again assume, the first matrix is  U  (unitary matrix), the middle one is  Σ  (eigenmatrix) ,...

  MATLAB Code clc; clear; close all; % Parameters Rb = 1e6; % Bit rate (1 Mbps) SNR_dB = 0:2:20; % SNR range in dB beta_values = [0, 0.2, 0.5, 0.8, 1.0]; % Different roll-off factors numBits = 1e5; % Number of bits disp("For different roll-off (β) factors and a symbol rate of 1 MHz:"); % Simulation BER = zeros(length(beta_values), length(SNR_dB)); for b = 1:length(beta_values) beta = beta_values(b); bandwidth = (1 + beta) * (Rb / 2); % Bandwidth calculation timeBandwidthProduct = (1 + beta) / 2; % Time-bandwidth product calculation fprintf('Beta = %.1f, Bandwidth = %.2f MHz, Time-Bandwidth Product = %.2f\n', beta, bandwidth / 1e6, timeBandwidthProduct); for s = 1:length(SNR_dB) snr = 10^(SNR_dB(s) / 10); % Convert dB to linear EbN0 = snr * Rb / bandwidth; % Adjust for bandwidth noiseVar = 1 / (2 * EbN0); % Transmit random BPSK symbols bits = randi([0, 1], numBits, 1); symbols = 2 * bits - 1; noise = sqrt(noiseVar) * randn(numBits, 1); received = symbols...

  MATLAB Code clc; clear; close all; % Parameters fs = 1000; % Sampling frequency msgLength = 100; % Length of the message pnLength = 50; % Length of PN sequence silenceLength = 20; % Length of silence before and after lagAmount = 50; % Amount of lag (can be negative for lead) threshold = 0.5; % Threshold for correlation peak detection % Generate Unique PN Sequences pnPrefix = 2 * (randi([0, 1], 1, pnLength) - 0.5); pnPostfix = 2 * (randi([0, 1], 1, pnLength) - 0.5); % Generate Message originalMessage = (randi([0, 1], 1, msgLength)); message = 2*originalMessage - 1; % Construct Dataframe dataframe = [pnPrefix, message, pnPostfix]; % Introduce Lag or Lead if lagAmount > 0 %laggedFrame = [zeros(1, lagAmount), dataframe(1:end - lagAmount)]; laggedFrame = [zeros(1, lagAmount), dataframe]; else laggedFrame = [dataframe(-lagAmount + 1:end), zeros(1, -lagAmount)]; end % Correlation with PN Sequences corrPrefix = xcorr(laggedFrame, pnPrefix); corrPostfix = xcorr(laggedFrame, pnPostfi...