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MATLAB Code for MUSIC

  MATLAB Code clc; clear; close all ; %% Step 1: Define Parameters M = 8; % Number of array sensors d = 0.5; % Sensor spacing (lambda/2) K = 2; % Number of signals N = 200; % Number of snapshots theta = [-20 30]; % True signal angles (degrees) SNR = 10; % Signal-to-noise ratio (dB) fprintf( 'Step 1: Parameters Initialized\n' ); %% Step 2: Generate Signal Sources t = 1:N; s1 = exp(1j*2*pi*0.05*t); s2 = exp(1j*2*pi*0.1*t); S = [s1; s2]; figure; plot(real(S(1,:))) title( 'Signal 1 (Real Part)' ) xlabel( 'Samples' ) ylabel( 'Amplitude' ) figure; plot(real(S(2,:))) title( 'Signal 2 (Real Part)' ) xlabel( 'Samples' ) ylabel( 'Amplitude' ) fprintf( 'Step 2: Source Signals Generated\n' ); %% Step 3: Construct Steering Matrix A = zeros(M,K); for k = 1:K A(:,k) = exp(-1j*2*pi*d*(0:M-1)'*sin(theta(k)*pi/180)); end fprintf( 'Step 3: Steering Matr...
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MATLAB code for BER vs SNR for M-QAM, M-PSK, QPSK, BPSK (with Simulation)

🧮 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; snr_db = -5:2:25; 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) ber_psk_results(i, :) = berawgn(snr_db, 'psk', psk_orders(i), 'nondiff'); end for i = 1:length(qam_orders) ber_qam_results(i, :) = berawgn(snr_db, 'qam', qam_orders(i)); end figure; semilogy(snr_db, ber_psk_results(1, :), 'o-', 'LineWidth', 1.5, 'DisplayName', 'BPSK'); hold on; for i = 2:length(psk_orders) semilogy(snr_db, ber_psk_results(i, :), 'o-', 'DisplayName', sprintf('%d-PSK', psk_or...
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Theoretical BER vs SNR for BPSK

Theoretical Bit Error Rate (BER) vs Signal-to-Noise Ratio (SNR) for BPSK in AWGN Channel Let’s simplify the explanation for the theoretical Bit Error Rate (BER) versus Signal-to-Noise Ratio (SNR) for Binary Phase Shift Keying (BPSK) in an Additive White Gaussian Noise (AWGN) channel. Key Points Fig. 1: Constellation Diagrams of BASK, BFSK, and BPSK [↗] BPSK Modulation Transmits one of two signals: +√Eb or −√Eb , where Eb is the energy per bit. These signals represent binary 0 and 1 . AWGN Channel The channel adds Gaussian noise with zero mean and variance N₀/2 (where N₀ is the noise power spectral density). Receiver Decision The receiver decides if the received signal is closer to +√Eb (for bit 0) or −√Eb (for bit 1) . Bit Error Rat...
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PSD Calculation with FFT: MATLAB Tutorial for Signal Analysis

  Implementation Steps 1. FFT Computes the Frequency Content of a Signal FFT converts a time-domain signal to the frequency domain. If: The signal is sampled at rate $f_s$ You compute an $N_{\text{FFT}}$-point FFT Then each FFT bin corresponds to a frequency resolution of: $$\Delta f = \frac{f_s}{N_{\text{FFT}}}$$ So the FFT gives you accurate frequency content, assuming the signal is stationary and adequately sampled (Nyquist criterion met).  2. Magnitude Squared Gives Power (Not Amplitude) $$P[k] = |X[k]|^2$$ This gives power at each frequency bin, not just amplitude. It represents how much energy is present at each frequency. It's a key step for PSD.  3. Normalization Makes the PSD Physically Meaningful The equation: $$\text{PSD}[k] = \frac{|X[k]|^2}{N_{\text{FFT}} \cdot f_s \cdot U}$$ is derived from first principles and ensures that the u...
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Direction of Arrival (DoA) Online Simulator (using MUSIC)

Interactive DOA Simulator X-axis XY angle (deg): 45 XZ angle (deg): 30 Noise: 0.05 Y-axis XY angle (deg): 60 YZ angle (deg): 45 Noise: 0.05 Z-axis XZ angle (deg): 60 YZ angle (deg): 30 Noise: 0.05 Estimated DOA (deg): 0 Simulation Workflow and Mathematical Background This simulator demonstrates Direction of Arrival (DOA) estimation using three-axis sensor signals (X, Y, Z), Maximal Ratio Combining (MRC) , and the MUSIC algorithm . It allows interactive control of signal angles and noise for teaching purposes. 1. Signal Generation A pure sinewave signal of frequency f is projected onto three axes using user-defined angles in different planes: X-axis: θ XY , θ XZ Y-axis: θ XY , θ YZ Z-axis: θ XZ , θ YZ Mathematically, for each time sample t : x(t) = s(t) * cos(θ_xy_x) * cos(θ_xz_x) + n_x(t) y(t) = s(t) * sin(θ_xy_y) * cos(θ_yz_y) + n_y(t) z(t) = s(t) * sin(θ_xz_z) * sin(θ_yz_z) + n_z(t) wh...
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Power Spectral Density Calculation Using FFT in MATLAB

📘 📘 Overview 🧮 🧮 Steps to calculate 💻 🧮 MATLAB Codes 📚 📚 Further Reading Power spectral density (PSD) tells us how the power of a signal is distributed across different frequency components, whereas Fourier Magnitude gives you the amplitude (or strength) of each frequency component in the signal. Steps to calculate the PSD of a signal Firstly, calculate the fast Fourier transform (FFT) of a signal. Then, calculate the Fourier magnitude (absolute value) of the signal. Square the Fourier magnitude to get the power spectrum. To calculate the Power Spectral Density (PSD), divide the squared magnitude by the product of the sampling frequency (fs) and the total number of samples (N). Formula: PSD = |FFT|^2 / (fs * N) Sampling frequency (fs): The rate at which the continuous-time signal is sampled (in Hz). ...
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OFDM Symbols and Subcarriers Explained

This article explains how OFDM (Orthogonal Frequency Division Multiplexing) symbols and subcarriers work. It covers modulation, mapping symbols to subcarriers, subcarrier frequency spacing, IFFT synthesis, cyclic prefix, and transmission. Step 1: Modulation First, modulate the input bitstream. For example, with 16-QAM , each group of 4 bits maps to one QAM symbol. Suppose we generate a sequence of QAM symbols: s0, s1, s2, s3, s4, s5, …, s63 Step 2: Mapping Symbols to Subcarriers Assume N sub = 8 subcarriers. Each OFDM symbol in the frequency domain contains 8 QAM symbols (one per subcarrier): Mapping (example) OFDM symbol 1 → s0, s1, s2, s3, s4, s5, s6, s7 OFDM symbol 2 → s8, s9, s10, s11, s12, s13, s14, s15 … OFDM sym...
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MUSIC Algorithm Explained (with MATLAB + Simulator)

Practical Implementation of the MUSIC Algorithm The focus is on how the algorithm works computationally , not just theory, and it explains the denominator (a H E n E n H a) mathematically and intuitively. 1. Introduction The MUSIC (Multiple Signal Classification) algorithm is a high-resolution method used in signal processing and array processing to estimate the Direction of Arrival (DOA) of signals received by a sensor array. Unlike classical beamforming methods, MUSIC uses eigenvector decomposition of the covariance matrix to separate the signal subspace and noise subspace , allowing it to achieve much higher angular resolution. In practical implementations, MUSIC works by: Simulating or collecting array signals Computing the covariance matrix Performing eigenvalue decomposition Separating signal and noise subspaces Scanning possible angles using a steering vector Constructing a pseudo-spectrum where peaks indicate signal directions 2. Signal Mo...
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