NSRD/RD - MUSIC algorithm implementation on an URA.

Hello dear Community,

Has anyone tried implementing RD-MUSIC or NSRD-MUSIC algorithm to estimate the direction of arrival angle. I am trying to implement NSRD algorithm given in below link but unable to get proper results.

https://www.hindawi.com/journals/ijap/2015/127621/

Thanks in advance,

Kumar Vishal

Answer 1

[Garmit Pant]

Hello Kumar Vishal Rai

I understand that you are trying to implement the NSRD-MUSIC algorithm for estimation of the direction of arrival angle in MATLAB.

While the implementation of this particular algorithm is not present in MATLAB, the task of estimation of DOA angle can be achieved using in-built MATLAB functions. 2D direction of arrival can be estimated by using the “phased.MUSICEstimator2D” System object. The code snippet below illustrates how to estimate the DOAs of two signals.

% Define the frequencies of two signals in Hz 
f1 = 450.0;  
f2 = 600.0;  

% Define the direction of arrival (DOA) of the two signals in degrees 
% DOA is specified as [Azimuth; Elevation] 
doa1 = [-37; 0]; % DOA of the first signal 
doa2 = [17; 20]; % DOA of the second signal 

% Define the carrier frequency of the signals in Hz 
fc = 150e6;  

% Calculate the wavelength of the signals using the speed of light 
c = physconst('LightSpeed'); % Speed of light in m/s 
lam = c / fc; % Wavelength in meters 

% Define the sampling frequency in Hz 
fs = 8000;  

% Create a Uniform Rectangular Array (URA) of antennas 
array = phased.URA('Size', [11 11], 'ElementSpacing', [lam/2 lam/2]); 
array.Element.FrequencyRange = [50.0e6 500.0e6]; % Set the operational frequency range of the array elements 

% Generate time vector for 1 second duration with the specified sampling frequency 
t = (0:1/fs:1).'; % Time vector 

% Generate the two signals as cosine waves at their respective frequencies 
x1 = cos(2*pi*t*f1); % Signal 1 
x2 = cos(2*pi*t*f2); % Signal 2 

% Simulate the reception of the plane waves by the antenna array 
% 'collectPlaneWave' collects the plane waves coming from specified DOAs 
x = collectPlaneWave(array, [x1 x2], [doa1, doa2], fc); 

% Add complex Gaussian noise to the received signals 
% Noise is complex to simulate real-world scenarios (I and Q channels) 
noise = 0.1*(randn(size(x)) + 1i*randn(size(x))); % Noise with 0.1 scaling factor 

% Create a MUSIC estimator object for 2D DOA estimation 
estimator = phased.MUSICEstimator2D('SensorArray', array, ... 
    'OperatingFrequency', fc, ... 
    'NumSignalsSource', 'Property', ... 
    'DOAOutputPort', true, 'NumSignals', 2, ... 
    'AzimuthScanAngles', -50:.5:50, ... 
    'ElevationScanAngles', -30:.5:30); 

% Estimate the DOAs of the incoming signals using the MUSIC algorithm 
% The noisy signals are used as input 
[~, doas] = estimator(x + noise); 

% Plot the spatial spectrum estimated by the MUSIC algorithm 
% This plot helps visualize the directions from which the signals are arriving 
plotSpectrum(estimator); 

MATLAB also has the functionality to implement the MUSIC algorithm for DOA estimation of signals on ULA. You can use the “musicdoa” function of the Phased Array System Toolbox to do the same.

For further understanding, refer to the links to the MATLAB documentation given below:

1. “phased.MUSICEstimator2D” System object- https://www.mathworks.com/help/releases/R2022a/phased/ref/phased.musicestimator2d-system-object.html
2. “musicdoa” function – https://www.mathworks.com/help/releases/R2022a/phased/ref/musicdoa.html
3. Documentation on Super Resolution DOA – https://www.mathworks.com/help/releases/R2022a/phased/ug/music-super-resolution-doa-estimation.html

I hope you find the above explanation and suggestions useful!

[Garmit Pant]

@Kumar Vishal Rai if the answer was helpful, please consider accepting it.