## 2D-MUSIC algorithm for range-azimuth mapping in MATLAB

Started by 3 years ago●4 replies●latest reply 4 months ago●716 views``` f1 = 17000; f2 = 19000; doa1 = [40;10]; doa2 = [-60;20]; thetas = 90*pi/180 p = -pi/2:pi/180:pi/2; doa = [doa1 doa2]; fc = 18000; c = physconst('LightSpeed') lam = c/fc fs = 48000; array = phased.URA('Size',[15 12],'ElementSpacing',[lam/2 lam/2]); array.Element.FrequencyRange = [18e5 23.0e5]; fileId = fopen('D:\signal123.mat'); signal1 = fileId; %signal_reshape = reshape(signal,[],2) x = collectPlaneWave(array,[signal1,signal1],doa,fc) %noise = 0.1*(randn(size(x))+1i*randn(size(x))); estimator = phased.MUSICEstimator2D('SensorArray',array,... 'OperatingFrequency',fc,... 'NumSignalsSource','Property',... 'DOAOutputPort',true,'NumSignals',2,... 'AzimuthScanAngles',-90:.5:90,... 'ElevationScanAngles',-90:.5:90) [~,doas] = estimator(x) plotSpectrum(estimator); ```

You haven't said what the problem is. Since you are just using MATLAB's pre-packaged functions, I suggest you read the MATLAB documentation (which is typically quite good).

You seem to be getting confused between azimuth, elevation and range. In its basic form, the two dimensions in "2D" MUSIC are azimuth and elevation. (Or it can be re-parameterized into a different coordinate system, such as cone angles).

However, range is significantly different. Range is not a direction. You can still use the MUSIC algorithm to estimate delay (and therefore range), but the formulation is completely different.

One way of estimating both direction and range is using the concept of the "spatio-temporal array manifold" (google can give you plenty of information about that). However, this is very sub-optimal and better results are achieved (with much less computational effort) by simply splitting the problem into two 1D searches. First estimate range (using any method you like - you can even use MUSIC to search over a "temporal" manifold). Then you can isolate the signal subspace associated with each delay (range) using geometric projections and, for each discrete range, perform a 1D azimuth search over the spatial manifold to obtain a direction estimate.

Hi dear weetabixharry !

If I want to estimate the range only with MUSIC algorithm, how will I estimate it using MATLAB? Can you write the code here please? Further if I want to estimate the amplitudes of the incoming signals, how will I do it?

Regards,

hello @

for estimating range and azimuth, do you know any advantage of using spatio-temporal array manifold over splitting the problem into two 1d searches? i have a hard time finding online a comparison between these two techniques. for instance, (Manokhin, 2015) and (Belfiori, 2012) don't mention this 2-1D-searches technique, i believe.

@corvoattano I don't know any advantage of using the spatiotemporal array manifold (and i cannot imagine any advantage). In all the cases I ever analyzed, splitting into two 1D searches yielded better performance with less computation.

The key to understanding this is that the number of spatiotemporal snapshots is smaller than the number of ordinary (spatial) snapshots by a factor of Nc (where Nc is the code length of the spreading sequence).

So, you can't just think that the spatiotemporal manifold increases the length of the manifold vector for free. It costs a proportional drop in the number of snapshots.