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Compressed Sensing in DOA processing


Junior Member level 2
Apr 24, 2015
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Hello everybody,
I'm trying to apply the compressed sensing theory (CoSaMP algorithm) to the DOA estimation in FMCW ULA (made of 48 elements). In the dechirped signals processing I use a first FFT to solve the range and then instead to apply another FFT along the cross-range direction (following the standard 2D FFT) I use CoSaMP algorithm to get the direction of arrival bin by bin.

If we refer to the equation (per each single range bin): y = Φ Ψ s

y contains all the 48 FFT complex values, Φ is the measurement matrix that I use to select 30 out 48 antennas, Ψ is the representing FFT basis matrix, and s the sparse solution I look for (the same length of y vector)

In the below figure 1 the range-angle radar images that I got using: a)CoSaMP (30 out 48 randomly chosen antennas) on the real part of the first (range) FFT complex output and b)FFT of order 180 on the first (range) FFT complex output. I have two main questions:

  1. Is it possible to run the CoSaMP (or another CS algorithm) on complex values? As you can see in the image1 I got a symmetrical output due to the fact I'm applying the CoSaMP to the real values of the complex FFT output (range).
  2. How I can improve the resolution in the sparse domain? This is subjected to the basis matrix dimension (in my case 48*48).

Thanks, regards, and happy New Year

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