# MIMO Radar - Using statistical properties of the Fourier transform phase for detection

I currently researching the phase (between real and imaginary part) of the fourier transformation. It seems that one can use it for detection.

For the signal processing I use two fft transforms. One to compress range and one to compress azimuth. Then I want to apply detection. At this point calibration and corrections are done. The scene is stationary anyway thus one can ignore doppler correction.

Claim: For a stationary target the phase of the cross-fft is stable and I can do the following:

$$\text{Var}(\angle_N(Re(X_{i,j}), Im(X_{i,j})) = \sigma_{i,j}$$,

whereas $$N$$ the number of used samples and $$X$$ is the spectrum of the signal (after cross fft) with dimension $${i,j}$$ for range and azimuth.

For a phase stable pixel of the data matrix the variance $$\sigma$$ should be low. To find the most stable pixels I can do:

$$f(\sigma) = \text{sort}(\sigma_{i,j})< T = \text{detections}$$,

whereas $$T$$ can be constant or adaptive.

The method is intuitive and easy to implement. It cost alot ressources, but this point can be excluded at this point.

I cannot find any paper where someone researched ground based radars that image a stationary scene (forest, house, whatever) without using SAR. Also I cannot find a paper that exploit the phase of the fourier transformation.

Has anyone a clue if this is worth to investigate further or do I missunderstand a common pitfall which is maybe too obvious for everyone else? I am grateful for papers, references, ideas, corrections, ...

This is non-profit academic research (thesis)

• How do you compute the variance of a single sample? Commented Jul 12, 2023 at 20:26
• I dont, I store N frames of the recorded scene and calculate the variance with 12-25 of them.
– magi
Commented Jul 18, 2023 at 15:35
• It's not clear to me what you are proposing, and I am going to guess from the lack of any other responses that it is not clear to others either. The idea of a phase-only detector seems far-fetched and, honestly, like a bad idea. Commented Jul 18, 2023 at 18:46