# Pulse Doppler Radar: how to filter its Range-Doppler matrix?

I want to simulate a Pulse Doppler Radar with medium pulse repetition frequency (PRF about $100\textrm{ kHz}$, about $500$ pulses in pulse train).

It's rather powerful, and should discriminate targets with $1\textrm{ m}^2$ RCS in ranges up to $200\textrm{ km}$. Okay, let's build its range-speed image (about $\pm 750\textrm{ m/s}$ in speed dimension, about $1500\textrm{ m}$ in range).

But there is a problem: when there are some targets nearby (about $10\textrm{ km}$) they give not just a peak that can exceed the discrimination threshold, but a cross-like figure (sidelobes in range dimension, end, especially, sidelobes in speed dimension). And if the target is close enough, freaky sidelobes still can exceed the threshold and be treated as target candidates.

Even if I use window function with heaviest sidelobe-cancelling effect (Blackman-Harris), the sidelobes became smaller bus weren't wided out completely (and still give me ghost targets).

I think that I missed some important step in Range-Doppler matrix processing. Maybe some additional filtering. Cannot you tell me, what shoud I do to get rid of the sidelobes? Here's some illustration: on the top row there are Range-Doppler matrices for different PRF ratios, and on the bottom row there is the range-speed matrix slice by speed (left) and range(right) in the target peak. The speed dimension annoyes me most = )

P.S. The number of DFT bins: 540 by speed, about 1200 by range (1200, 1280 and 1360, because PRFs varies).

About the size of the sidelobes -- I don't know how to add the colorbar to such a multi-plot figure, but I've added two additional plots to the bottom. In the left-bottom corner there is the signal power with different speeds (with the fixed range of the max peak range) and in the right-bottom corner there is the signal power with different ranges (with the fixed speed of the max peak speed). The units are power dB.

• can you add the colorbar, so that one can assess the seriousness of the sidelobes, as well as specify the number of DFT bins in each applicable direction? – Marcus Müller Feb 23 '17 at 18:18
• The number of DFT bins: 540 by speed, about 1200 by range (1200, 1280 and 1360, because PRFs varies). About the size of the sidelobes -- I don't know how to add the colorbar to such a multi-plot figure, but I've added two additional plots to the bottom. In the left-bottom corner there is the signal power with different speeds (with the fixed range of the max peak range) and in the right-bottom corner there is the signal power with different ranges (with the fixed speed of the max peak speed). The units are power dB. – Felix Feb 23 '17 at 18:58
• ah, cool. If you've got time, please edit your question to include all the info you're giving in the comments – makes it easier to read for the fellow signal processing folks on here :) – Marcus Müller Feb 23 '17 at 19:51

## 1 Answer

Two suggestions that may independently, or combined, help to solve your problem.

1. Consider using a different window/weighting function for your FFT processing. There are window functions with low uniform sidelobes such as the Chebyshev window. This window function allows for selection of a constant sideline level response.
2. It sounds like you are using a fixed detection threshold, consider using an adaptive detection threshold so that the threshold can vary with the combination of background noise and sidelobe artifacts. Mathworks has a pretty good description for a simple case at Constant False Alarm Rate (CFAR) Detection.
• This is already a good answer, and this is an old question, so just to add some discussion: OP wrote that high sidelobes appear in particular in the situation of two nearby target peaks, right? This means that there is some "coherence effect" wherein the sidelobes from both peaks interfere constructively. So it may be good to consider how these targets are exactly simulated, I think. – mateC Sep 9 '19 at 8:45