I am new to radars and I am trying to understand their functioning. I have understood that after the so-called pre-processing of the baseband signals we get from the radar the so-called 4D radar cube measurement (range, relative radial velocity, azimuth, and elevation). After this step there is the Target List creation. The goal of this part is to go from the 4D radar cube to a target list.

One of the tools to get this part done is the Constant False Alarm Rate (CFAR) power detection. I have read that in this step the power values of the radar cube are compared with a threshold that is based on a locally calculated statistic of the noise power.

Therefore, my questions are the following:

1. does the CFAR threshold depend on the type of radar used?
2. what are the other variables that influence the choice/change of this threshold (e.g., atmospheric conditions)?

I’ll add a different perspective as someone who designs operational radars for a living:

Yes, the CFAR threshold absolutely depends on the radar system at hand. Ignoring the academic topics of detection theory and such which we use to set the CFAR bias, operational radars need a bit more than statistical rigor. Most commonly you’ll see CFAR detectors implemented in what’s called “cell-averaging CFAR” (CA-CFAR) where a local noise floor is estimated using a sliding window, and then some bias term is added such that a specific probability of detection is achieved given some probability of false alarm. There are several types of CA which are all basically just riffs on estimating a local mean. Depending on the operational environment, you may prefer some methods over the others.

For you second question, obviously the thermal noise of the system is a driving factor in choosing how you calculate your CFAR, but there are loads of others.

1. How stationary is the noise floor?
2. Are there a lot of targets closely spaced together?
3. How wide/extended are your targets after pulse compression? You’ll want to set up a “guard band” if they’re more than a few samples wide
4. Are you expecting any interference of any sort? This may introduce a non-stationary response that you should adjust for
5. What kind of clutter are you dealing with (ground, sea, airborne), and can you sufficiently cancel it? I

Here’s an example: Let’s say I have one low power target and one high power amplitude target in very close proximity. If I just do a regular sliding window, the power from the big target will corrupt/skew my moving average very high, and therefore I might miss the detection of the small target. In this case you would want to use some form of censoring or two-pass CFAR to try to alleviate this issue.

Another example: Let’s say you have a lot of sea clutter with nasty sidelobes that you can’t 100% remove. This may skew your local noise floor, so with the help of some clutter mapping you may be able to construct a CFAR implementation that purposefully excludes the clutter region.

I recognized I’ve used some jargon in this post, but these are all pretty standard things in the radar community, so do consult a textbook/IEEE papers if you’re looking for more specifics.

• Thanks for the response! This is very helpful :) Sep 25, 2021 at 0:42
• I agree, your answer really shed some light in the understanding of CFAR for me. As you suggested, the next step is to look at some papers/books. Don't hesitate to add resources that you find useful. Just by quickly googling I found for example a Seminar only on Radar Clutter Modelling (ieeexplore.ieee.org/xpl/conhome/4476384/proceeding). Which I did not know it existed before you mentioned it. Sep 29, 2021 at 9:22

The main goal of a radar is target detection. If you were to frame this as a mathematical problem, then you would model this as a hypothesis testing problem. Let's assume a simple case: single target surrounded in background noise, where the noise is additive white Gaussian. Then, mathematically, we can write this as: \begin{align} y(t) &= x(t) + b(t) + n(t), \quad \mathcal{H}_1: \mbox{if there is a target} \\ y(t) &= b(t) + n(t), \quad \mathcal{H}_0: \mbox{no target}, \end{align} where $$x(t)$$ is the received signal from the target, $$n(t)$$ and $$b(t)$$ are due to receiver noise and background clutter. The general approach is to compute a test-statistic and the distribution of the test statistic by taking the log-likelihood ratio test (LRT) or generalized log-likelihood ratio test (GLRT) if there are some unknowns. If the distribution of the test-statistic under the null hypothesis ($$\mathcal{H}_0$$) does not depend on the covariance of clutter and thermal noise, nor on the transmitted signal, then it is called a CFAR detector, i.e., if we compute expression for probability of false alarm, and it turns out to be independent of the properties of noise or clutter, then the detector is a CFAR detector. This is of huge advantage and reduces computation complexity because one does not have to compute this distribution for every cell.

Edit: CFAR threshold is determined by the probability of false alarm value that one selects for a radar. For example, if the $$P_{FA}=0.05$$, then the threshold is obtained by finding the inverse cumulative distribution function at that $$P_{FA}$$. This is exactly why you need to find the distribution of the test statistic under the null-hypothesis.

• thanks for your comment, it is useful but I am not sure I got the answer I was looking for. What you mean is: if we compute expression for probability of false alarm, and it turns out to be independent of the properties of noise or clutter, then the detector is a CFAR detector that is independent from noise or clutter. So what you meant is: we cannot say in advance what influences the CFAR threshold? Sep 22, 2021 at 16:18
• CFAR threshold is determined by the probability of false alarm value that one selects for a radar. For example, if the $P_{FA} = 0.05$, then the threshold is obtained by finding the inverse cumulative distribution function at that $P_{FA}$. This is exactly why you need to find the distribution of the test statistic under the null-hypothesis. Sep 23, 2021 at 4:42