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I will describe now a low cost system for setting an exponential adaptive threshold in radar, using positive feedback
The great challenge in radar is separating targets from clutter (the inherent, ever present noise, interference and unwanted echos).
To distinguish between targets and clutter in radar, received echos are compared with a preset threshold: if the received signal is above the threshold, it is a target; else it is clutter.

Setting the value of the threshold is difficult- if the threshold is too low, the radar will be innundated in false alarms; if the threshold is too high, desired targets will be blocked together with the clutter, that is to throw away the baby with the water...

In radar techspeak, one refers to the probabity of detection versus the false alarm rate. As the threshold increases, the former increases whereas the latter decreases.

The groundbreaking research on the subject is detailed in Marcum, J. I. : A Statistical Theory of Target Detection by Pulsed Radar. IRE Trans., vol. IT-6, April 1960.

Setting the optimal threshold is not good enough: the radar operates in an ever-changing environment, with a variable level of received clutter. The solution is an adaptive threshold. That is, the threshold varies aiming to keep the probability of detection and the false alarm rate, at predefined desired values.

How then to compute or evaluate the optimal threshold? You can use a microcomputer, but sometimes there are real-life limitations, such as cost, power consumption, available space, etc.

The solution I devised for this particular design, to address project's requirements, was a simple circuit using positive feedback to implement the adaptive, variable threshold.

And this is how it works: received signals 11 are compared with a threshold 12 in comparator 1. The comparator output 13 is a digital signal, 1 if the decision is "target" and 0 if the decision is "only clutter". The signal 13 is then transferred for further processing in the radar (you thought radar is that simple, did you?).

The signal 13 is also applied to a low pass filter 2 to generate a signal representing the average value of the decision process in the comparator 1.

The value of this analog signal is indicative of the probability of detection and the false alarm rate:
A strong signal indicate many (possibly too many) target detection decisions; a weak signal indicates a low rate of detection. An analog adder 3 subtracts a fixed value 31 from the above average.
The value 31 defines the desired rate of targets detection.

The output of the adder is positive if the rate of detection is too high (the threshold 12 is too low), and negative if the rate is too low (the threshold 12 is too high).

This signal can be used in a closed loop control system, to correct the detection rate and to bring it to a desired value:
One can apply the signal to the comparator 2 as the threshold value 12. A closed control loop is thus implemented: if the detection rate is too high, the duty cycle of signal 13 increases; the signal at the output of unit 2 increases as well, so ultimately the threshold 12 increases, to bring back the detection rate to the desired (lower) value.

However, an essential component is missing in the above system:
According to Marcum, the statistical relationship between the value of the threshold and the detection rate is exponential rather than linear. For the circuit to implement its desired task, an exponential signal is required.

Here we implemented an exponential rate of change using a positive feedback circuit.
Electronics engineers usually fight positive feedback, which causes oscillations and other undesired effects (on the other hand, building simple oscillators is easy- just build an amplifier and let it do its worst).

In this circuit, the positive feedback amplifier 4 creates an exponentially increasing signal 41 which is applied as the threshold 12 to the comparator 1.
The absolute value of signal 41 increases exponentially, as a positive signal for a positive value of signal 33, or a negative signal for negative values of signal 33.

Thus, a simple, low cost circuit performs a complex, useful task. And it works, the project including this little circuit was a success.

The radar operation described above is only intended to present background material for understanding the invention detailed here.
It is not intended as a course in radar. Radar is an universe unto itself, and the interested reader can learn radar elsewhere, if they so desire.

When writing about radar, one must mention Dr Serge Landsman, the famous radar expert. He teached the Israel industry radar, and educated the first generation of radar professionals here.
I had the privilege of working as a consultant and subcontractor for Dr Landsman. When we first met, after a short discussion, he pronounced his unforgettable sentence: "Marc, you don't know radar." I was greatly offended and felt insulted, but also challenged.
So I was stimulated to learn radar, and I did.

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### Disclaimer

This is not professional advice. Before doing anything, you should consult with professionals: Engineers, Accountant, Patent attorney, Lawyer, Sales and marketing experts, PR, Product design, Safety and standards consultants, etc.
You should learn as much as possible about the subject of your interest: from other sites on the Internet, as well as books, periodicals, products and services now offered on the market, etc.

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### Marc Zuta, Electronics Engineer & Patent Attorney

P.O. Box 2162, Petah Tikva 4912003, ISRAEL
zutam@yahoo.com

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