## 10.1 Introduction

One of most important signal processing objectives in target detection in locally varying homogeneous noise or clutter is to maintain the false-alarm rate as a constant. Constant false-alarm rate (CFAR) processing is one of maybe half a dozen indispensable types of signal processing for the successful operation of a radar system.

The classic theory of target detection assumes that the noise is distributed as Gaussian with unknown power. When an antenna sweeps the surveillance sectors, the radar receives noise and clutter returns, and they may not be distributed as Gaussian; clutter may be distributed as lognormal, Weibull, gamma or K distribution, or the like. We shall investigate a few CFAR processing methods in Gaussian noise and Weibull clutter.

## 10.2 Cell-Averaged CFAR (CA-CFAR)

Finn and Johnson [1] have reported a CFAR processing method for use when the target signal received is embedded in Gaussian noise of unknown power level. The probability density function of noise is Gaussian; the unknown is the locally varying noise power. We follow their analysis.

When the input to a square-law detector is narrowband Gaussian noise with zero mean and unknown variance (noise power), the output is distributed as exponential with unknown variance [2-4]. (See Figure 10.1.)

Figure 10.1: Probability density functions: Gaussian and exponential

We note that the mean of the exponential is E{y}= ? y, and the average of the random variable y is equal to the standard deviation of y. In radar literature we call f y(y) the probability density...

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