A probabilistic model of the radar signal-to-clutter and noise ratio for Weibull-distributed clutter

We consider four effects relevant to the determination of the ratio of radar signal to clutter and noise. These effects are atmospheric turbulence, target fluctuations based on the Swerling models, zero-mean Gaussian background and receiver noise, and Weibull-distributed clutter. Radar return signal levels are affected by target fluctuations and atmospheric turbulence, characterized by target fluctuations according to the Swerling models and a lognormal distribution, respectively. Since these distributions are not independent and identically distributed (IID), they cannot be simply added, and must be treated by combining them in a manner similar to convolution. Also, clutter and noise are not IID, and must be combined in a similar way. The ratio of these two combinations comprises a probabilistic model of the ratio of radar signal to clutter and noise. This ratio is the probability that a given signal level will be achieved in the presence of atmospheric and target scintillations divided by the probability that a given clutter and noise level will be observed. To determine the ratio of the actual signal to clutter and noise, we must multiply these probabilities by the mean powers resulting from these phenomena, as will be shown later. We treat several cases of interest by varying the average radar cross section, the log intensity standard deviation of turbulence, the radar threshold-to-noise and signal-to-noise ratios, and the distribution of Weibull clutter mentioned above.