Energy Distribution of Multiple Target Signal With Application to Target Counting

The paper extends our earlier work on the sum of a complex Gaussian and the product of two complex Gaussians (a scalar and a vector) by incorporating multiple targets. We derive the joint probability density function (pdf) of the resulting vector, after which we derive the pdf, cumulative distribution function (cdf), and moments of the square norm of the vector (signal energy). A novel integral function is introduced to make the analysis possible. The case of high signal-to-noise ratio (SNR) and a single observation has been treated as a special case. The obtained theoretical results are then used to develop maximum likelihood and moment matching estimators, for estimating the number of targets. Numerical results validate the obtained results and characterize the performance of the proposed estimators.

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