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.

中文翻译：

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多目标信号的能量分布及其在目标计数中的应用

该论文通过合并多个目标扩展了我们早期关于复数高斯和两个复数高斯（一个标量和一个向量）的乘积之和的工作。我们推导出结果向量的联合概率密度函数 (pdf)，然后推导出 pdf、累积分布函数 (cdf) 和向量的平方范数的矩（信号能量）。引入了一个新的积分函数，使分析成为可能。高信噪比 (SNR) 和单一观测的情况被视为特例。然后将获得的理论结果用于开发最大似然和矩匹配估计器，用于估计目标的数量。数值结果验证了所获得的结果并表征了所提出的估计器的性能。