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PDF's, confidence regions, and relevant statistics for a class of sample covariance-based array processors

机译:一类样本基于协方差的数组处理器的PDF,置信区域和相关统计信息

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We add to the many results on sample covariance matrix (SCM) dependent array processors by (i) weakening the traditional assumption of Gaussian data and (ii) providing for a class of array processors additional performance measures that are of value in practice. The data matrix is assumed drawn from a class of multivariate elliptically contoured (MEC) distributions. The performance measures include the exact probability density functions (PDFs), confidence regions, and moments of the weight vector (matrix), beam response, and beamformer output of certain SCM-based (SCB) array processors. The array processors considered include the SCB: (i) maximum-likelihood (ML) signal vector estimator, (ii) linearly constrained minimum variance beamformer (LCMV), (iii) minimum variance distortionless response beamformer (MVDR), and (iv) generalized sidelobe canceller (GSC) implementation of the LCMV beamformer. It is shown that the exact joint PDFs for the weight vectors/matrices of the aforementioned SCB array processors are a linear transformation from a complex multivariate extension of the standardized t-distribution. The SCB beam responses are generalized t-distributed, and the PDFs of the SCB beamformer outputs are given by Kummer's function. All but the beamformer outputs are shown to be completely invariant statistics over the class of MECs considered.
机译:通过(i)削弱传统的高斯数据假设,以及(ii)为一类阵列处理器提供在实践中有价值的附加性能指标,我们在依赖样本协方差矩阵(SCM)的阵列处理器上增加了许多结果。假定从一类多元椭圆轮廓(MEC)分布中提取数据矩阵。性能度量包括某些基于SCM的(SCB)阵列处理器的精确概率密度函数(PDF),置信区域和权重矢量的矩(矩阵),波束响应和波束形成器输出。所考虑的阵列处理器包括SCB:(i)最大似然(ML)信号矢量估计器,(ii)线性约束最小方差波束形成器(LCMV),(iii)最小方差无失真响应波束形成器(MVDR),以及(iv)广义LCMV波束形成器的旁瓣消除器(GSC)实现。结果表明,上述SCB阵列处理器的权重向量/矩阵的精确联合PDF是对标准化t分布的复杂多元扩展的线性变换。 SCB波束响应是广义的t分布,而SCB波束形成器输出的PDF由Kummer函数给出。除了波束形成器的输出外,其他所有输出均显示为所考虑的MEC类的完全不变统计量。

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