Fisher information for a complex Gaussian random variable: beamforming applications for wave propagation in a random medium
Fisher information for a complex Gaussian random variable: beamforming applications for wave propagation in a random medium
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DOI：
10.1109/tsp.2005.857046
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发表时间：
2005-11
影响因子：
5.4
通讯作者：
S. Collier
中科院分区：
文献类型：
--
作者：
S. Collier
我们推导了一类特殊的复高斯随机变量的Fisher信息的一般表达式，其均值和协方差可以用一个特定的参数化线性变换表示。确定性未知参数的情况下被认为是。这类信号描述了在均匀或非均匀介质中传播的信号，也出现在许多波束成形应用中。这里推导出的Fisher信息涵盖了广泛的先前推导出的，众所周知的结果复高斯信号在均匀介质中传播，也适用于最近的模型在非均匀介质中传播的信号。研究了单色平面波和球面波在随机介质中传播时方位角和仰角的估计与干扰参数的估计解耦的条件。对于在各向异性介质中的传播，人们发现，在一般情况下，整个未知参数集的Cramer-Rao下界（CRLB）将耦合。对于在各向同性介质中传播的特殊情况，发现对于平面波，到达角的CRLB将与其他未知数的CRLB近似解耦，而对于球面波，到达角的CRLB将总是耦合到所有其他未知数的CRLB，尽管在某些条件下耦合可以最小化。
We derive a general expression for the Fisher information for a special class of complex Gaussian random variables, whose mean and covariance may be expressed in terms of a specific parameterized linear transformation. The deterministic unknown parameter case is considered. This class is descriptive of signals that propagate in a homogeneous or inhomogeneous medium and also occurs in numerous beamforming applications. The Fisher information derived here encompasses a wide range of previously derived, well-known results for complex Gaussian signals propagating in a homogeneous medium and is also applicable to more recent models for signals propagating in an inhomogenous medium. The conditions for the estimates of the azimuth and elevation to decouple from the estimates of the nuisance parameters are studied for monochromatic plane-wave and spherical-wave propagation in a random medium. For propagation in an anisotropic medium, it is found that, in general, the Cramer-Rao lower bounds (CRLBs) of the entire unknown parameter set will be coupled. For special cases of propagation in an isotropic medium, it is found that for plane waves, the CRLBs of the angles of arrival will be approximately decoupled from the CRLBs of the other unknowns, and for spherical waves, the CRLBs of the angles of arrival will be always be coupled to the CRLBs of all other unknowns, although the couplings may be minimized under certain conditions.