论文标题

复杂值图信号的广泛线性MMSE估计

Widely-Linear MMSE Estimation of Complex-Valued Graph Signals

论文作者

Amar, Alon, Routtenberg, Tirza

论文摘要

在本文中,我们考虑了恢复具有复杂值的随机图信号的问题。对于一般的贝叶斯对复合值载体的估计,众所周知,与线性最小值MSE(LMMSE)估计器相比,广泛的最小值均值错误(WLMMSE)估计器可以达到均值率越低的均值错误(MSE)。受WLMMSE估计量的启发,在本文中,我们开发了图形信号处理(GSP)-WLMMSE估计器,该估计器将MSE最小化为表示图形滤波器的两通道输出,即广泛线性GSP估计器。我们讨论了提出的GSP-WLMMSE估计量的特性。特别是,我们表明GSP-WLMMSE估计器的MSE始终等于或低于GSP-LMMSE估计器的MSE。 GSP-WLMMSE估计器基于图频域中的对角线协方差矩阵,因此与WLMMSE估计器相比,复杂性降低了。当使用基于培训数据集的这些估计器的样本均值版本时,此属性尤为重要。然后,我们陈述了低复杂性GSP-WLMMSE估计器与WLMMSE估计器一致的条件。在模拟中,我们研究了两个合成估计问题(使用线性和非线性模型)以及电力系统中的状态估计问题。对于这些问题,结果表明,GSP-WLMMSE估计器的表现优于GSP-LMMSE估计器,并且具有与WLMMSE估计器相似的性能。

In this paper, we consider the problem of recovering random graph signals with complex values. For general Bayesian estimation of complex-valued vectors, it is known that the widely-linear minimum mean-squared-error (WLMMSE) estimator can achieve a lower mean-squared-error (MSE) than that of the linear minimum MSE (LMMSE) estimator. Inspired by the WLMMSE estimator, in this paper we develop the graph signal processing (GSP)-WLMMSE estimator, which minimizes the MSE among estimators that are represented as a two-channel output of a graph filter, i.e. widely-linear GSP estimators. We discuss the properties of the proposed GSP-WLMMSE estimator. In particular, we show that the MSE of the GSP-WLMMSE estimator is always equal to or lower than the MSE of the GSP-LMMSE estimator. The GSP-WLMMSE estimator is based on diagonal covariance matrices in the graph frequency domain, and thus has reduced complexity compared with the WLMMSE estimator. This property is especially important when using the sample-mean versions of these estimators that are based on a training dataset. We then state conditions under which the low-complexity GSP-WLMMSE estimator coincides with the WLMMSE estimator. In the simulations, we investigate two synthetic estimation problems (with linear and nonlinear models) and the problem of state estimation in power systems. For these problems, it is shown that the GSP-WLMMSE estimator outperforms the GSP-LMMSE estimator and achieves similar performance to that of the WLMMSE estimator.

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