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Keywords = complex matrixed samples
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17 pages, 934 KB  
Article
Complex Parameter Rao and Wald Tests for Assessing the Bandedness of a Complex-Valued Covariance Matrix
by Zhenghan Zhu
Signals 2024, 5(1), 1-17; https://doi.org/10.3390/signals5010001 - 4 Jan 2024
Viewed by 1658
Abstract
Banding the inverse of a covariance matrix has become a popular technique for estimating a covariance matrix from a limited number of samples. It is of interest to provide criteria to determine if a matrix is bandable, as well as to test the [...] Read more.
Banding the inverse of a covariance matrix has become a popular technique for estimating a covariance matrix from a limited number of samples. It is of interest to provide criteria to determine if a matrix is bandable, as well as to test the bandedness of a matrix. In this paper, we pose the bandedness testing problem as a hypothesis testing task in statistical signal processing. We then derive two detectors, namely the complex Rao test and the complex Wald test, to test the bandedness of a Cholesky-factor matrix of a covariance matrix’s inverse. Furthermore, in many signal processing fields, such as radar and communications, the covariance matrix and its parameters are often complex-valued; thus, it is of interest to focus on complex-valued cases. The first detector is based on the complex parameter Rao test theorem. It does not require the maximum likelihood estimates of unknown parameters under the alternative hypothesis. We also develop the complex parameter Wald test theorem for general cases and derive the complex Wald test statistic for the bandedness testing problem. Numerical examples and computer simulations are given to evaluate and compare the two detectors’ performance. In addition, we show that the two detectors and the generalized likelihood ratio test are equivalent for the important complex Gaussian linear models and provide an analysis of the root cause of the equivalence. Full article
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24 pages, 559 KB  
Article
Cooperative Spectrum Sensing Using Eigenvalue Fusion for OFDMA and Other Wideband Signals
by Dayan A. Guimarães, Carlos R. N. Da Silva and Rausley A. A. De Souza
J. Sens. Actuator Netw. 2013, 2(1), 1-24; https://doi.org/10.3390/jsan2010001 - 7 Jan 2013
Cited by 21 | Viewed by 7749
Abstract
In this paper, we propose a new approach for the detection of OFDMA and other wideband signals in the context of centralized cooperative spectrum sensing for cognitive radio (CR) applications. The approach is based on the eigenvalues of the received signal covariance matrix [...] Read more.
In this paper, we propose a new approach for the detection of OFDMA and other wideband signals in the context of centralized cooperative spectrum sensing for cognitive radio (CR) applications. The approach is based on the eigenvalues of the received signal covariance matrix whose samples are in the frequency domain. Soft combining of the eigenvalues at the fusion center is the main novelty. This combining strategy is applied to variants of four test statistics for binary hypothesis test, namely: the eigenvalue-based generalized likelihood ratio test (GLRT), the maximum-minimum eigenvalue detection (MMED), the maximum eigenvalue detection (MED) and the energy detection (ED). It is shown that the eigenvalue fusion can outperform schemes based on decision fusion and sample fusion. A tradeoff is also established between complexity and volume of data sent to the fusion center in all combining strategies. Full article
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