Decentralized largest eigenvalue test for multi-sensor signal detection

Multi-sensor signal detection based on the the largest eigenvalue of the received sample covariance matrix is known to be optimal (asymptotically in the sample size and under Gaussian assumption) in the Neyman-Pearson sense. In this paper we propose two decentralized algorithms to implement this type of signal detector in distributed wireless networks without fusion center. The proposed solutions are based on iterative numerical algorithms (power method and Lanczos algorithm), implemented in a decentralized manner with matrix and vector products computed via average consensus. Numerical results show that such methods, in particular the decentralized Lanczos method, outperform the recently proposed decentralized energy detector after a very small number of iterations.

[1]  Roberto Garello,et al.  Cooperative spectrum sensing based on the limiting eigenvalue ratio distribution in wishart matrices , 2009, IEEE Communications Letters.

[2]  Thomas Kailath,et al.  Detection of signals by information theoretic criteria , 1985, IEEE Trans. Acoust. Speech Signal Process..

[3]  Stephen P. Boyd,et al.  Randomized gossip algorithms , 2006, IEEE Transactions on Information Theory.

[4]  Roberto Garello,et al.  Performance of Eigenvalue-Based Signal Detectors with Known and Unknown Noise Level , 2011, 2011 IEEE International Conference on Communications (ICC).

[5]  Nicholas R. Jennings,et al.  Consensus acceleration in multiagent systems with the Chebyshev semi-iterative method , 2011, AAMAS.

[6]  Robb J. Muirhead,et al.  Latent Roots and Matrix Variates: A Review of Some Asymptotic Results , 1978 .

[7]  Alfred O. Hero,et al.  Decomposable Principal Component Analysis , 2009, IEEE Transactions on Signal Processing.

[8]  G. G. Stokes.  "J." , 1890, The New Yale Book of Quotations.

[9]  Boaz Nadler,et al.  Non-Parametric Detection of the Number of Signals: Hypothesis Testing and Random Matrix Theory , 2009, IEEE Transactions on Signal Processing.

[10]  Slawomir Stanczak,et al.  Fast average consensus in clustered wireless sensor networks by superposition gossiping , 2012, 2012 IEEE Wireless Communications and Networking Conference (WCNC).

[11]  Keith Q. T. Zhang.  Advanced Detection Techniques for Cognitive Radio , 2009, 2009 IEEE International Conference on Communications.

[12]  Soummya Kar,et al.  Distributed Consensus Algorithms in Sensor Networks: Quantized Data and Random Link Failures , 2007, IEEE Transactions on Signal Processing.

[13]  Masoumeh Nasiri-Kenari,et al.  Multiple antenna spectrum sensing in cognitive radios , 2010, IEEE Transactions on Wireless Communications.

[14]  Anna Scaglione,et al.  Distributed Principal Subspace Estimation in Wireless Sensor Networks , 2011, IEEE Journal of Selected Topics in Signal Processing.

[15]  Pascal Bianchi,et al.  Performance of Statistical Tests for Single-Source Detection Using Random Matrix Theory , 2009, IEEE Transactions on Information Theory.

[16]  Gene H. Golub,et al.  Matrix computations , 1983 .

[17]  Richard M. Murray,et al.  Consensus problems in networks of agents with switching topology and time-delays , 2004, IEEE Transactions on Automatic Control.

[18]  Sergio Barbarossa,et al.  Distributed Consensus Over Wireless Sensor Networks Affected by Multipath Fading , 2008, IEEE Transactions on Signal Processing.

[19]  Yonghong Zeng,et al.  Eigenvalue-based spectrum sensing algorithms for cognitive radio , 2008, IEEE Transactions on Communications.

[20]  Zhiqiang Li,et al.  A Distributed Consensus-Based Cooperative Spectrum-Sensing Scheme in Cognitive Radios , 2010, IEEE Transactions on Vehicular Technology.

[21]  Yousef Saad,et al.  Iterative methods for sparse linear systems , 2003 .

[22]  Olav Tirkkonen,et al.  Cooperative spectrum sensing of OFDM signals using largest eigenvalue distributions , 2009, 2009 IEEE 20th International Symposium on Personal, Indoor and Mobile Radio Communications.

[24]  Andrea Montanari,et al.  Gossip PCA , 2011, SIGMETRICS.

[25]  Stephen P. Boyd,et al.  Fast linear iterations for distributed averaging , 2003, 42nd IEEE International Conference on Decision and Control (IEEE Cat. No.03CH37475).