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.