Multiple Blind Beacon Estimation of Signals of Opportunity Based on Tensor Canonical Polyadic Decomposition

Estimation of repetitive beacon sequences from signals of opportunity (SOPs) is crucial for achieving cognitive opportunistic positioning and navigation. Existing algorithms based on the Generalized Likelihood Ratio (GLR) perform maximum likelihood estimation in the frequency domain to determine the Doppler shift of each SOP and estimate the beacon sequences through signal subspace projection. In this paper, we employ a tensor decomposition framework to address this problem. Firstly, we explore the diversity of received signals in the antenna spatial domain, frequency domain, and time domain to obtain a tensor representation of the beacon sequences and construct the corresponding factor matrices with a Vandermonde structure. Secondly, we propose an algorithm based on invariant signal subspace matching to estimate the number of SOPs and determine the rank of the tensor. Subsequently, by fully utilizing the special structure of the factor matrices, we introduce a series of algorithms to achieve the Canonical Polyadic Decomposition (CPD) of the tensor and estimate the direction of arrival (DOA), carrier frequency offset (CFO), and beacon sequence of each SOP. The proposed methods are search-free, and all computations can be performed in a closed-form manner, eliminating the need for numerical iterations. Simulations demonstrate the superiority of the proposed methods over existing methods in terms of estimation accuracy and computational complexity.