| Multidimensional low rank decomposition and harmonic retrieval have an impressive array of applications in diverse disciplines. A fundamental issue associated with multi-way array analysis is to determine the maximum number of low rank components or harmonics that can be theoretically resolved for a given data/sample size, i.e., identifiability. Another is to determine the data/sample size needed to meet performance specifications. This thesis is focused on the development of identifiability results and decomposition algorithms, as well as various performance metrics for low rank decomposition and harmonic retrieval of multi-way arrays, with applications in frequency hopped spread spectrum (FHSS) communications. FHSS is an appealing spread spectrum technique for military and commercial wireless communications. Based on the theory of multilinear low rank and harmonic analysis, we design a high resolution code blind reception scheme for FHSS systems. Utilizing an antenna array, the code blind receiver is able to separate multiple frequency hopped signals transmitted from different directions-of-arrival (DOA), and track switching frequencies of single or multiple users, without knowledge of DOA, hop pattern (hop code), hop timing, and hop rate of the users. The proposed scheme can track more users than the number of antenna array elements, while jointly estimating hop timing and frequency. |
