Multiple Invariance ESPRIT for Nonuniform Linear Arrays: A Coupled Canonical Polyadic Decomposition Approach

The Canonical Polyadic Decomposition (CPD) of higher-order tensors has proven to be an important tool for array processing. CPD approaches have so far assumed regular array geometries such as uniform linear arrays. However, in the case of sparse arrays such as nonuniform linear arrays (NLAs), the CPD approach is not suitable anymore. Using the coupled CPD we propose in this paper a multiple invariance ESPRIT method for both one- and multi-dimensional NLA processing. We obtain a multiresolution ESPRIT method for sparse arrays with multiple baselines. The coupled CPD framework also yields a new uniqueness condition that is relaxed compared with the CPD approach. It also leads to an eigenvalue decomposition based algorithm that is guaranteed to reduce the multi-source NLA problem into decoupled single-source NLA problems in the noiseless case. Finally, we present a new polynomial rooting procedure for the latter problem, which again is guaranteed to find the solution in the noiseless case. In the presence of noise, the algebraic algorithm provides an inexpensive initialization for optimization-based methods.