Tensor MUSIC in multidimensional sparse arrays

Tensor-based MUSIC algorithms have been successfully applied to parameter estimation in array processing. In this paper, we apply these for sparse arrays, such as nested arrays and coprime arrays, which are known to boost the degrees of freedom to O(N2) given O(N) sensors. We consider two tensor decomposition methods: CANDECOMP/PARAFAC (CP) and high-order singular value decomposition (HOSVD) to derive novel tensor MUSIC spectra for sparse arrays. It will be demonstrated that the tensor MUSIC spectrum via HOSVD suffers from cross-term issues while the tensor MUSIC spectrum via CP identifies sources unambiguously, even in high- dimensional tensors.