Multidimensional Unitary Tensor-ESPRIT for non-circular sources

Recently, many authors have shown that high-resolution parameter estimation schemes can be significantly improved if the sources are non-circular. For example, enhanced versions of root MUSIC and standard ESPRIT for non-circular sources as well as the entirely real-valued NC unitary ESPRIT algorithm have been proposed. We can achieve further enhancements in the R-dimensional (R-D) case by using tensor algebra to express and manipulate multidimensional signals in their natural R-D structure. This has led to tensor-based parameter estimation algorithms with enhanced estimation accuracy such as R-D unitary tensor- ESPRIT. In this paper we demonstrate how to achieve both benefits at the same time. This is not straightforward since the usual method to exploit non-circular sources destroys the tensor structure and therefore a new approach had to be found. This approach allows us to derive the NC R-D unitary tensor-ESPRIT algorithm which exploits the non-circularity of the sources and the R-D structure of the measured signals jointly. Numerical computer simulations demonstrate the benefit in terms of a significantly improved accuracy compared to state of the art algorithms.