Efficient Estimation of Non-Circular (NC) Wavefronts via R-D Tensorized NC Tensor-ESPRIT-type Algorithms

Subspace-based methods for R-D harmonic retrieval with non-circular (NC) sources provide advantages like improved resolution but face high computational demands. To address this, we propose a tensor-based framework that directly structures the augmented measurement tensor inherent to NC sources. We develop two variants: R-D Tensorized NC Standard Tensor ESPRIT and its real-valued counterpart R-D Tensorized NC Unitary Tensor ESPRIT. Our complexity analysis reveals that both proposed variants reduces the computations by $\frac{{R - 1}}{R}*100\% $ (e.g., 75% for R=4) compared to their respective conventional NC R-D ESPRIT counterparts by leveraging a unified higher-dimensional structure. Simulations confirm that R-D Tensorized NC Unitary Tensor ESPRIT retains the benefits of NC signal processing, including enhanced resolution and identifiability, while achieving comparable accuracy to standard approaches at a significantly reduced computational cost.