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

Abstract

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 Tensor ESPRIT (Non-Circular Standard Tensor ESPRIT) and its real-valued counterpart R-D Tensorized NC Unitary Tensor ESPRIT (Non- Circular Unitary Tensor ESPRIT). Our complexity analysis reveals that R-D Tensorized NC Tensor ESPRIT reduces the computations by 75% for R=4 case compared to existing NC R-D ESPRIT methods by leveraging a unified higher dimensional structure with NC sources. Simulations confirm that R-D Tensorized NC Unitary Tensor ESPRIT retains the benefits of NC signal processing—enhanced resolution and identifiability—while achieving comparable accuracy to standard approaches at a significantly reduced computational cost.