A Tensor-Based Data-Driven Approach for Multidimensional Harmonic Retrieval and Its Application for MIMO Channel Sounding

In wireless channel sounding, accurately estimating multiple parameters within a multipath signal, such as azimuth, elevation, Doppler shift, and delay, necessitates addressing the challenges posed by the multidimensional harmonic retrieval (MHR) problem. To overcome these complexities, we propose a framework based on high-order dynamic mode decomposition (HODMD) that designed for robustly estimating frequencies of interest from high-dimensional sinusoidal signals, particularly in additive white Gaussian noise conditions. The HODMD approach, a hybrid algorithm amalgamating high-order singular value decomposition (HOSVD) and dynamic mode decomposition (DMD), operates by initially decomposing observed tensorial data into a core tensor and R mode matrices through HOSVD. Subsequently, DMD is applied to analyze each mode matrix individually, decomposing it into dynamic modes and DMD eigenvalues. The imaginary component of the DMD eigenvalues yields frequencies along the rth dimension. By uniformly applying this analysis to all mode matrices, multiple frequencies of interest are efficiently obtained. Furthermore, the integration of HOSVD, DMD, and moving average techniques in the proposed method is designed to mitigate noise interference during the MHR process. We conduct several numerical experiments and present a real-life example, i.e., the double-direction multiple-input and multiple-output (MIMO) channel sounding, to validate the effectiveness of the proposed HODMD approach. Results demonstrate that HODMD outperforms comparable approaches, particularly in scenarios characterized by high signal-to-noise ratios. Notably, the proposed method exhibits the capability to estimate the number of tones in undamped cases during the decomposition process. Hence, our work contributes a practical and effective tensor-based solution to the MHR problem, particularly in the context of channel parameter estimation for MIMO systems.