Multi-dimensional sinusoidal order estimation using angles between subspaces

Multi-dimensional harmonic retrieval (HR) in white noise is required in numerous applications such as channel estimation in wireless communications and imaging in multiple-input multiple-output radar. In this paper, we propose two R-dimensional (R-D) extensions of the subspace-based MUSIC model order selection scheme, for R≥2, to detect the number of multi-dimensional cisoids. The key idea in the algorithm development is to utilize the principle angles between multilinear signal subspaces via the truncated higher-order singular value decomposition. The first method is designed for multiple-snapshot scenarios. It considerably outperforms existing algorithms in terms of both detection accuracy and identifiability particularly when a large number of snapshots are available. However, its computational cost is relatively quite high. The second method is computationally much simpler and performs almost as well as the first one when the number of snapshots is small. Simulation results are conducted to demonstrate the performance of the proposed estimators.