DoA Estimation Via Manifold Separation for Arbitrary Array Structures

In this paper, we consider the manifold separation technique (MST), which stems from the wavefield modeling formalism developed for array processing. MST is a method for modeling the steering vector of antenna arrays of practical interest with arbitrary 2-D or 3-D geometry. It is the product of a sampling matrix (dependent on the antenna array only) and a Vandermonde structured coefficients vector depending on the wavefield only. This allows fast direction-of-arrival (DoA) algorithms designed for linear arrays to be used on arrays with arbitrary configuration. In real-world applications, the calibration measurements used to determine the sampling matrix are corrupted by noise. This impairs the performance of MST-based algorithms. In particular, we study the effect of noisy calibration measurements on subspace-based DoA algorithms using MST. Expressions describing the error in the DoA estimates due to calibration noise and truncation are derived. This allows predicting the performance of MST-based algorithms in real-world applications. The analysis is verified by simulations. We established a link between the optimal number of selected modes and the statistics of calibration noise. We analyze the modeling error when MST is used for 1-D (azimuth) DoA estimation.