Identifiability Analysis of Sensor Arrays with Sensors off Half-Wavelength Grid

Abstract

In this paper, we analyze the effect of sensor placement to the achievable number of degrees-of-freedom (DOFs) when the sensors deviate from a half-wavelength grid. More specifically, we consider two variations of a uniform linear array (ULA), namely, when one or more sensors are shifted from half-wavelength grid positions and when the inter-element spacing of the ULA is smaller than a half-wavelength. The numerical rank and the rank-revealing QR factorization of the array data covariance matrix are examined and the number of DOFs of the array is studied in terms of the rank of the array data covariance matrix. A threshold based on the rank-revealing QR factorization is proposed to separate the eigenvalues respectively corresponding to the signal and noise subspaces, and thus the numerical rank of the array data covariance matrix is estimated. Simulation results are provided to justify the findings and provide insights on sensor placements to preserve the array DOFs.