Identifiability Analysis of Non-Integer Antenna Arrays in the Presence of Mixed (Strong and Weak) Signals

In this paper, we consider the direction-of-arrival (DOA) estimation problem using a non-integer antenna array, and our objective is to examine the effect of sensor placement on the number of array degrees-of-freedom (DOFs) in the presence of a mixture of strong and weak signals. Two scenarios corresponding to off-grid sensor placement are considered: (1) when a single sensor of a uniform linear array (ULA) is in an off-grid position and (2) when the entire ULA is compressed. The smallest signal-subspace eigenvalue corresponding to the weak signals is compared with the rank-revealing QR factorization-based threshold that separates the signal subspace from the noise subspace, providing insights into the numerical rank of the data covariance matrix and serving as a measure of the DOFs of the array. Furthermore, the effect of signal strength on the eigenvalues of the data covariance matrix is studied. The effect of off-grid sensor placement and the variation of the signal strengths on the array DOFs is demonstrated with simulation results.