A Study on the Upper Bound of Anti-interference Number of Polarization Sensitive Array

In order to solve the problem of the upper bound of anti-interference number for polarization sensitive array, the upper bound of the anti-interference number is formulated to the maximum number of linearly independent steering vectors. From the perspective of Khatri-Rao product, the deterministic and general conditions for the linearly independent steering vectors are provided. For the N-element orthogonal dipole uniform linear arrays, it is proved that the sufficient and necessary condition for the steering vectors to be linearly independent is the number of signals K≤N. When no more than two signals have the same incident angles, it is proved that the sufficient and necessary condition for the steering vectors to be linearly independent with probability 1 is the number of signals K≤2N. Theoretical results show that when the number of completely polarized mainlobe interferences does not exceed 1, the polarization sensitive array can suppress at most 2N-1 interferences. While there are 2 completely polarized mainlobe interferences or 1 partially polarized mainlobe interference, the polarization sensitive array can not completely suppress interferences. Simulation experiments validate the correctness of the theoretical conclusions too. The research provides theoretical guidance for the application of polarization sensitive arrays in radar, communication, navigation, and electronic countermeasures.