Self-Calibration for Sparse Uniform Linear Arrays with Unknown Direction-Dependent Sensor Phase by Deploying an Individual Standard Sensor

Calibration of the unknown direction-dependent (DD) sensor phase and aliasing-free directions of arrival (DOA) estimation for sparse linear arrays are difficult tasks. In this work, we deploy an individual standard sensor with a known sensor phase response along the axis of the uncalibrated sparse linear array, a self-calibration method is proposed, in which the unknown DD sensor phase and the aliasing-free DOAs are both estimated. The proposed method is realized with a two-step scheme. In the first step, the sensor phase is eliminated by the Kronecker product of the covariance matrices in two different frequency bins, and the frequency difference satisfies the spatial Nyquist sampling theorem. Then, the DOAs can be robustly estimated without the influences of grating lobes and unknown sensor phase parameters. In the second step, the steering matrix is estimated with the known phase parameters of the deployed standard sensor. Then, the DD sensor phase is extracted from the steering matrix using the DOAs obtained in the first step. Hence, the disadvantages of iteration-based strategies in conventional calibration algorithms (e.g., local minima convergence) can be avoided. The performance of the proposed method is evaluated using simulation data and compared with that of Cramer–Rao bounds.