Modeling of the Fault Detection Problem for a 3-D Hybrid Antenna Array: Analysis and Evaluation

Research in the field of fault detection has steadily been developing for monitoring the performance of array antennas in the presence of errors in excitation phases and amplitudes. The presence of faulty elements degrades significantly the radiation characteristics and performance of antenna arrays. The measured errors in excitation phases and amplitudes at outputs of elements of the 3D HAAwBE are characterized by a few sparse non-zero vectors. A regularized $l_{2,1}$ -norm problem is designed to model errors of faulty elements and noise. In this work, we have implemented the ADMM method under the joint sparsity setting to solve the regularized $l_{2,1}$ -norm problem for a number of samples of the degraded radiation pattern of the HAAwBE rather than computing its array factor, which requires significant and complex mathematical computation. The proposed ADMM technique under the joint sparsity setting allows for minimizing the cost function of the problem with respect to both model parameters and variable vectors. We have further increased accuracy and stability of the performance of the HAAwBE in the two problems of fault detection and DoA estimation by deploying three different optimization methods: LS-SVM, NN-RBF, and NN-MLP, and compared to each other. Consequently, the superior performance of the HAAwBE has been numerically verified by the high success rates of 91.83%, 91.24%, and 88.33%, by performing the LS-SVM, NN-MLP, and NN-RBF optimization methods, respectively, in the presence of 50% faulty elements. Furthermore, results of DoA estimation by the HAAwBE have represented the high resolution in recognizing locations of three signal sources with performing the optimization method.