Doubly Weighted Average algorithm for DOA estimation on UCA with array failure

Failed elements will destroy the array performance, therefore methods to compensate for array element failures are important. Generally, there are two different lines to address this problem, reconstructing missing array element signals and reoptimize the weights of the remaining array elements according to a desired performance criterion. In this paper, a novel way termed Doubly Weighted Average (DWA) algorithm, which combines Weighted Average of Uniform Arc Arrays (WAUAA) algorithm and Non-uniform Circle Array (NCA) algorithm, is proposed for DOA estimation on Uniform Circle Array (UCA) with array failures. The theoretical derivation of its property is presented. This method is able to provide smaller Root Mean Square Error (RMSE) than NCA and even perfect UCA method. Simulation results show that DWA algorithm can substantially improve the DOA estimation performance. The RMSE of DWA is at least 1.5 dB less than WAUAA, which confirms the theoretical derivation. Especially with a small number of snapshots or a low source SNR, the proposed method provides more accurate estimates than the other compared methods. Furthermore, the DWA method can be used for multiple source and two-dimensional DOA estimation, and be expanded on the Uniform Linear Array (ULA).