SFA: A Robust Sparse Fractal Array for Estimating the Directions of Arrival of Signals

In correlation-based processing, sparse arrays offer the capacity to resolve a greater number of uncorrelated sources than physical sensors due to the considerable breadth of their difference coarrays, originating from variations in the locations of elements. Consequently, there is significant interest in devising sparse arrays with sizable difference coarrays and expanding the analysis to encompass additional array characteristics like symmetry, resilience, and cost-effective engineering. We present a scalable and systematic methodology for designing large sparse arrays. Considering several attributes and factors, we can address Fractal arrays that were used for low-side lobe antenna array designing and have very low degrees of freedom; hence, sparsity is introduced to design a hole-free difference coarray which not only increases the number of degrees of freedom in fractal arrays but also aids in better beamforming applications and enhanced DoA results due to regularization in coarrays. We develop an innovative sparse fractal array to enhance the accuracy of DoA estimation for predicting a maximum number of uncorrelated sources with a minimum possible actual sensors. First, the 1D sparse fractal array is constructed and then it is extended to a 2D sparse fractal array for both azimuth and elevation angle estimation. Comprehensive robustness analysis is conducted on the proposed sparse fractal array, encompassing one-dimensional (1D) and two-dimensional (2D) configurations, in response to sensor failures. RMSE analysis shows that the proposed 1D and 2D arrays possess the minimum error when used for direction estimation.