Improved Beam-Scannable Ultra-Wideband Sparse Antenna Arrays by Iterative Convex Optimization Based on Raised Power Series Representation

A novel method is presented to design beam-scannable ultra-wideband (UWB) sparse arrays. A concept of design frequency is introduced which transforms the beam-scannable UWB array design to the problem of synthesizing a broadside-beam array at single frequency. The raised power series (RPS) representation with appropriate parameter selection is adopted to generate initial element positions, and then an iterative convex optimization is applied to successively optimize the element positions for further sidelobe level (SLL) reduction. Multiple constraints for controlling the first-order Taylor expansion accuracy, the minimum element spacing, and the array aperture are incorporated in the iterative convex optimization to obtain stable and practical synthesis results. Several examples for synthesizing UWB arrays with different frequency bands, beam scanning, ranges and element counts are conducted to validate the effectiveness and advantages of the proposed method. It is shown that the proposed method achieves much lower SLLs than those by the original RPS method for all test cases, and it also significantly outperforms some conventional stochastic optimization methods for large UWB array cases.