Circular Harmonics-Inspired Analytical Beampattern Synthesis with Beam-Steering Flexibility for Symmetric Uniform Circular Array Apertures

Beam-steering flexibility and frequency invariant response about symmetric uniform circular arrays (UCA) beampatterns synthesis are the critical issues addressed in this paper. The optimal approximation of beamformer’s beampattern is obtained with UCA via Jacobi-Anger expansion from the least-squares error perspective. We show how steering information can be initiated into the wanted beampattern. In addition, we propose a method for the modeling and synthesis of any wanted symmetric UCA beampattern, where the beampattern is flexible enough to be steered to any required direction. As such, we realized a beampattern synthesis with beam-steering flexibility and frequency-invariant response for symmetric UCA. With the method developed, clear-cut derivation of directivity pattern (DF) and white noise array gain (WNAG) are presented, and we clearly explained the amplification problem of white noise at low frequencies and how DF is degraded at high frequencies. To demonstrate the proposed method, we attempt to synthesize 16-element second-order dipole of 2 cm radius, operating at 2 GHz, in various signal directions, θs ∈[0°, 15°, 30°, 60°, 80°, 100°, 120°, 150°]. The numerical experiment and results obtained show the validity and effectiveness of the proposed method. Frequency invariant response is observed below 4 GHz. An increase in the number of elements constantly improves the gain. In addition, the proposed method is a generalization of UCA apertures.