Algorithm of broadband beamformer based on Bessel function

We present a novel broadband beamformer using a Bessel function based weight vector, aiming at solving the pattern distortion of wideband signals received by a uniform linear array.Owing to the similarity of the Bessel series and the pattern function of the uniform linear array, we design an weight vector based on Bessel functions of the first kind by deducing the relationship between the truncated position of Bessel series and the number of array elements.Simulation results show that the uniform linear array with a proper weight vector can receive wideband signal from 1 to 3 GHz with negligible distortions.The relative amplitude error for pattern functions at different frequencies remains below 10^-3, and it can be further reduced by increasing the number of the array elements.In comparison with the existing methods, our proposed broadband beamformer directly uses the coefficients of the truncated Bessel series expansions as the weight vector, possesses high precision, and reduces the computational complexity significantly.