Influence of filter amplitude error on the frequency-domain broadband beamforming

In an array system,the amplitude error of the filter in each element will affect the performance of the broadband beamforming.Based on the frequency-domain broadband beamforming algorithm and the filter amplitude error model,the influence of the filter amplitude error on the frequency-domain broadband beamforming is discussed.To analyze the error influence,the covariance matrix of the frequency-domain broadband beamforming in error case is calculated.Through the analysis of the covariance matrix in error case,it is shown that the rank of the covariance matrix will increase and therefore more degrees of freedom are desired. Besides,the performance will become worsen due to the errors.The relationship of the error and the performance lose is also given,which may be beneficial for the design of the filter in broadband phased array.