Design Of Frequency Invariant Beamformer

When the impinging direction of the wideband signal deviates from the array look-direction,different frequency components suffer from inequable attenuation in the output of the conventional wideband beamformer,which leads to the distortion(especially amplitude distortion)of the output signal.This phenomenon is caused by the beamwidth being inversely proportional to the frequency and equivalent to a lowpass filtering to the signal.To tackle this problem,it is necessary to design the frequency invariant beamformer.In this thesis,this topic is studied,and the main content is summarized as below.The first part introduces the structure of the beamformer,the preconditions of the following content,and the focus of this thesis.Our work starts by introducing the narrowband array structure.Considering the shortcoming of this structure in the wideband scene,the author then introduces the wideband beamformer.At last,after studying the drawback of the conventional wideband beamformer,the author brings the reader to the topic of the thesis,the design of the frequency invariant beamformer(FIB).The second part studies the FIB design based on convex optimization.The global design is firstly introduced.However,its performance greatly depends on the quality of the reference beam pattern,the design of which is a hard work.To avoid this problem,a method based on spatial response variation(SRV)constraints is then studied.However,in both of these two methods,all the time-domain coefficients are synthesized at one time,which makes the dimension of the variation usually very large.In this case,it is difficult to obtain a reliable solution by the convex optimization toolbox,which restricts the application of this class of method.Aiming at this problem,the author then studies the “two-step” design method.In this method,the beamformer design problem is divided into two independent steps,the spatial-domain filter optimization and the time-domain filter optimization.This method greatly reduces the dimension of the variation to be optimized in each step and enlarges the application scope of the convex optimization based method.The third part studies the FIB design based on Fourier transform.Aiming at the unsolved problem in the previous literature,the reference beam design,a rule is proposed.In this method,the relationship between the reference weight length and the signal bandwidth in the design of the unconstrained reference beam is firstly deducted.Then based on this relationship,a method for the reference beam design under constraints is proposed.Our work improves the efficiency of the reference beam design,and is suitable for any FIB design method whose performance depends on the reference beam.The fourth part studies a class of FIB design based on interpolation-resampling.In this part,two types of this method,the Sinc function interpolation-resampling method and the DFT interpolation method,are studied.Our research shows that: In this method,the result is actually truncated,which leads to a truncation error.This error increases with the frequency decreasing.What's more,the reference frequency also affects the performance of this method.When the frequency is higher than the reference frequency,the corresponding pattern of the beamformer at this frequency may be affected by the spectrum-aliasing.It will greatly degrade the frequency invariant performance of the designed wideband beam,when the relative bandwidth of the signal is very large.As a result,to obtain a wideband beam with a good frequency invariant property over the frequency range of interest,the reference frequency should better be selected as the highest frequency.The fifth part compares the performance of the methods introduced in this thesis and points out the deficiencies of our work and some problems to be solved in the future.