The Application Of Fourier Transform To Planar, Cylindrical And Spherical Array Beamforming And DOA Estimation

The technique of array processing used for object detection and parameter estimation, which dependents on its own superiority, shows a wide application in recent years. On the application background of the underwater object detection and DOA estimation, the thesis resolves the problem of large amount of data operation for improving the efficiency of array processing in different kinds of arrays. Then this thesis analyses and deduces the Fourier transform and its fast algorithm which is applied to beamforming. Finally, simulations and experiments are carried out and theoretical results are tested.According to the assumption that signal is plane-wave and different wave number (k|â†') represents different signal DOA, the theory and algorithm of Fourier transform beamforming to planar, cylindrical and spherical array beamforming are investigated. Based on the fundamental theory of time-delay (phased-shift) summation, transform bases of Fourier transform can be phasor, Bessel function or spherical function, and their ensembles are phased-shift of each array element. Then through weighting and summing, beamforming is achieved. This operation is considered as a spatial Fourier transform and it transforms the signal in the form of space domain into the form of wave number domain.By time domain Fourier transform, Fourier transform beamforming transforms each array receiving data from the form of time domain into the form of frequency domain (t â†' f ), and then transforms it from space domain to wave number domain ((x|â†') â†'(k|â†')). Spatial Fourier transform of planar, which is used for DOA estimation, is one dimension when it's on the condition of linear array, while it's two dimensions for rectangular and hexagonal array. All of their transform bases are phasors. Though spatial Fourier transform of cylindrical, spherical array and circular array which is plane are two dimensions, their transform bases are Bessel function or spherical function. So these beamforming are regarded as Generalized Fourier Transform beamforming.In this thesis, Fourier transform and its fast algorithm of linear array, rectangular array and hexagonal array which are composed of transform bases based on phasors are investigated theoretically and experimentally at first. Then Fourier transform of circular, cylindrical or spherical array, which are composed of transform bases basedon Bessel function or spherical function respectively, are also studied theoretically and experimentally. At last, a system of hexagonal array is devised and its experiment is carried out to confirm the theory of hexagonal array Fourier transform beamforming and its fast algorithm in laboratory waveguide, which makes a good foundation on further nautical experimental research of X X X 973 project. The innovations of this thesis are as follow:1. To various kinds of arrays, this thesis makes research on the spatial Fourier transform or generalized spatial Fourier transform which based on the bases of phasor, Bessel function and spherical function.2. Apply hexagonal array Fourier transform to hexagonal array Fourier transform beamforming successfully, and finish an experiment to testify it. The satisfied results are obtained.