Study Of Digital Beamforming Technique For Sparse Array Based On Data Reconstruction

In bistatic radar systems,digital beamforming receiving array antennas are urgently needed so that the receiving antenna beams can cover the transmitting antenna beam flexibly.To obtain high antenna gain and high angular measurement accuracy,an antenna array with a large number of antenna elements should be used.In radio astronomy systems,there is also a serious need for receiving antenna arrays with a large number of antenna elements.On the other hand,for a large-scale adaptive array,the high cost is a major drawback.Each antenna needs a T/R component.To reduce the number of radio frequency(RF)frontends without reducing the antenna aperture,we can use sparse arrays.Sparse arrays are attractive because they can reduce number of elements as compared with a fully populated array.This is of particular interest in radar applications because a large aperture facilitates high performance with regard to angular accuracy,resolution,and detection of targets close to interference directions.By employing sparse arrays,this can be achieved by reduced receiving channels,weight,power consumption,and cost as well as easier platform integration.In order to overcome the shortcomings of the existing sparse array beamforming technology,a new sparse digital beamforming algorithm based on data recovery is proposed in this paper.The main works of this paper are listed as follows:(1)A system principle diagram of the sparse array beamforming based on data recovery is proposed.Two modules are added to the original DBF system.One is the compressed sampling network.It is added between the antenna and the receivers.The other is the data reconstruction module.It is added between analog-to-digital converters and the DBF processor.The echo signals received by the antennas send to the compressed sampling network.Then we get M channels' signal where M<<N.So only M receivers and M A/D converters are needed.It is greatly reduced.After getting the digital signals we use reconstruction algorithm to recover N channels' signal of full arrays.At last the recovery signal are used to form the digital beams.This algorithm greatly reduces the number of the RF front-ends without reducing the antenna aperture.It keeps the preferences of full arrays.(2)Under the system framework which is discussed above,an adaptive digital beamforming algorithm based on compressed sensing is proposed.Firstly,the mathematical model of this algorithm is given.Secondly,a compressed sampling network which can be easily applied to system is proposed.According to the relationship between the sampling matrix and the projection matrix,an optimization method of arrays' positions based on genetic algorithm is proposed.Thirdly,two reconstruction algorithms are discussed:orthogonal matching pursuit algorithm(OMP)and the smooth l0 norm method(SLO).And some comparison results between these two algorithms are given.But the recovery errors become large when the targets are not on the grid.To solve this problem,a non-uniform grid method is adopted.In the end,some simulation results of linear array and plane array are given.The simulation results show that the beam patterns obtained by the adaptive digital beamforming algorithm based on compressed sensing have low side-lobes and deep nulls in the direction of interferences.(3)In order to further solve the problem that when targets are not on the grid the recovery error will be large,an adaptive digital beamforming algorithm based on low-rank matrix completion is proposed.For the sparsity of the echo signal in space,we use the undersampling signals to structure low-rank matrix.The low-rank matrixes can be structured by single or multi snapshots.For the single snapshot,the echo signals are rearranged into Hankel matrix.Then we use the inexact augmented Lagrange multipliers method(IALM)to fill the missing elements in the matrix.For the multi snapshots,the echo signals consist of a low-rank matrix which is positive semi definite.Then we use alternating direction method of multipliers(ADMM)to fill the missing elements in the matrix.These two method solve the problem that when targets are not on the grid the recovery error will be large.The recovery errors of each angle are the same.The algorithms better solve the problem of the target off the grid.Simulation results show the correctness of the algorithms.(4)To further reduce the amount of calculation,an improved optimization algorithm with adaptive grid adjustment based on joint orthogonal matching pursuit(J-OMP)algorithm is proposed.The first order of Taylor expansion is used to approximate the actual signal in J-OMP.It improve the recovery accuracy when targets are off the grid.With the DO As of the targets changing slowly,an improved algorithm is proposed.We use the support sets and the angle deviations to adjust the grid.Then new gird can be achieved.It is better than J-OMP.The repeated atomic screening process is removed in this improved algorithm.So the amount of this algorithm is great reduced.To solve the problem that the signal will be lost when the signal is week,multi-snaphots are used.Another kind of compressed sampling network called irregular subarray is proposed.It is better than sparse array.(5)The verification of algorithm principle in practical system is given in the end.Based on the application requirements,a DBF radar system of X-band is carried out.Then the transmit and receive channel calibrations are investigated,and the actual calibration results are given in the paper.Finally the principle of the algorithm is verified in the system.The test results demonstrate the correctness and feasibility of the proposed sparse digital beamforming based on data recovery.