Study On Transmit Beampattern Design And Robust Beamforming Based On SDP

Transmit pattern Design and robust beamforming via semi-definite programming(SDP) were studied in this dissertation. SDP optimization model possesses convexoptimization features, and the optimization model of beamforming with SDP can obtainglobal optimal solution. The traditional vector weighted transmit pattern design methodand robust beamforming didn’t controlle the mainlobe shape effectively. The transmitsignal covariance matrix is the optimization variable of MIMO radar transmit patterndesign, and the more available degree of freedom can be used than traditional methods,the desired mainlobe shape and low sidelobe pattern can be designed under thecondition of more available degree of freedom. The transmit signal covariance matrixcan be regarded as a weighted vector covariance matrix, which is the optimizationvariable in beamforming methods, and the desired beam pattern can be designed byoptimizing the weighted vector covariance matrix.Specific contents of this dissertation: low sidelobe transmit pattern design forMIMO radar, MIMO radar transmit pattern design via array structure divided,optimization of array elements position via SDP, robust beamforming via matrixweighted and semi-definite rank relaxation (SDR), robust beamforming via time variableweighted vector.1. Low sidelobe transmit pattern of MIMO radar can concentrate majority energyin the mainlobe region to improve the target detection, and reduce the energy of clutterand false targets from sidelobe, so as to enhance the signal-to-noise ratio(SNR) of echo.(1) Two low sidelobe transmit pattern optimization algorithms for MIMO radar areproposed. Based on a modified non-diagonal elements of transmit signal covariancematrix, and a low sidelobe transmit pattern optimization algorithm for MIMO radar ispresented. Firstly, the pattern matching design method is implemented to obtain thedesired mainlobe shape of transmit pattern, and the results are set as the initial value.Secondly, the cost function can be formulated as the minimization of peak-sidelobe orintegrated-sideloble; the mainlobe shape distortion can be constrained by the Frobeniusnorm of modification matrix, and the modified transmit signal covariance matrix needsto be positive semi-definite.(2) The cost function can be formulated as theminimization of peak-sidelobe or integrated-sideloble, the amplitude ripple of mainlabe,null depth and cross correlation of mainlobes (multiple beam pattern) can be constrained;The cost function can be formulated as the minimization of the amplitude ripple ofmainlabe, the peak-sidelobe level, null depth and cross correlation of mainlobes (multiple beam pattern) can be constrained. The desired mainlobe shape and lowsidelobe pattern can be obtaibed with the proposed methods, the null depth and crosscorrelation of mainlobes can be controlled effectively in second method. The aboveoptimization problem is SDP convex optimization problem, we can get the globaloptimal solution.2. The transmit pattern methods available for the MIMO radar can not be extendedinto the large array of the MIMO radar. MIMO radar transmit pattern design viadividing array structure is presented on this dissertation.(1) The large array is dividedinto the same subarray, each subarray transmitted different signal, the same signal wastransmitted by each element in subarray, the first subarray element formed a new sparsearray of MIMO radar, and the sum transmit pattern is the pattern product of sparse arrayMIMO radar and subarray. The size of transmit signal covariance matrix and anglerange with pattern design, the amount of calculation of transmit pattern design methodcan be reduced effectively.(2) With the application of the base-beam and probabilityselection methods, an approach to design the transmit pattern for the planer arrayMIMO radar is presented in this dissertation, which is based on the idea that thepattern of planer array can be synthetised by the pattern of a horizontal and vertical linearray. First, the desired pattern is accumulated along the azimuth and consequently the1-D pattern along the elevation can be formed; the elevation base-beam collection of thevertical line array and the corresponding probability selecting optimization model areformulated. Then, the azimuth base-beam collection of the horizontal line array and thecorresponding probability selecting optimization model can also be formulated for thedesired azimuth pattern of a candidate elevation. Finally, the2-D base-beam collectionis synthetised and the corresponding selected probability of the collection elements canbe calculated. The above optimization problem is SDP convex optimization problem,we can obtain the global optimal solution.3. The elements position is the optimization variable in the proposed methods,usually expressed in exponential function, thus the optimization problem isn’t convex.To solve this problem, optimization of array elements position via SDP is proposed inthis dissertation, implementation steps of the proposed method are described asfollows: Firstly, the region of array elements position can be divided in to many smallgrid, there is an array element to be selected on each grid point; Secondly, set selectionprobability of each element as optimization variables, and the transmit pattern with thefeature of strong directivity can be designed; Finally, the array element position isaggregated with the selection probability and gravity method under the minimum array element distance constraint, the sparse array can be obtained by this method. Thismethod can be regarded as transmit pattern design method that optimization variable isthe weighted vector of selection probability. The optimization problem is SDP convexoptimization problem, we can obtain the global optimal solution, and the different sparsearray can be selected in the single result.4. The robust beamforming via matrix weighted and semi-definite rank relaxation(SDR) methods are proposed in this dissertation.(1) Compared with the availablemethods, matrix weighted beamforming method which constrains the magnitude ripplerange of the mainlobe can control the shape of the mainlobe, the sidelobe level and thenull depth of pattern more effectively, the estimation of signal power is robust to thenoise and systematic errors. The covariance matrix of the weighting matrix can beobtained by the matrix weighted beamforming method, and the weighting matrix can beobtained by the eigen-decomposition of the covariance matrix. And the minimum scaleof the weighting matrix dimension can be determined by the dominant eigenvalues. Withthe beampattern shape controlled, this method can be able to maintain the performanceof the signal power estimation and the system complexity can be reduced efficiently.(2)Because The system implementation complexity of matrix weighted beamformingmethod is more complex than vector weighted beamforming method. In order to solvethese problems, this dissertation presents new robust beamforming approach based onsemi-definite rank relaxation (SDR). Detailed description of the proposed method aregiven as: the optimal model has the same objective as that of the Capon algorithm; theoptimization variable is the covariance matrix of weighting vector with constraints posedon the ripple of mainlobe amplitude and sidelobe level, and the rank of covariancematrix is1; the covariance matrix of the weighting vector can be obtained by the SDRmethod, and each row or column of the matrix is translated into weight vector, then aweighting vector is chosen which allows it become minimal one in the maximumdistortions between the mainlobe of pattern and0dB. The system implementationcomplexity of the proposed method is the same as the vector weighted methods, and thesignal power estimation performance is similar to the matrix weighted method.5. Although matrix weighted robust beamforming method can estimate signalpower accurately, and more robust to errors, this method has a disadvantage that thesystem implementation complexity is more complex than vector weighted beamforming.In order to solve this problem, the time-varing vector weighted robust beamforming isproposed in this dissertation. Each snapshot signal multiplies the same weighted vectoror weighted matrix in the available beamforming methods, we use the idea of MIMO radar that the different moment snapshot signal multiplies different weighted vector,weighted vectors formed weighted vector group, the same optimization model can beformulated which is the same as matrix weighted robust beamforming method, and thecovariance matrix of weighted vector group is the optimization variable. The signalpower estimation performance is equal to the matrix weighted method, but the matchedfilter output of system would arise signal to interference noise ratio (SINR) loss. TheSINR loss can be reduced by constraining magnitude response of weighted vector group,which can be solved by explicitly.