Study On Radar Waveform Design And Array Pattern Synthesis Based On Convex Optimization

Convex optimization is a special class of mathematical optimization problems, which includes least-squares and linear programming problems. For a convex optimization problem, the global optimal solution can be guaranteed and it can be solved reliably and efficiently with a numerical method, which make the convex optimization widly used in practice. Based on this consideration, the convex optimization method is applied to the radar waveform design and the array pattern synthesis in the dissertation. Based on the convex optimization, the lower sidelobe pulse compression filter design, the optimal design combined arbitrary phase codes with pulse compression filters optimization, the optimal design for non-linear frequency modulation signal and the pattern synthesis method with the constraint of weight amplitude dynamic range are analysised mainly in the dissertation, and also the pattern synthesis methods with desired magnitude response and the thinned array synthesis method with lower sidelobe, based on the combination of convex optimization and genetic algorithm are studied in the dissertation. The primary contributions include in the dissertation can be summarized as follows:1. To the problem of the high-sidelobe with the match filtering of the coded-signals, a method of sidelobe suppression filter design based on second-order cone programming is proposed. The design of minimum sidelobe filter, considering the maximum loss in process gain, is converted to a Second-order Cone Programming problem, which can be solved efficiently by interior-point methods. The optimal tradeoff among the sidelobe level, the loss in process gain and the filter orders is provided in proposed method, which has many advantages over those available, such as flexible design, high accuracy and good convergence. The validity of method is confirmed by the result of the simulate data and the measured data.2. For the polyphase codes with arbitrary phase, an optimal design method combined with pulse compression filters is proposed. Under the constraint of the maximum gain loss, The minimum peak sidelobe suppression correlator for an existing phase codes is given by convex optimization, and based on which, a novel phase codes is presented. Its range sidelobe can be farther decreased by multi-iterative operations. The simulation results demonstrates that a nearly optimal peak sidelobe level is achieved by the presented method with less loss of process gain, without increasing the length of pulse compression filters.3. An improved method for Non-Linear Frequency Modulation (NLFM) signal design is proposed based on window functions method. The minimum peak sidelobe suppression correlator of NLFM signal, based on window functions, is solved by convex optimization, and based on which a new NFLM signal is presented. its range sidelobe can be farther decreased by multi-iterative operations. Given the limited mainlobe width, a lower range sidelobe can be obtained by the presented method with an appropriate relaxation on the constant constraint of amplitude, and also, the presented algorithm is suitable for the NLFM signal design with small time-frequency product. The validity of method is demonstrated by the simulation results.4. A pattern synthesis with desired magnitude response, based on the combination of genetic algorithm and convex optimization, is proposed. The phase in mainlobe is used as the optimal variables for genetic algorithm, and the fitness function is constructed with the desired magnitude of mainlobe. The optimal fitness values of the corresponding individual can be obtained by convex optimization, which greatly improves the algorithm search performance. The phase optimization with the proposed algorithm has no relation to the array reference point, and the algorithm is suitable for the arbitrary array synthesized. The validity of method is confirmed by the simulation result and theory analysis.5. For the elements position distribution of thinned array whose elements are thinned from the uniform grid, an optimal algorithm of Genetic Algorithm based on integer coded is proposed. The search space is reduced greatly because of the adoption of integer coding. The manner of individual description improves the optimization efficiency of GA, and the better optimized results compared with conventional ones is obtained. The proposed method can be used for the requirement of the array aperture, the elements thinned ratio and the minimum element space constraints, which has the advantages of flexible design and quick convergence.6. An improved pattern synthesis algorithm based on optimization theory is proposed. The non-convex problem of array pattern synthesis with a dynamic range constraint in amplitude is converted to two convex formulations, and the dynamic range of the optimal weight in amplitude is confined to a certain bound. The simulation results demonstrates that an optimal tradeoff among the mainlobe pattern, the sidelobe level and the dynamic range in weight amplitude can be obtained by the proposed mithod.