基于凸优化的雷达波形设计及阵列方向图综合算法研究
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摘要
凸优化是一类包含最小二乘和线性规划问题在内的特殊数学优化,凸优化可以保证得到全局最优解,并且具有高效、可靠的数值求解方法使得凸优化在实际中获得了广泛的应用。本文将凸优化方法应用到雷达波形设计和阵列方向图综合中,主要研究了基于凸优化的低旁瓣脉压滤波器优化设计、任意相位编码信号及其脉压滤波器的联合优化、非线性调频信号的优化设计方法以及具有幅度加权动态约束的阵列方向图综合设计方法,同时研究了基于凸优化和遗传算法相结合的阵列方向图模值综合和低旁瓣稀布阵方向图综合优化方法。
本论文的创新点如下:
1.针对编码信号的高旁瓣问题提出一种基于二阶锥规划的低旁瓣滤波器设计方法。将最大增益处理损失约束下的旁瓣抑制滤波器设计转化为二阶锥规划问题,采用内点法进行高效求解。在给定最大增益处理损失及滤波器长度的条件下可以获得最优的旁瓣电平。和已有方法相比,所提方法可以同时兼顾旁瓣电平、增益处理损失和滤波器长度三方面的指标,具有设计灵活、精度高和收敛性好的优点。仿真和实测数据设计结果验证了方法的有效性。
2.针对具有任意相位的多相编码信号提出一种编码信号与脉压滤波器联合优化的设计方法。该方法采用凸优化求解现有相位编码信号在给定最大增益处理损失约束下的最小峰值旁瓣抑制相关器,从而构造一种新的相位编码信号,并通过多次迭代进一步降低其距离旁瓣,获得了性能良好的信号波形及脉压滤波器系数。仿真结果表明,该方法在不增加脉压滤波器长度的情况下,以很小的增益处理损失为代价获得了接近理想的峰值旁瓣电平。
3.在窗函数法的基础上提出一种改进的非线性调频信号设计方法。该方法采用凸优化求解窗函数法设计的非线性调频信号的最小峰值旁瓣抑制相关器,并基于此构造一种新的非线性调频信号,通过多次迭代可进一步降低其距离旁瓣。适当松弛信号波形幅度的恒模约束,改进的设计方法在给定的主瓣宽度条件下可以获得更低的距离旁瓣,而且适用于小时宽带宽积的非线性调频信号设计。仿真数据的设计结果验证了方法的有效性。
4.提出一种遗传算法和凸优化相结合的方向图模值综合方法。将方向图主瓣的相位值作为遗传算法的优化变量,结合期望主瓣的模值构造适应度函数。利用凸优化理论求解该适应度函数可得相应个体适应度的最优值,有效提高了算法的搜索性能。相位的优化使得该方法综合结果与阵列参考点的选择无关,而且适用于任意阵。理论分析和仿真结果验证了方法的有效性。
5.针对稀布阵列的阵元分布综合,提出一种基于整数编码遗传算法的优化设计方法。该方法采用整数编码的个体描述方式在保证阵元稀布率恒定的同时,减小了搜索的空间。并且在优化阵元分布的基础上采用凸优化方法进一步优化阵列权值,显著降低了阵列方向图的旁瓣。所提方法可以同时兼顾阵列孔径、阵元稀布率以及最小阵元间距约束三方面的要求。
6.提出一种权值幅度动态约束的阵列方向图综合方法。将权值幅度动态约束下的方向图综合这一非凸问题转换为两次凸优化进行求解,使优化所得权值的幅度动态控制在一定的范围内。仿真结果表明,采用所提方法可以同时兼顾主瓣形状、旁瓣电平和加权幅度动态三方面的性能指标。
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.
本论文的创新点如下:
1.针对编码信号的高旁瓣问题提出一种基于二阶锥规划的低旁瓣滤波器设计方法。将最大增益处理损失约束下的旁瓣抑制滤波器设计转化为二阶锥规划问题,采用内点法进行高效求解。在给定最大增益处理损失及滤波器长度的条件下可以获得最优的旁瓣电平。和已有方法相比,所提方法可以同时兼顾旁瓣电平、增益处理损失和滤波器长度三方面的指标,具有设计灵活、精度高和收敛性好的优点。仿真和实测数据设计结果验证了方法的有效性。
2.针对具有任意相位的多相编码信号提出一种编码信号与脉压滤波器联合优化的设计方法。该方法采用凸优化求解现有相位编码信号在给定最大增益处理损失约束下的最小峰值旁瓣抑制相关器,从而构造一种新的相位编码信号,并通过多次迭代进一步降低其距离旁瓣,获得了性能良好的信号波形及脉压滤波器系数。仿真结果表明,该方法在不增加脉压滤波器长度的情况下,以很小的增益处理损失为代价获得了接近理想的峰值旁瓣电平。
3.在窗函数法的基础上提出一种改进的非线性调频信号设计方法。该方法采用凸优化求解窗函数法设计的非线性调频信号的最小峰值旁瓣抑制相关器,并基于此构造一种新的非线性调频信号,通过多次迭代可进一步降低其距离旁瓣。适当松弛信号波形幅度的恒模约束,改进的设计方法在给定的主瓣宽度条件下可以获得更低的距离旁瓣,而且适用于小时宽带宽积的非线性调频信号设计。仿真数据的设计结果验证了方法的有效性。
4.提出一种遗传算法和凸优化相结合的方向图模值综合方法。将方向图主瓣的相位值作为遗传算法的优化变量,结合期望主瓣的模值构造适应度函数。利用凸优化理论求解该适应度函数可得相应个体适应度的最优值,有效提高了算法的搜索性能。相位的优化使得该方法综合结果与阵列参考点的选择无关,而且适用于任意阵。理论分析和仿真结果验证了方法的有效性。
5.针对稀布阵列的阵元分布综合,提出一种基于整数编码遗传算法的优化设计方法。该方法采用整数编码的个体描述方式在保证阵元稀布率恒定的同时,减小了搜索的空间。并且在优化阵元分布的基础上采用凸优化方法进一步优化阵列权值,显著降低了阵列方向图的旁瓣。所提方法可以同时兼顾阵列孔径、阵元稀布率以及最小阵元间距约束三方面的要求。
6.提出一种权值幅度动态约束的阵列方向图综合方法。将权值幅度动态约束下的方向图综合这一非凸问题转换为两次凸优化进行求解,使优化所得权值的幅度动态控制在一定的范围内。仿真结果表明,采用所提方法可以同时兼顾主瓣形状、旁瓣电平和加权幅度动态三方面的性能指标。
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.
引文
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