基于分式二次规划的互模糊函数赋形方法

Cross-ambiguity Function Shaping Through Fractional Quadratic Programming

在开展认知雷达波形设计时,由于发射波形与接收滤波器的非匹配体制,互模糊函数赋形相比传统模糊函数赋形优化自由度更高。该文针对强杂波条件下微弱运动目标检测问题,以最大化信干噪比为优化准则,提出了一种联合发射相位编码序列与接收滤波器设计的互模糊函数赋形方法。在恒模约束下,优化问题被建模为二次分式规划形式;然后通过引入辅助变量,并利用共轭梯度法求解Stiefel流形空间上的最小化问题,非凸优化据此转化为恒模约束二次优化问题;通过交替循环和类幂迭代算法求得最优解。此外考虑到发射波形受硬件限制而难以实现严格恒模,该文构建了一种低峰均比约束二次优化问题模型,并利用最近邻向量法求得最优解。最后,不同参数下的仿真与实测数据实验表明,该文赋形方法相较于传统方法具有较高的信干噪比增益和收敛速度。

Due to the mismatch between transmit waveforms and receive filters,Cross-Ambiguity Function(CAF)shaping plays an important role in the design of cognitive radar waveforms and allows more freedom for waveform optimization problem than conventional ambiguity function shaping.A CAF shaping method is proposed for designing phase-shift keying transmit waveforms and receive filters jointly to maximize the output Signal-to-Interference-plus-Noise Ratio(SINR),thereby solving the problem of weaking-moving target detection under strong clutter conditions.The optimization problem is first modeled as a quadratic fractional programming problem under the Constant Modulus(CM)constraint of the transmit waveform.The conjugated gradient method is utilized to solve the minimization problem of the Stiefel manifold space through the introduction of auxiliary variables;furthermore the nonconvex optimization problem is converted into a unimodular quadratic programming problem.An algorithm based on alternately iterative maximization and power method-like iteration is proposed to solve the quadratic optimization problem.Since transmit waveforms are limited by hardware and achieving CM is difficult,the nearest vector method is employed under the constraint of a low peak-to-average power ratio.Finally,the experiments with simulated and real measured data under different parameters reveal that the transmit waveforms and receive filters designed using the proposed method exhibit better SINR performance and faster convergence speed compared with other existing algorithms.