基于稀疏矩阵和相关函数联合优化的MIMO-OFDM线性调频波形复用设计与实现方法

多输入多输出合成孔径雷达(Multiple-Input Multiple-Output Synthetic Aperture Radar, MIMO SAR)发射信号应该具有大时间带宽积和良好的模糊函数特性。该文联合优化稀疏矩阵和相关函数来设计多路正交的MIMO SAR 正交频分复用线性调频(OFDM chirp)信号，首先将MIMO SAR波形设计转化为跳频频率与跳频幅度的联合设计，并提出以最小化稀疏矩阵块相关系数及信号互相关峰值和为约束条件，采用迭代搜索法求解最佳编码矩阵；并以最小化信号自相关旁瓣峰值与互相关峰值之和为约束条件，采用遗传算法确定最佳幅度矩阵；最后采用组合优化搜索法设计出最佳信号。文中还分析了发射阵元数目、跳频总间隔数及总频率选择数与信号性能之间的关系。仿真结果表明此方法可以设计多路正交大时间带宽积OFDM chirp信号，同时降低信号的互相关峰值与自相关旁瓣峰值、提高互模糊性能。 

MIMO-OFDM Chirp Waveform Diversity Design and Implementation Based on Sparse Matrix and Correlation Optimization

The waveforms used in Multiple-Input Multiple-Output (MIMO) Synthetic Aperture Radar (SAR) should have a large time-bandwidth product and good ambiguity function performance. A scheme to design multiple orthogonal MIMO SAR Orthogonal Frequency Division Multiplexing (OFDM) chirp waveforms by combinational sparse matrix and correlation optimization is proposed. First, the problem of MIMO SAR waveform design amounts to the associated design of hopping frequency and amplitudes. Then a iterative exhaustive search algorithm is adopted to optimally design the code matrix with the constraints minimizing the block correlation coefficient of sparse matrix and the sum of cross-correlation peaks. And the amplitudes matrix are adaptively designed by minimizing the cross-correlation peaks with the genetic algorithm. Additionally, the impacts of waveform number, hopping frequency interval and selectable frequency index are also analyzed. The simulation results verify the proposed scheme can design multiple orthogonal large time-bandwidth product OFDM chirp waveforms with low cross-correlation peak and sidelobes and it improves ambiguity performance.