基于原子范数的MIMO雷达发射波形设计方法

针对现有多输入多输出(MIMO)雷达发射波形设计方法存在运算量高的问题，该文提出一种基于原子范数的MIMO雷达发射波形设计方法。根据原子范数的信号模型，该算法首先选择一个具有特殊结构的发射滤波器组以及一组正交信号，将MIMO雷达发射波形设计问题转化为原子范数最小化问题，然后采用半正定规划(SDP)对原子范数进行求解，得到(半)正定Toeplitz矩阵，并对其进行范德蒙分解实现发射滤波器组的估计，最后综合发射滤波器组与正交信号获得MIMO雷达的发射波形。理论分析与仿真结果表明，该算法满足等能量发射准则以及小的峰均功率比(PAPR)。同时，该算法相比于现有算法有较低的运算量以及良好的匹配性能。

An Atomic Norm-Based Transmit Waveform Design Method in MIMO Radar

For the fact that exsiting MIMO transmit beampattern design methods suffer from huge computational burden, a novel MIMO transmit beampattern design method based on atomic norm is proposed. According to the signal model of atomic norm, firstly a multi-rank transmit beamformer and a set of orthogonal signals are selected. Then the transmit beampattern matching design problem is formulated into an atomic norm minimization problem. The multi-rank transmit beamformer is achieved by Vandermonde decomposition method of positive semidefinite Toeplitz matrix, which is attained by the solution of the atomic norm minimization problem with Semi-Definite Programming (SDP). Finally, the transmit waveforms can be acquired from the resulting multi-rank transmit beamformer and existing orthogonal waveforms. The theoretical analysis and simulation results verify that the proposed method satisfies the uniform element power constraint and low Peak to Average Power Ratio (PAPR). Simultaneously, compared with current methods, the proposed method has lower computational burden and comparable matching performance.