基于秩亏傅里叶变换的交替投影编码波形设计

Coded Waveform Design via Alternating Projection Based on Rank Deficient Fourier Transform

本文提出了一种在设定区间具有极低功率谱和自相关幅值的恒模波形设计方法.该方法首先将波形设计的信号模型转化为相位提取问题,通过定义三个代表不同设计目标和约束的集合,利用交替投影的方法来实现波形优化.由于利用了色噪声协方差矩阵与功率谱的近似关系,算法中基于秩亏傅立叶变换矩阵的投影算子能由快速傅里叶变换高效实现,提高了计算效率.最后,计算机仿真验证了算法的有效性.算法所设计的波形可用于雷达、声呐和无线通信系统,以抑制色噪声、有源干扰和距离旁瓣干扰.

A method is presented to design constant modulus waveforms with low magnitude of power spectral density and autocorrelation in desired intervals .The waveform design problem is transformed into a phase retrieval one ,and three sets corre-sponding to different design objects and constraints are defined .The waveform optimization problem is solved via alternating projec-tion .According to the relationship between the covariance matrix and the power spectral density of the colored noise ,the projector used in the algorithm is implemented efficiently based on fast Fourier transformation .Thus the computational efficiency is improved . Finally ,the numerical simulations demonstrate the effectiveness of this algorithm .The waveforms designed by this algorithm can be used in radar ,sonar ,and wireless communication systems to suppress colored noise ,active interference and range sidelobes .