It is known that unimodular sequence set with low cross- and auto-correlation peak sidelobe level (C/A-PSL) can improve the detection ability of the signal-of-interest in the presence of multipath propagation and/or clutters, while that with specified spectral power null/notch in certain frequency bands can prevent mutual interference of the systems that are operating in the same frequency bands. However, it is exceedingly difficult to design such a unimodular sequence set because nonsmooth quadratic objective function as well as nonlinear unimodular and spectral constraints are involved. In this paper, under the unimodular and spectral constraints, we formulate the sequence set design problem based on minimum C/A-PSL. Then, we apply block successive upper-bound minimization to solve the corresponding NP-hard problem and use the relation of the sequence auto-correlation and its fast Fourier transform (FFT) and inverse FFT to devise an efficient algorithm. Numerical examples show that the proposed method can effectively produce spectrally constrained sequence set with low C/A-PSL.

已知具有低互相关和自相关峰值旁瓣电平（C / A-PSL）的单模序列集可以在存在多径传播和/或杂波的情况下提高目标信号的检测能力，而在某些频带中具有指定频谱功率的空/陷波可以防止在相同频带中运行的系统的相互干扰。然而，由于涉及非光滑二次目标函数以及非线性单模和频谱约束，因此设计这样的单模序列集是极其困难的。本文在单模和频谱约束下，提出了基于最小C / A-PSL的序列集设计问题。然后，我们应用块连续上界最小化来解决相应的NP-hard问题，并利用序列自相关与其快速傅里叶变换（FFT）和逆FFT的关系设计一种有效的算法。数值算例表明，该方法可以有效地生成低C / A-PSL的频谱约束序列集。