Sequences with low autocorrelation sidelobes has applications in various fields like wireless communications, radar, sonar, cryptography to name a few. In this paper, we propose an approach to construct sequences, in particular unimodular sequences, by directly minimizing the peak sidelobe level (PSL) metric. The underlying optimization problem involved is a minimax problem which is in general difficult to tract. We address this issue and propose an iterative algorithm named Sequence with LOw Peak sidelobE level (SLOPE) based on the technique of Majorization Minimization, which can be implemented efficiently using the Fast Fourier Transform tool. Further, we also discuss the extension of SLOPE to incorporate energy, peak-to-average-power ratio (PAPR) and spectral constraints on the sequence. We show through numerical simulations that the proposed algorithm can generate sequences of considerably longer lengths with lower peak sidelobe level when compared to the state-of-the-art algorithms and in the end we also evaluate the performance of the sequences designed via SLOPE in the context of channel estimation application.

具有低自相关旁瓣的序列在无线通信、雷达、声纳、密码学等各个领域都有应用。在本文中，我们提出了一种通过直接最小化峰值旁瓣电平 (PSL) 度量来构建序列的方法，尤其是单模序列。所涉及的潜在优化问题是一个极小极大问题，通常难以解决。我们解决这个问题，并提出命名的迭代算法小号层序与LO W ^ P EAK sidelob Ë水平（坡) 基于 Majorization Minimization 技术，可以使用快速傅立叶变换工具有效地实现。此外，我们还讨论了 SLOPE 的扩展，以在序列上包含能量、峰均功率比 (PAPR) 和频谱约束。我们通过数值模拟表明，与最先进的算法相比，所提出的算法可以生成长度相当长的序列和较低的峰值旁瓣水平，最后我们还评估了通过 SLOPE 设计的序列的性能信道估计应用的上下文。