Unimodular/Phase-only sequence having impulse like aperiodic auto-correlation function plays a central role in the applications of RADAR, SONAR, Cryptography, and Wireless (CDMA) Communication Systems. In this paper, we propose a fast iterative algorithm to design phase-only sequences of arbitrary lengths by minimizing the Integrated Side-lobe Level (ISL) metric, which is very closely related to the auto-correlation property of a sequence. The ISL minimization problem is solved iteratively by using the Majorization-Minimization (MM) technique, which ensures a monotonic convergence to the stationary minimum point. To highlight the performance of a proposed algorithm, we conduct the numerical experiments for different sequence lengths using different initializations and also compare them with the existing algorithms. Numerical simulations show that irrespective of the sequence length and initialization, the proposed algorithm is performing better than the state-of-the-art algorithms in terms of speed of convergence. We also show a computationally efficient way to implement our proposed algorithm by using the FFT and IFFT operations.

具有脉冲（如非周期性自相关函数）的单模/仅相位序列在RADAR，SONAR，密码学和无线（CDMA）通信系统的应用中起着核心作用。在本文中，我们提出了一种快速迭代算法，可通过最小化集成旁瓣电平（ISL）度量来设计任意长度的仅相位序列，该算法与序列的自相关特性密切相关。ISL最小化问题通过使用“最小化-最小化”（MM）技术来迭代解决，该技术可确保单调收敛到固定的最小点。为了突出所提出算法的性能，我们使用不同的初始化方法对不同序列长度进行了数值实验，并将其与现有算法进行了比较。数值仿真表明，无论序列长度和初始化如何，在收敛速度方面，该算法的性能均优于最新算法。我们还展示了一种通过使用FFT和IFFT运算来高效实现我们提出的算法的方法。