Pilot sequence design over doubly selective channels (DSC) is challenging due to the variations in both the time- and frequency-domains. Against this background, the contribution of this paper is twofold: Firstly, we investigate the optimal sequence design criteria for efficient channel estimation in orthogonal frequency division multiplexing systems under DSC. Secondly, to design pilot sequences that can satisfy the derived criteria, we propose a new metric called oversampled ambiguity function (O-AF), which considers both fractional and integer Doppler frequency shifts. Optimizing the sidelobes of O-AF through a modified iterative twisted approximation (ITROX) algorithm, we develop a new class of pilot sequences called ``oversampled low ambiguity zone (O-LAZ) sequences". Through numerical experiments, we evaluate the efficiency of the proposed O-LAZ sequences over the traditional low ambiguity zone (LAZ) sequences, Zadoff-Chu (ZC) sequences and m-sequences, by comparing their channel estimation performances over DSC.

翻译：在双选择性信道（DSC）下，由于时域和频域均存在变化，导频序列的设计具有挑战性。在此背景下，本文的贡献主要有两方面：首先，我们研究了在DSC下的正交频分复用系统中，用于高效信道估计的最优序列设计准则。其次，为了设计能够满足所推导准则的导频序列，我们提出了一种称为过采样模糊函数（O-AF）的新度量，该度量同时考虑了分数和整数多普勒频移。通过改进的迭代扭曲逼近（ITROX）算法优化O-AF的旁瓣，我们开发了一类新的导频序列，称为“过采样低模糊区（O-LAZ）序列”。通过数值实验，我们比较了所提出的O-LAZ序列与传统低模糊区（LAZ）序列、Zadoff-Chu（ZC）序列以及m序列在DSC下的信道估计性能，从而评估了O-LAZ序列的有效性。