This paper studies Flag sequences for lowcomplexity delay-Doppler estimation by exploiting their distinctive peak-curtain ambiguity functions (AFs). Unlike the existing Flag sequence designs that are limited to prime lengths and periodic auto-AFs, we aim to design Flag sequence sets of arbitrary lengths and with low (nontrivial) periodic/aperiodic auto- and cross-AFs. Since every Flag sequence consists of a Curtain sequence and a Peak sequence, we first investigate the algebraic design of zone-based Curtain sequence sets of arbitrary lengths. Our proposed design gives rise to novel Curtain sequence sets with ideal curtain auto-AFs and low/zero cross-AFs within the delay-Doppler zone of interest. Leveraging these Curtain sequence sets, two optimization problems are formulated to minimize the summed customized weighted integrated sidelobe level (SCWISL) of the Flag sequence set. Accelerated Parallel Partially Majorization-Minimization Algorithms are proposed to jointly optimize the transmit Flag sequences and matched/mismatched reference sequences stored in the receiver. Simulations demonstrate that our proposed Flag sequences lead to improved SCWISL and customized peak-to-max-sidelobe ratio compared with the existing Flag sequences. Additionally, our Flag sequences under Flag method exhibit Mean Squared Errors that approach the Cramer-Rao Lower Bound and the Sampling Bound at high signal-to-noise power ratios.

翻译：本文研究利用旗标序列独特的峰值-帘幕模糊函数实现低复杂度时延-多普勒估计。针对现有旗标序列设计局限于素数长度及周期自模糊函数的不足，我们旨在设计具有任意长度且低（非平凡）周期/非周期自模糊函数与互模糊函数的旗标序列集。由于每个旗标序列由帘幕序列和峰值序列组成，我们首先研究任意长度基于区域帘幕序列集的代数设计方法。所提设计产生了具有理想帘幕自模糊函数及所关注时延-多普勒区域内低/零互模糊函数的新型帘幕序列集。基于这些帘幕序列集，我们构建了两个最小化旗标序列集求和定制加权综合旁瓣电平的优化问题，并提出加速并行部分最小化-最大化算法，以联合优化发射旗标序列及接收端存储的匹配/失配参考序列。仿真结果表明，与现有旗标序列相比，所提旗标序列在求和定制加权综合旁瓣电平和定制峰值最大旁瓣比上均有改进。此外，在高信噪比条件下，采用旗标方法的序列均方误差趋近于克拉美-罗下界和采样界。