This paper reexamines and fundamentally improves the Schmidl-and-Cox (S&C) algorithm, which is extensively used for packet detection in wireless networks, and enhances its adaptability for multi-antenna receivers. First, we introduce a new "compensated autocorrelation" metric, providing a more analytically tractable solution with precise expressions for false-alarm and missed-detection probabilities. Second, this paper proposes the Pareto comparison principle for fair benchmarking packet-detection algorithms, considering both false alarms and missed detections simultaneously. Third, with the Pareto benchmarking scheme, we experimentally confirm that the performance of S&C can be greatly improved by taking only the real part and discarding the imaginary part of the autocorrelation, leading to the novel real-part S&C (RP-S&C) scheme. Fourth, and perhaps most importantly, we utilize the compensated autocorrelation metric we newly put forth to extend the single-antenna algorithm to multi-antenna scenarios through a weighted-sum approach. Two optimization problems, minimizing false-alarm and missed-detection probabilities respectively, are formulated and solutions are provided. Our experimental results reveal that the optimal weights for false alarms (WFA) scheme is more desirable than the optimal weights for missed detections (WMD) due to its simplicity, reliability, and superior performance. This study holds considerable implications for the design and deployment of packet-detection schemes in random-access networks.

翻译：本文重新审视并从根本上改进了Schmidl-and-Cox（S&C）算法，该算法广泛应用于无线网络中的包检测，并增强了其对多天线接收机的适应性。首先，我们引入了一种新的“补偿自相关”度量，提供了更易于解析求解的方案，并给出了虚警概率和漏检概率的精确表达式。其次，本文提出了帕累托比较原则，用于对包检测算法进行公平基准测试，同时考虑虚警和漏检。第三，通过帕累托基准测试方案，我们实验证实，仅保留自相关的实部并舍弃虚部即可大幅提升S&C的性能，从而提出了新型实部S&C（RP-S&C）方案。第四，或许也是最重要的，我们利用新提出的补偿自相关度量，通过加权求和的方式将单天线算法扩展到多天线场景。我们分别构建了以最小化虚警概率和漏检概率为目标的优化问题，并给出了求解方法。实验结果表明，最优虚警权重（WFA）方案因简单、可靠且性能优越，优于最优漏检权重（WMD）方案。本研究对随机接入网络中包检测方案的设计与部署具有重要启示。