[{"data":1,"prerenderedAt":-1},["ShallowReactive",2],{"doc-detail-81674-en":3,"doc-seo-81674-105":30,"detail-sidebar-cat-0-en-105":91},{"code":4,"msg":5,"data":6},0,"success",{"doc_id":7,"user_id":8,"nickname":9,"user_avatar":10,"doc_module":4,"category_id":11,"category_name":12,"doc_title":13,"doc_description":14,"doc_content":15,"file_id":16,"file_url":17,"file_type":18,"file_size":19,"view_count":20,"is_deleted":4,"is_public":21,"is_downloadable":21,"audit_status":21,"page_count":22,"language":23,"language_code":24,"site_id":25,"html_lang":24,"table_of_contents":26,"faqs":27,"seo_title":13,"seo_description":14,"update_tm":28,"read_time":29},81674,1649267921044,"Ava Thompson","https://us-avatar.wpscdn.com/avatar/1800007509477c92dfb?_k=1782875107921204101",8,"Research & Report","Auto-correlation Function Keying","Auto-correlation Function Keying (ACFK) proposes a new ISAC waveform that embeds random communication data while directly controlling the peak sidelobe level (PSL) of the periodic autocorrelation function (P-ACF). Unlike methods that target the expected sidelobe level, ACFK formulates a mutual-information maximization problem under PSL and power constraints, proving asymptotic optimality via continuous ACF-domain uniform distribution at high SNR. It maps finite-constellation symbols to ACF-domain sidelobes and uses independent phase symbols for additional degrees of freedom. Exact nominal P-ACF control is achieved under power spectral non-negativity, with non-negativity violation probability and PSLR degradation bounds, plus reference transceiver BER analysis.","Auto-correlation Function Keying  \nWeijiang Zhao, Yifeng Xiong, Member, IEEE, Fan Liu, Senior Member, IEEE, Shuangyang Li, Member, IEEE,  \nShi Jin, Fellow, IEEE, and Jianhua Zhang, Fellow, IEEE  \nJul 2026  \nAbstract—We propose ACFK: Auto-correlation Function Keying, a new integrated sensing and communication (ISAC) waveform that carries random communication data while directly controlling the peak sidelobe level (PSL) of the periodic autocorrelation function (P-ACF). In contrast to existing works aiming at controlling the expected sidelobe level (ESL), which fails to characterize realization-specific sidelobe behaviors, we formulatea mutual information maximization problem under PSL and power constraints, and show that a continuous ACF-domain uniform distribution is asymptotically optimal at high signalto-noise ratio (SNR) over quasi-static frequency-flat channels.  \nMotivated by this principle, ACFK maps finite-constellation symbols onto auto-correlation function (ACF)-domain sidelobesand uses independent phase symbols to exploit the remaining degrees of freedom. The resulting waveform enables exact control of the nominal P-ACF, which coincides with the actual P-ACF when the power spectral non-negativity condition is satisfied. We further analyze the non-negativity violation probability and bound the corresponding peak sidelobe level ratio (PSLR) degradation. A reference ISAC transceiver and its high-SNR approximate bit error rate (BER) analysis are also provided. Numerical results show that ACFK achieves stronger PSLR control, and improved weak-target detection performance, thana generalized probabilistic amplitude shaping (PAS) baseline at similar data rate and BER.  \n10  \nIndex Terms—Integrated sensing and communication, modulation scheme design, peak sidelobe level, mutual information maximization, periodic auto-correlation function design.  \nE  \n[ cs .IT]  \nI. INTRODUCTION  \nNVISIONED as a transformative paradigm, integrated sensing and communication (ISAC) has been formally  \narXiv :2606 . 17970v3  \ndesignated by the International Telecommunication Union as one of the six core usage scenarios for sixth-generation (6G) wireless networks [1] . By coordinating wireless resources such as time, frequency, beam, and power across sensing and communication functionalities over a unified hardware platform, ISAC effectively empowers numerous emerging applications, including autonomous driving, digital twins and lowaltitude economy [2]–[4] . One of the fundamental challenges in ISAC lies in designing high-performance dual-functional waveforms that are capable of supporting both accurate target sensing and reliable information delivery tasks in a resourceefficient manner [5]–[7] . Due to low implementation costs and seamless compatibility with legacy cellular infrastructure,  \nThis work was supported in part by the National Natural Science Foundation of China (NSFC) under Grant U25B2009, Grant 62522107, and Grant 62331023. (Corresponding authors: Yifeng Xiong; Fan Liu.)  \nW. Zhao and Y. Xiong are with the Department of Communication Engineering, Beijing University of Posts and Telecommunications, Beijing 100876, China (e-mail: [zhaoweijiang@bupt.edu.cn](zhaoweijiang@bupt.edu.cn), [yifengxiong@bupt.edu.cn](yifengxiong@bupt.edu.cn)).  \nF. Liu and S. Jin are with the National Mobile Communications Research Laboratory, Southeast University, Nanjing 210096, China (email: [fan.liu@seu.edu.cn](fan.liu@seu.edu.cn), [jinshi@seu.edu.cn](jinshi@seu.edu.cn)).  \nShuangyang Li is with the Faculty of Electrical Engineering and Computer Science, Technical University of Berlin, 10587 Berlin, Germany (e-mail: [shuangyang.li@tu-berlin.de](shuangyang.li@tu-berlin.de)).  \nJianhua Zhang is with the State Key Laboratory of Networking and Switching Technology, Beijing University of Posts and Telecommunications, Beijing 100876, China (e-mail: [jhzhang@bupt.edu.cn](jhzhang@bupt.edu.cn)).  \nthe communication-centric designs are viewed as a promising paradigm for f","cbCaiu7tuhSgxTQr","https://ap.wps.com/l/cbCaiu7tuhSgxTQr","pdf",1898632,2,1,25,"English","en",105,"# Abstract\n# Index Terms\n# I. Introduction\n## Motivation and background of ISAC\n## Communication-centric designs and reference signals\n## Deterministic-random tradeoff (DRT) and payload-based sensing","[{\"question\":\"What does ACFK control in the periodic autocorrelation function framework?\",\"answer\":\"ACFK directly controls the peak sidelobe level (PSL) of the periodic autocorrelation function (P-ACF), enabling sidelobe behavior management tied to realization-specific properties rather than only expectations.\"},{\"question\":\"How does the proposed optimization differ from existing expected sidelobe level approaches?\",\"answer\":\"ACFK maximizes mutual information under explicit PSL and power constraints, instead of optimizing only the expected sidelobe level, which is insufficient to characterize realization-specific sidelobe behavior.\"},{\"question\":\"When does the nominal P-ACF match the actual P-ACF in ACFK?\",\"answer\":\"The nominal P-ACF coincides with the actual P-ACF when the power spectral non-negativity condition is satisfied; otherwise, the document bounds the non-negativity violation probability and the resulting peak sidelobe ratio degradation.\"}]",1784175341,63,{"code":4,"msg":31,"data":32},"ok",{"site_id":25,"language":24,"slug":33,"title":13,"keywords":34,"description":14,"schema_data":35,"social_meta":86,"head_meta":88,"extra_data":90,"updated_unix":28},"auto-correlation-function-keying","",{"@graph":36,"@context":85},[37,53,68],{"@type":38,"itemListElement":39},"BreadcrumbList",[40,44,47,50],{"item":41,"name":42,"@type":43,"position":21},"https://docshare.wps.com","Home","ListItem",{"item":45,"name":46,"@type":43,"position":20},"https://docshare.wps.com/document/","Document",{"item":48,"name":12,"@type":43,"position":49},"https://docshare.wps.com/document/research-report/",3,{"item":51,"name":13,"@type":43,"position":52},"https://docshare.wps.com/document/auto-correlation-function-keying/81674/",4,{"url":51,"name":13,"@type":54,"author":55,"headline":13,"publisher":57,"fileFormat":60,"inLanguage":24,"description":14,"dateModified":61,"datePublished":62,"encodingFormat":60,"isAccessibleForFree":63,"interactionStatistic":64},"DigitalDocument",{"name":9,"@type":56},"Person",{"url":41,"name":58,"@type":59},"DocShare","Organization","application/pdf","2026-07-24","2026-07-16",true,{"@type":65,"interactionType":66,"userInteractionCount":20},"InteractionCounter",{"@type":67},"ViewAction",{"@type":69,"mainEntity":70},"FAQPage",[71,77,81],{"name":72,"@type":73,"acceptedAnswer":74},"What does ACFK control in the periodic autocorrelation function framework?","Question",{"text":75,"@type":76},"ACFK directly controls the peak sidelobe level (PSL) of the periodic autocorrelation function (P-ACF), enabling sidelobe behavior management tied to realization-specific properties rather than only expectations.","Answer",{"name":78,"@type":73,"acceptedAnswer":79},"How does the proposed optimization differ from existing expected sidelobe level approaches?",{"text":80,"@type":76},"ACFK maximizes mutual information under explicit PSL and power constraints, instead of optimizing only the expected sidelobe level, which is insufficient to characterize realization-specific sidelobe behavior.",{"name":82,"@type":73,"acceptedAnswer":83},"When does the nominal P-ACF match the actual P-ACF in ACFK?",{"text":84,"@type":76},"The nominal P-ACF coincides with the actual P-ACF when the power spectral non-negativity condition is satisfied; 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