[{"data":1,"prerenderedAt":-1},["ShallowReactive",2],{"doc-detail-83474-en":3,"doc-seo-83474-105":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},83474,1099513958762,"Logic","https://ap-avatar.wpscdn.com/avatar/1000023916a998db790?x-image-process=image/resize,m_fixed,w_180,h_180&k=1784791008015729253",8,"Research & Report","Performance Evaluation of A Certain Transceiver Architecture for Multiple-Input Multiple-Output Phase-Modulated Channels","Performance evaluation focuses on a specific transceiver architecture for multiple-input multiple-output (MIMO) phase-modulated channels, where a unitary transformation converts the channel matrix into a rowechelon form. The MIMO link becomes scalar sub-channels with two phase inputs, producing an annulus constellation under additive white Gaussian noise and weak self-interference. The study derives two upper bounds via convex-geometry capacity constraints and a lower bound via the entropy power inequality, with tight gaps at high signal-to-noise ratios for Rayleigh fading and RIS-assisted symbiotic communication scenarios.","Performance Evaluation of A Certain Transceiver Architecture for Multiple-Input Multiple-Output Phase-Modulated Channels  \narXiv :2607 .00356v 1 [ cs .IT] 1 Jul 2026  \n1st Hengyu Cui  \nDepartment of Information Physics and Engineering Nanjing University of Science and Technology Nanjing, China [1719170887@qq.com](1719170887@qq.com)  \n3nd Zhenyao He Sixty-Third Research Institute National University of Defense Technology  \nNanjing, China  \n[zyhe1111@nudt.edu.cn](zyhe1111@nudt.edu.cn)  \n2rd Ru-Han Chen Sixty-Third Research Institute National University of Defense Technology Nanjing, China [tx_rhc22@nudt.edu.cn](tx_rhc22@nudt.edu.cn)  \n4th Shijun Zhu Department of Information Physics and Engineering Nanjing University of Science and Technology Nanjing, China [shijunzhu@njust.edu.cn](shijunzhu@njust.edu.cn)  \n5th Ruoqi Sun Sixty-Third Research Institute National University of Defense Technology Nanjing, China [202412491635@nuist.edu.cn](202412491635@nuist.edu.cn)  \n6th Yeqin Tai Department of Information Physics and Engineering Nanjing University of Science and Technology Nanjing, China [taiyeqin1412@163.com](taiyeqin1412@163.com)  \nAbstract—For multiple-input multiple-output (MIMO) channels with phase modulation, we recently proposed a method of unitarily transforming the channel matrix into a certain rowechelon form, by which the original MIMO channel can be converted into a certain number of scalar sub-channels with two phase inputs, thereby forming an annulus constellation geometry, and corrupted by both the additive white Gaussian noise and weak self-interference. In this paper, several bounds are derived to evaluate the fundamental limit of such a specific transceiver architecture. Two upper bounds are obtained by upper-bounding the capacity of a scalar channel with an annulus support constraint from the perspective of the convex geometry, while a lower bound is obtained by the standard entropy power inequality. Numerical results show that the gaps between these bounds are small at high signal-to-noise ratios for the MIMO phase-modulated channels over the Rayleigh fading and the single-input multiple-output symbiotic communication system assisted by a reconfigurable intelligent surface.  \nIndex Terms—Channel capacity, multiple-input multipleoutput, non-Gaussian noise, phase modulation, reconfigurable intelligent surface, symbiotic radio.  \nI. INTRODUCTION  \nIn multiple-input multiple-output (MIMO) communication systems, the constant-envelope transmitted signal can signifi  \nThis work is supported in part by the National Natural Science Foundation of China under Grant No. 62401593 and 12374275, the Young Elite Scientists Sponsorship Program by the China Association for Science and Technology, and Innovation Research Foundation of National University of Defense Technology. (Corresponding Authors: Ru-Han Chen and Shijun Zhu)  \ncantly improve the efficiency of power amplifiers, which highlights the importance of phase modulation [1],[2] . Meanwhile, to reduce the implementation cost, the concept of the single radio-frequency (RF) MIMO has been proposed in [3]–[5], by which a MIMO phase-modulated communication system can be equivalently realized by using only one RF chain at the transmitter and temporal-spatial coding of a low-cost reconfigurable intelligent surface (RIS) .  \nDifferent from the classic MIMO channel subject to a total average-power constraint, the MIMO phase-modulated channel is governed by the non-convex support constraint, since the information can only be modulated onto the phases of input signals. To the best of the authors’ knowledge, the degrees of freedom (DoFs) of this channel are exactly characterized in [6, Thm. 2], whereas its capacity remains unknown. Existing relevant results are limited to special cases, e.g. scalar phasemodulated channels [7] or certain discrete alphabets [8] . In our previous work [5], we have derived the achievable rate of the transceiver based on the QR decomposition and the succ","cbCaisRTg4aqxSns","https://ap.wps.com/l/cbCaisRTg4aqxSns","pdf",686243,2,1,6,"English","en",105,"# Abstract\n# Introduction\n# System Model and Problem Formulation\n## System Model","[{\"question\":\"What is the core idea behind the proposed transceiver architecture for MIMO phase-modulated channels?\",\"answer\":\"A unitary transformation converts the channel matrix into a rowechelon form, decomposing the MIMO channel into scalar sub-channels whose phase inputs form an annulus constellation geometry.\"},{\"question\":\"How are the capacity bounds in the paper derived?\",\"answer\":\"Two upper bounds come from bounding the scalar-channel capacity under an annulus support constraint using convex geometry, and one lower bound is obtained using the entropy power inequality (EPI).\"},{\"question\":\"What do the numerical results indicate about the tightness of the bounds?\",\"answer\":\"The gaps between the upper and lower bounds are small at high signal-to-noise ratios for Rayleigh fading and for the single-input multiple-output symbiotic communication system assisted by a reconfigurable intelligent surface.\"}]",1784188243,15,{"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},"performance-evaluation-of-a-certain-transceiver-architecture-for-multiple-input-multiple-output-phase-modulated-channels","",{"@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/performance-evaluation-of-a-certain-transceiver-architecture-for-multiple-input-multiple-output-phase-modulated-channels/83474/",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","2026-07-22","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 is the core idea behind the proposed transceiver architecture for MIMO phase-modulated channels?","Question",{"text":75,"@type":76},"A unitary transformation converts the channel matrix into a rowechelon form, decomposing the MIMO channel into scalar sub-channels whose phase inputs form an annulus constellation geometry.","Answer",{"name":78,"@type":73,"acceptedAnswer":79},"How are the capacity bounds in the paper derived?",{"text":80,"@type":76},"Two upper bounds come from bounding the scalar-channel capacity under an annulus support constraint using convex geometry, and one lower bound is obtained using the entropy power inequality (EPI).",{"name":82,"@type":73,"acceptedAnswer":83},"What do the numerical results indicate about the tightness of the bounds?",{"text":84,"@type":76},"The gaps between the upper and lower bounds are small at high signal-to-noise ratios for Rayleigh fading and for the single-input multiple-output symbiotic communication system assisted by a reconfigurable 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