{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,10,12]],"date-time":"2025-10-12T03:21:33Z","timestamp":1760239293689,"version":"build-2065373602"},"reference-count":38,"publisher":"MDPI AG","issue":"21","license":[{"start":{"date-parts":[[2020,10,31]],"date-time":"2020-10-31T00:00:00Z","timestamp":1604102400000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"funder":[{"DOI":"10.13039\/501100001809","name":"National Natural Science Foundation of China","doi-asserted-by":"publisher","award":["61372134"],"award-info":[{"award-number":["61372134"]}],"id":[{"id":"10.13039\/501100001809","id-type":"DOI","asserted-by":"publisher"}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Sensors"],"abstract":"<jats:p>The normal operations of radar systems and communication systems under the condition of spectrum coexistence are facing a huge challenge. This paper uses game theory to study power allocation problems between multistatic multiple-input multiple-output (MIMO) radars and downlink communication. In the case of spectrum coexistence, radars, base station (BS) and multi-user (MU) have the working state of receiving and transmitting signals, which can cause unnecessary interferences to different systems. Therefore, when they work together, they should try to suppress mutual interferences. Firstly, the signal from BS is considered as interference when radar detects and tracks targets. A supermodular power allocation game (PAG) model is established and the existence and uniqueness of the Nash equilibrium (NE) in this game are proved. In addition, the power allocation problem from BS to MU is also analyzed, and two Stackelberg PAG models are constructed. It is proved that the NE of each game exists and is unique. Simultaneously, two Stackelberg power allocation iterative algorithms converge to the NEs. Finally, numerical results verify the convergence of the proposed PAG algorithms.<\/jats:p>","DOI":"10.3390\/s20216216","type":"journal-article","created":{"date-parts":[[2020,10,31]],"date-time":"2020-10-31T21:39:56Z","timestamp":1604180396000},"page":"6216","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":1,"title":["Multiple Power Allocation Game Schemes for Spectrum Coexistence Model Between Multistatic MIMO Radar Sensors and MU Communication"],"prefix":"10.3390","volume":"20","author":[{"ORCID":"https:\/\/orcid.org\/0000-0003-3328-7688","authenticated-orcid":false,"given":"Bin","family":"He","sequence":"first","affiliation":[{"name":"National Laboratory of Radar Signal Processing, Xidian University, Xi\u2019an 710071, China"}]},{"given":"Hongtao","family":"Su","sequence":"additional","affiliation":[{"name":"National Laboratory of Radar Signal Processing, Xidian University, Xi\u2019an 710071, China"}]}],"member":"1968","published-online":{"date-parts":[[2020,10,31]]},"reference":[{"key":"ref_1","doi-asserted-by":"crossref","first-page":"1","DOI":"10.1109\/TCCN.2017.2666266","article-title":"Radar-Communications Convergence: Coexistence, Cooperation, and Co-Design","volume":"3","author":"Chiriyath","year":"2017","journal-title":"IEEE Trans. Cogn. Commun. Netw."},{"key":"ref_2","doi-asserted-by":"crossref","unstructured":"Li, J., and Stoica, P. (2009). MIMO Radar Signal Processing, Wiley.","DOI":"10.1002\/9780470391488"},{"key":"ref_3","doi-asserted-by":"crossref","first-page":"898","DOI":"10.1109\/TAES.2014.130088","article-title":"Power allocation and waveform design for the compressive sensing based MIMO radar","volume":"50","author":"Yu","year":"2014","journal-title":"IEEE Trans. Aerosp. Electron. Syst."},{"key":"ref_4","unstructured":"Chernyak, V.S. (1998). Fundamentals of Multisite Radar Systems: Multistatic Radars and Multistatic Radar Systems, Gordon and Breach Science Publishers."},{"key":"ref_5","doi-asserted-by":"crossref","first-page":"1081","DOI":"10.1049\/iet-rsn.2016.0356","article-title":"Jamming power allocation strategy for MIMO radar based on MMSE and mutual information","volume":"11","author":"Wang","year":"2017","journal-title":"IET Radar Sonar Navig."},{"key":"ref_6","doi-asserted-by":"crossref","first-page":"331","DOI":"10.1016\/j.sigpro.2017.06.026","article-title":"Multiobjective optimal waveform design for OFDM integrated radar and communication systems","volume":"141","author":"Liu","year":"2017","journal-title":"Signal Process."},{"key":"ref_7","doi-asserted-by":"crossref","first-page":"28","DOI":"10.1109\/MAES.2016.150236","article-title":"Co-designed radar-communication using linear frequency modulation waveform","volume":"31","author":"Nowak","year":"2016","journal-title":"IEEE Aerosp. Electron. Syst. Mag."},{"key":"ref_8","doi-asserted-by":"crossref","first-page":"4264","DOI":"10.1109\/TSP.2018.2847648","article-title":"Toward Dual-functional Radar-Communication Systems: Optimal Waveform Design","volume":"66","author":"Liu","year":"2018","journal-title":"IEEE Trans. Signal Process."},{"key":"ref_9","doi-asserted-by":"crossref","first-page":"2755","DOI":"10.1109\/TWC.2018.2803045","article-title":"MU-MIMO Communications With MIMO Radar: From Co-Existence to Joint Transmission","volume":"17","author":"Liu","year":"2018","journal-title":"IEEE Trans. Wirel. Commun."},{"key":"ref_10","doi-asserted-by":"crossref","first-page":"632","DOI":"10.1049\/iet-rsn.2017.0405","article-title":"Fusion of radar sensing and wireless communications by embedding communication signals into the radar transmit waveform","volume":"12","author":"Geng","year":"2018","journal-title":"IET Radar Sonar Navig."},{"key":"ref_11","doi-asserted-by":"crossref","first-page":"8709","DOI":"10.1109\/JSEN.2018.2868542","article-title":"Embedding Communication Symbols into Radar Waveform with Orthogonal FM Scheme","volume":"18","author":"Gu","year":"2018","journal-title":"IEEE Sens. J."},{"key":"ref_12","doi-asserted-by":"crossref","first-page":"2168","DOI":"10.1109\/TSP.2015.2505667","article-title":"Dual-Function Radar-Communications: Information Embedding Using Sidelobe Control and Waveform Diversity","volume":"64","author":"Hassanien","year":"2016","journal-title":"IEEE Trans. Signal Process."},{"key":"ref_13","doi-asserted-by":"crossref","first-page":"1185","DOI":"10.1109\/TAES.2010.5545182","article-title":"Intrapulse Radar-Embedded Communications","volume":"46","author":"Blunt","year":"2010","journal-title":"IEEE Trans. Aerosp. Electron. Syst."},{"key":"ref_14","doi-asserted-by":"crossref","unstructured":"Gaglione, D., Clemente, C., Ilioudis, C.V., Persico, A.R., Proudler, I.K., and Soraghan, J.J. (2016, January 2\u20136). Fractional fourier based waveform for a joint radar-communication system. Proceedings of the 2016 IEEE Radar Conference (RadarConf), Philadelphia, PA, USA.","DOI":"10.1109\/RADAR.2016.7485314"},{"key":"ref_15","doi-asserted-by":"crossref","first-page":"671","DOI":"10.1109\/TVT.2018.2883796","article-title":"Multibeam for Joint Communication and Radar Sensing Using Steerable Analog Antenna Arrays","volume":"68","author":"Zhang","year":"2019","journal-title":"IEEE Trans. Veh. Technol."},{"key":"ref_16","doi-asserted-by":"crossref","unstructured":"Liu, F., and Masouros, C. (2019, January 12\u201317). Hybrid Beamforming with Sub-arrayed MIMO Radar: Enabling Joint Sensing and Communication at mmWave Band. Proceedings of the 2019 IEEE International Conference on Acoustics, Speech and Signal Processing (ICASSP), Brighton, UK.","DOI":"10.1109\/ICASSP.2019.8683591"},{"key":"ref_17","doi-asserted-by":"crossref","first-page":"374","DOI":"10.1109\/LWC.2017.2693985","article-title":"Robust MIMO Beamforming for Cellular and Radar Coexistence","volume":"6","author":"Liu","year":"2017","journal-title":"IEEE Wirel. Commun. Lett."},{"key":"ref_18","doi-asserted-by":"crossref","first-page":"1911","DOI":"10.1109\/TAES.2013.6558027","article-title":"Interference Mitigation Processing for Spectrum-Sharing Between Radar and Wireless Communications Systems","volume":"49","author":"Deng","year":"2013","journal-title":"IEEE Trans. Aerosp. Electron. Syst."},{"key":"ref_19","doi-asserted-by":"crossref","unstructured":"Singh, K., Biswas, S., Taghizadeh, O., and Ratnarajah, T. (2019, January 12\u201317). Beamforming Design for Coexistence of Full-duplex Multi-cell MU-MIMO Cellular Network and MIMO Radar. Proceedings of the 2019 IEEE International Conference on Acoustics, Speech and Signal Processing (ICASSP), Brighton, UK.","DOI":"10.1109\/ICASSP.2019.8683071"},{"key":"ref_20","doi-asserted-by":"crossref","first-page":"556","DOI":"10.1109\/TCCN.2018.2830758","article-title":"Transceiver Design and Power Allocation for Full-Duplex MIMO Communication Systems With Spectrum Sharing Radar","volume":"4","author":"Singh","year":"2018","journal-title":"IEEE Trans. Cogn. Commun. Netw."},{"key":"ref_21","doi-asserted-by":"crossref","unstructured":"Shi, C., Wang, F., Salous, S., and Zhou, J. (2019, January 12\u201317). Distributed Power Allocation for Spectral Coexisting Multistatic Radar and Communication Systems Based on Stackelberg Game. Proceedings of the 2019 IEEE International Conference on Acoustics, Speech and Signal Processing (ICASSP), Brighton, UK.","DOI":"10.1109\/RADAR.2019.8835607"},{"key":"ref_22","doi-asserted-by":"crossref","first-page":"253","DOI":"10.1109\/LWC.2018.2868819","article-title":"Resource Allocation for a Wireless Powered Integrated Radar and Communication System","volume":"8","author":"Zhou","year":"2019","journal-title":"IEEE Wirel. Commun. Lett."},{"key":"ref_23","doi-asserted-by":"crossref","first-page":"4928","DOI":"10.1109\/JSEN.2015.2424393","article-title":"Target Detection Performance of Spectrum Sharing MIMO Radars","volume":"15","author":"Khawar","year":"2015","journal-title":"IEEE Sens. J."},{"key":"ref_24","doi-asserted-by":"crossref","first-page":"464","DOI":"10.1109\/TSP.2015.2483485","article-title":"Inner Bounds on Performance of Radar and Communications Co-Existence","volume":"64","author":"Chiriyath","year":"2016","journal-title":"IEEE Trans. Signal Process."},{"key":"ref_25","doi-asserted-by":"crossref","first-page":"972","DOI":"10.1109\/LAWP.2015.2487368","article-title":"Coexistence Analysis Between Radar and Cellular System in LoS Channel","volume":"15","author":"Khawar","year":"2016","journal-title":"IEEE Antennas Wirel. Propag. Lett."},{"key":"ref_26","doi-asserted-by":"crossref","unstructured":"Surender, S.C., Narayanan, R.M., and Das, C.R. (2010, January 6\u201310). Performance Analysis of Communications amp; Radar Coexistence in a Covert UWB OSA System. Proceedings of the 2010 IEEE Global Telecommunications Conference GLOBECOM, Miami, FL, USA.","DOI":"10.1109\/GLOCOM.2010.5683837"},{"key":"ref_27","doi-asserted-by":"crossref","first-page":"282","DOI":"10.1016\/j.dsp.2018.06.017","article-title":"Performance tradeoff in a unified system of communications and passive radar: A secrecy capacity approach","volume":"82","author":"Chalise","year":"2018","journal-title":"Digit. Signal Process."},{"key":"ref_28","doi-asserted-by":"crossref","first-page":"107","DOI":"10.1016\/j.dsp.2018.07.014","article-title":"Non-orthogonal multiple access based cooperative spectrum sharing between MIMO radar and MIMO communication systems","volume":"83","author":"Rihan","year":"2018","journal-title":"Digit. Signal Process."},{"key":"ref_29","doi-asserted-by":"crossref","first-page":"1576","DOI":"10.1109\/LCOMM.2018.2837913","article-title":"Multistatic Radar Placement Optimization for Cooperative Radar-Communication Systems","volume":"22","author":"Gagnon","year":"2018","journal-title":"IEEE Commun. Lett."},{"key":"ref_30","doi-asserted-by":"crossref","first-page":"194","DOI":"10.1109\/LSP.2018.2880836","article-title":"Performance Gains From Cooperative MIMO Radar and MIMO Communication Systems","volume":"26","author":"He","year":"2019","journal-title":"IEEE Signal Process. Lett."},{"key":"ref_31","doi-asserted-by":"crossref","first-page":"2846","DOI":"10.1109\/TAES.2017.2717518","article-title":"Joint Transmit Designs for Coexistence of MIMO Wireless Communications and Sparse Sensing Radars in Clutter","volume":"53","author":"Li","year":"2017","journal-title":"IEEE Trans. Aerosp. Electron. Syst."},{"key":"ref_32","unstructured":"Alpcan, T., Basar, T., Srikant, R., and Altman, E. (2001, January 4\u20137). CDMA uplink power control as a noncooperative game. Proceedings of the 40th IEEE Conference on Decision and Control (Cat. No.01CH37228), Orlando, FL, USA."},{"key":"ref_33","doi-asserted-by":"crossref","first-page":"3326","DOI":"10.1109\/TSP.2011.2135347","article-title":"Multiuser Downlink Beamforming in Multicell Wireless Systems: A Game Theoretical Approach","volume":"59","author":"Nguyen","year":"2011","journal-title":"IEEE Trans. Signal Process."},{"key":"ref_34","doi-asserted-by":"crossref","first-page":"3246","DOI":"10.1109\/TSP.2013.2259160","article-title":"Supermodular Game for Power Control in TOA-Based Positioning","volume":"61","author":"Moragrega","year":"2013","journal-title":"IEEE Trans. Signal Process."},{"key":"ref_35","doi-asserted-by":"crossref","first-page":"1081","DOI":"10.1109\/TAES.2011.5751244","article-title":"Game Theoretic Analysis of Adaptive Radar Jamming","volume":"47","author":"Bachmann","year":"2011","journal-title":"IEEE Trans. Aerosp. Electron. Syst."},{"key":"ref_36","doi-asserted-by":"crossref","first-page":"2760","DOI":"10.1109\/TAES.2016.150699","article-title":"Game theoretic analysis for MIMO radars with multiple targets","volume":"52","author":"Deligiannis","year":"2016","journal-title":"IEEE Trans. Aerosp. Electron. Syst."},{"key":"ref_37","doi-asserted-by":"crossref","first-page":"5423","DOI":"10.1109\/JSEN.2015.2431261","article-title":"Cooperative Game Approach to Power Allocation for Target Tracking in Distributed MIMO Radar Sensor Networks","volume":"15","author":"Chen","year":"2015","journal-title":"IEEE Sens. J."},{"key":"ref_38","doi-asserted-by":"crossref","first-page":"146","DOI":"10.1016\/j.dsp.2019.05.007","article-title":"Power control scheme for spectral coexisting multistatic radar and massive MIMO communication systems under uncertainties: A robust Stackelberg game model","volume":"94","author":"Shi","year":"2019","journal-title":"Digit. Signal Process."}],"container-title":["Sensors"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.mdpi.com\/1424-8220\/20\/21\/6216\/pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2025,10,11]],"date-time":"2025-10-11T10:27:24Z","timestamp":1760178444000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.mdpi.com\/1424-8220\/20\/21\/6216"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2020,10,31]]},"references-count":38,"journal-issue":{"issue":"21","published-online":{"date-parts":[[2020,11]]}},"alternative-id":["s20216216"],"URL":"https:\/\/doi.org\/10.3390\/s20216216","relation":{},"ISSN":["1424-8220"],"issn-type":[{"type":"electronic","value":"1424-8220"}],"subject":[],"published":{"date-parts":[[2020,10,31]]}}}