{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,10,12]],"date-time":"2025-10-12T04:19:51Z","timestamp":1760242791463,"version":"build-2065373602"},"reference-count":57,"publisher":"MDPI AG","issue":"7","license":[{"start":{"date-parts":[[2016,7,21]],"date-time":"2016-07-21T00:00:00Z","timestamp":1469059200000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Sensors"],"abstract":"<jats:p>In this paper, we study beamforming based full-duplex (FD) systems in millimeter-wave (mmWave) communications. A joint transmission and reception (Tx\/Rx) beamforming problem is formulated to maximize the achievable rate by mitigating self-interference (SI). Since the optimal solution is difficult to find due to the non-convexity of the objective function, suboptimal schemes are proposed in this paper. A low-complexity algorithm, which iteratively maximizes signal power while suppressing SI, is proposed and its convergence is proven. Moreover, two closed-form solutions, which do not require iterations, are also derived under minimum-mean-square-error (MMSE), zero-forcing (ZF), and maximum-ratio transmission (MRT) criteria. Performance evaluations show that the proposed iterative scheme converges fast (within only two iterations on average) and approaches an upper-bound performance, while the two closed-form solutions also achieve appealing performances, although there are noticeable differences from the upper bound depending on channel conditions. Interestingly, these three schemes show different robustness against the geometry of Tx\/Rx antenna arrays and channel estimation errors.<\/jats:p>","DOI":"10.3390\/s16071130","type":"journal-article","created":{"date-parts":[[2016,7,21]],"date-time":"2016-07-21T09:48:05Z","timestamp":1469094485000},"page":"1130","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":41,"title":["Beamforming Based Full-Duplex for Millimeter-Wave Communication"],"prefix":"10.3390","volume":"16","author":[{"given":"Xiao","family":"Liu","sequence":"first","affiliation":[{"name":"School of Electronic and Information Engineering, Beihang University, Beijing 100191, China"},{"name":"Collaborative Innovation Center of Geospatial Technology, Wuhan 430079, China"},{"name":"Beijing Key Laboratory for Network-Based Cooperative Air Traffic Management, and Beijing Laboratory for General Aviation Technology, Beijing 100191, China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-4884-542X","authenticated-orcid":false,"given":"Zhenyu","family":"Xiao","sequence":"additional","affiliation":[{"name":"School of Electronic and Information Engineering, Beihang University, Beijing 100191, China"},{"name":"Collaborative Innovation Center of Geospatial Technology, Wuhan 430079, China"},{"name":"Beijing Key Laboratory for Network-Based Cooperative Air Traffic Management, and Beijing Laboratory for General Aviation Technology, Beijing 100191, China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Lin","family":"Bai","sequence":"additional","affiliation":[{"name":"School of Electronic and Information Engineering, Beihang University, Beijing 100191, China"},{"name":"Collaborative Innovation Center of Geospatial Technology, Wuhan 430079, China"},{"name":"Beijing Key Laboratory for Network-Based Cooperative Air Traffic Management, and Beijing Laboratory for General Aviation Technology, Beijing 100191, China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-4895-6680","authenticated-orcid":false,"given":"Jinho","family":"Choi","sequence":"additional","affiliation":[{"name":"School of Electrical Engineerng and Computer Science, Gwangju Institute of Science and Technology (GIST), Gwangju 61005, Korea"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Pengfei","family":"Xia","sequence":"additional","affiliation":[{"name":"School of Electronics and Information Engineering and the Key Laboratory of Embedded System and Service Computing, Tongji University, Shanghai 200092, China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Xiang-Gen","family":"Xia","sequence":"additional","affiliation":[{"name":"Department of Electrical and Computer Engineering, University of Delaware, Newark, DE 19716, USA"}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"1968","published-online":{"date-parts":[[2016,7,21]]},"reference":[{"key":"ref_1","doi-asserted-by":"crossref","first-page":"1637","DOI":"10.1109\/JSAC.2014.2330193","article-title":"In-band full-duplex wireless: Challenges and opportunities","volume":"32","author":"Sabharwal","year":"2014","journal-title":"IEEE J. Sel. Areas Commun."},{"key":"ref_2","doi-asserted-by":"crossref","unstructured":"Ahmed, E., Eltawil, A., and Sabharwal, A. (2012, January 8\u201314). Simultaneous transmit and sense for cognitive radios using full-duplex: A first study. Proceedings of the IEEE Antennas and Propagation Society International Symposium (APSURSI), Chicago, IL, USA.","DOI":"10.1109\/APS.2012.6348493"},{"key":"ref_3","doi-asserted-by":"crossref","first-page":"4296","DOI":"10.1109\/TWC.2012.102612.111278","article-title":"Experiment-driven characterization of full-duplex wireless systems","volume":"11","author":"Duarte","year":"2011","journal-title":"IEEE Trans. Wirel. Commun."},{"key":"ref_4","doi-asserted-by":"crossref","first-page":"1160","DOI":"10.1109\/TVT.2013.2284712","article-title":"Design and characterization of a full-duplex multiantenna system for WiFi networks","volume":"63","author":"Duarte","year":"2014","journal-title":"IEEE Trans. Veh. Technol."},{"key":"ref_5","doi-asserted-by":"crossref","unstructured":"Jain, M., Choi, J.I., Kim, T., Bharadia, D., Seth, S., Srinivasan, K., Levis, P., Katti, S., and Sinha, P. (2011, January 19\u201323). Practical, real-time, full duplex wireless. Proceedings of the 17th Annual International Conference on Mobile Computing and Networking, Las Vegas, NV, USA.","DOI":"10.1145\/2030613.2030647"},{"key":"ref_6","doi-asserted-by":"crossref","unstructured":"Li, N., Zhu, W., and Han, H. (2012, January 21\u201323). Digital interference cancellation in single channel, full duplex wireless communication. Proceedings of the 8th International Conference on Wireless Communications, Networking and Mobile Computing (WiCOM), Shanghai, China.","DOI":"10.1109\/WiCOM.2012.6478497"},{"key":"ref_7","unstructured":"Li, S., and Murch, R.D. (2011, January 5\u20139). Full-duplex wireless communication using transmitter output based echo cancellation. Proceedings of the IEEE Global Telecommunications Conference (GLOBECOM 2011), Houston, TX, USA."},{"key":"ref_8","doi-asserted-by":"crossref","unstructured":"Choi, J.I., Jain, M., Srinivasan, K., Levis, P., and Katti, S. (2010, January 20\u201324). Achieving single channel, full duplex wireless communication. Proceedings of the 16th Annual International Conference on Mobile Computing and Networking (MobiCom 2010), Chicago, IL, USA.","DOI":"10.1145\/1859995.1859997"},{"key":"ref_9","doi-asserted-by":"crossref","unstructured":"Khojastepour, M.A., Sundaresan, K., Rangarajan, S., Zhang, X., and Barghi, S. (2011, January 14\u201315). The case for antenna cancellation for scalable full-duplex wireless communications. Proceedings of the 10th ACM Workshop on Hot Topics in Networks, Cambridge, MA, USA.","DOI":"10.1145\/2070562.2070579"},{"key":"ref_10","doi-asserted-by":"crossref","unstructured":"Bharadia, D., McMilin, E., and Katti, S. (2013, January 12\u201316). Full duplex radios. Proceedings of the Special Interest Group on Data Communication (SIGCOMM), Hong Kong, China.","DOI":"10.1145\/2486001.2486033"},{"key":"ref_11","doi-asserted-by":"crossref","first-page":"44","DOI":"10.1109\/MMM.2010.938581","article-title":"60 GHz wireless: Up close and personal","volume":"11","author":"Daniels","year":"2010","journal-title":"IEEE Microw. Mag."},{"key":"ref_12","doi-asserted-by":"crossref","unstructured":"Perahia, E., Cordeiro, C., Park, M., and Yang, L.L. (2010, January 9\u201312). IEEE 802.11 ad: Defining the next generation multi-Gbps Wi-Fi. Proceedings of the IEEE Consumer Communications and Networking Conference (CCNC), Las Vegas, NV, USA.","DOI":"10.1109\/CCNC.2010.5421713"},{"key":"ref_13","doi-asserted-by":"crossref","unstructured":"Yong, S.K., Xia, P., and Valdes-Garcia, A. (2011). 60GHz Technology for Gbps WLAN and WPAN: From Theory to Practice, Wiley.","DOI":"10.1002\/9780470972946"},{"key":"ref_14","doi-asserted-by":"crossref","first-page":"3791","DOI":"10.1109\/TWC.2014.2318053","article-title":"Tens of gigabits wireless communications over E-band LoS MIMO channels with uniform linear antenna arrays","volume":"13","author":"Wang","year":"2014","journal-title":"IEEE Trans. Wirel. Commun."},{"key":"ref_15","doi-asserted-by":"crossref","first-page":"168","DOI":"10.1109\/MCOM.2015.7010531","article-title":"Multi-gigabit millimeter wave wireless communications for 5G: From fixed access to cellular networks","volume":"53","author":"Wang","year":"2015","journal-title":"IEEE Commun. Mag."},{"key":"ref_16","doi-asserted-by":"crossref","first-page":"998","DOI":"10.1109\/JSAC.2016.2549418","article-title":"Energy-efficient hybrid analog and digital precoding for mmWave MIMO systems with large antenna arrays","volume":"34","author":"Gao","year":"2016","journal-title":"IEEE J. Sel. Areas Commun."},{"key":"ref_17","doi-asserted-by":"crossref","first-page":"6169","DOI":"10.1109\/TSP.2015.2463260","article-title":"Spatially common sparsity based adaptive channel estimation and feedback for FDD massive MIMO","volume":"63","author":"Gao","year":"2015","journal-title":"IEEE Trans. Signal Process."},{"key":"ref_18","doi-asserted-by":"crossref","first-page":"1266","DOI":"10.1109\/LCOMM.2014.2325027","article-title":"Super-resolution sparse MIMO-OFDM channel estimation based on spatial and temporal correlations","volume":"18","author":"Gao","year":"2014","journal-title":"IEEE Commun. Lett."},{"key":"ref_19","doi-asserted-by":"crossref","first-page":"2657","DOI":"10.1007\/s11276-015-0942-z","article-title":"A survey of millimeter wave communications (mmWave) for 5G: Opportunities and challenges","volume":"21","author":"Niu","year":"2015","journal-title":"Wirel. Netw."},{"key":"ref_20","doi-asserted-by":"crossref","first-page":"505","DOI":"10.1109\/LCOMM.2005.06006","article-title":"An iterative singular vectors estimation scheme for beamforming transmission and detection in MIMO systems","volume":"9","author":"Tang","year":"2005","journal-title":"IEEE Commun. Lett."},{"key":"ref_21","doi-asserted-by":"crossref","first-page":"1790","DOI":"10.1109\/LCOMM.2013.071813.131181","article-title":"Suboptimal Spatial Diversity Scheme for 60 GHz Millimeter-Wave WLAN","volume":"17","author":"Xiao","year":"2013","journal-title":"IEEE Commun. Lett."},{"key":"ref_22","doi-asserted-by":"crossref","first-page":"829","DOI":"10.1109\/LCOMM.2014.040214.140351","article-title":"Iterative Joint Beamforming Training with Constant-Amplitude Phased Arrays in Millimeter-Wave Communications","volume":"18","author":"Xiao","year":"2014","journal-title":"IEEE Commun. Lett."},{"key":"ref_23","doi-asserted-by":"crossref","first-page":"1260","DOI":"10.1109\/LCOMM.2012.060112.120793","article-title":"A Spatial Diversity Technique for IEEE 802.11 ad WLAN in 60 GHz Band","volume":"16","author":"Park","year":"2012","journal-title":"IEEE Commun. Lett."},{"key":"ref_24","doi-asserted-by":"crossref","unstructured":"Nsenga, J., Van Thillo, W., Horlin, F., Ramon, V., Bourdoux, A., and Lauwereins, R. (2009, January 14\u201318). Joint transmit and receive analog beamforming in 60 GHz MIMO multipath channels. Proceedings of the 2009 IEEE International Conference on Communications (ICC), Dresden, Germany.","DOI":"10.1109\/ICC.2009.5199125"},{"key":"ref_25","doi-asserted-by":"crossref","first-page":"703","DOI":"10.1109\/TVT.2013.2279694","article-title":"Efficient beamforming training for 60-GHz millimeter-wave communications: A novel numerical optimization framework","volume":"63","author":"Li","year":"2014","journal-title":"IEEE Trans. Veh. Technol."},{"key":"ref_26","doi-asserted-by":"crossref","first-page":"504","DOI":"10.1109\/TWC.2012.121412.110419","article-title":"On the Efficient Beam-Forming Training for 60GHz Wireless Personal Area Networks","volume":"12","author":"Li","year":"2013","journal-title":"IEEE Trans. Wirel. Commun."},{"key":"ref_27","doi-asserted-by":"crossref","unstructured":"Chun, B., and Lee, Y.H. (2010, January 18\u201321). A spatial self-interference nullification method for full duplex amplify-and-forward MIMO relays. Proceedings of the 2010 IEEE Wireless Communications and Networking Conference (WCNC), Sydney, Australia.","DOI":"10.1109\/WCNC.2010.5506436"},{"key":"ref_28","doi-asserted-by":"crossref","first-page":"5983","DOI":"10.1109\/TSP.2011.2164910","article-title":"Mitigation of loopback self-interference in full-duplex MIMO relays","volume":"59","author":"Riihonen","year":"2011","journal-title":"IEEE Trans. Signal Process."},{"key":"ref_29","doi-asserted-by":"crossref","first-page":"2680","DOI":"10.1109\/TWC.2012.060212.112214","article-title":"Distributed space-time coding for full-duplex asynchronous cooperative communications","volume":"11","author":"Liu","year":"2012","journal-title":"IEEE Trans. Wirel. Commun."},{"key":"ref_30","doi-asserted-by":"crossref","first-page":"6406","DOI":"10.1109\/TWC.2013.102313.130541","article-title":"Distributed linear convolutional space-time coding for two-relay full-duplex asynchronous cooperative networks","volume":"12","author":"Liu","year":"2013","journal-title":"IEEE Trans. Wirel. Commun."},{"key":"ref_31","doi-asserted-by":"crossref","first-page":"3494","DOI":"10.1109\/TMTT.2011.2172625","article-title":"Transmit\u2013receive duplexing using digital beamforming system to cancel self-interference","volume":"59","author":"Snow","year":"2011","journal-title":"IEEE Trans. Microw. Theory Tech."},{"key":"ref_32","doi-asserted-by":"crossref","first-page":"3309","DOI":"10.1109\/TIT.2011.2142270","article-title":"A distributed numerical approach to interference alignment and applications to wireless interference networks","volume":"57","author":"Gomadam","year":"2011","journal-title":"IEEE Trans. Inf. Theory"},{"key":"ref_33","doi-asserted-by":"crossref","unstructured":"Santamaria, I., Gonzalez, O., Heath, R., and Peters, S.W. (2010, January 6\u201310). Maximum sum-rate interference alignment algorithms for MIMO channels. Proceedings of the IEEE Global Telecommunications Conference (GLOBECOM 2010), Miami, FL, USA.","DOI":"10.1109\/GLOCOM.2010.5683919"},{"key":"ref_34","doi-asserted-by":"crossref","first-page":"206","DOI":"10.1109\/TVT.2010.2085459","article-title":"Cooperative algorithms for MIMO interference channels","volume":"60","author":"Peters","year":"2011","journal-title":"IEEE Trans. Veh. Technol."},{"key":"ref_35","doi-asserted-by":"crossref","first-page":"3476","DOI":"10.1109\/TSP.2013.2257761","article-title":"Comparison of distributed beamforming algorithms for MIMO interference networks","volume":"61","author":"Schmidt","year":"2013","journal-title":"IEEE Trans. Signal Process."},{"key":"ref_36","doi-asserted-by":"crossref","first-page":"1390","DOI":"10.1109\/JSAC.2009.091009","article-title":"Beam codebook based beamforming protocol for multi-Gbps millimeter-wave WPAN systems","volume":"27","author":"Wang","year":"2009","journal-title":"IEEE J. Sel. Areas Commun."},{"key":"ref_37","unstructured":"Maltsev, A., Maslennikov, R., Sevastyanov, A., Lomayev, A., Khoryaev, A., Davydov, A., and Ssorin, V. (2010, January 12\u201316). Characteristics of indoor millimeter-wave channel at 60 GHz in application to perspective WLAN system. Proceedings of the Fourth European Conference on Antennas and Propagation (EuCAP), Barcelona, Spain."},{"key":"ref_38","doi-asserted-by":"crossref","first-page":"122","DOI":"10.1109\/MCOM.2014.6979963","article-title":"MIMO precoding and combining solutions for millimeter-wave systems","volume":"52","author":"Alkhateeb","year":"2014","journal-title":"IEEE Commun. Mag."},{"key":"ref_39","doi-asserted-by":"crossref","first-page":"4391","DOI":"10.1109\/TCOMM.2013.090513.120848","article-title":"Millimeter wave beamforming for wireless backhaul and access in small cell networks","volume":"61","author":"Hur","year":"2013","journal-title":"IEEE Trans. Commun."},{"key":"ref_40","doi-asserted-by":"crossref","first-page":"66","DOI":"10.1109\/MCOM.2016.7470937","article-title":"Enabling UAV cellular with millimeter-wave communication: Potentials and approaches","volume":"54","author":"Xiao","year":"2016","journal-title":"IEEE Commun. Mag."},{"key":"ref_41","doi-asserted-by":"crossref","first-page":"366","DOI":"10.1109\/JPROC.2014.2299397","article-title":"Millimeter-wave cellular wireless networks: Potentials and challenges","volume":"102","author":"Rangan","year":"2014","journal-title":"Proc. IEEE"},{"key":"ref_42","doi-asserted-by":"crossref","first-page":"1499","DOI":"10.1109\/TWC.2014.011714.130846","article-title":"Spatially Sparse Precoding in Millimeter Wave MIMO Systems","volume":"13","author":"Rajagopal","year":"2014","journal-title":"IEEE Trans. Wirel. Commun."},{"key":"ref_43","doi-asserted-by":"crossref","first-page":"173","DOI":"10.1109\/8.45119","article-title":"Evaluation of adaptive phased array antenna, far-field nulling performance in the near-field region","volume":"38","author":"Fenn","year":"1990","journal-title":"IEEE Trans. Antennas Propag."},{"key":"ref_44","doi-asserted-by":"crossref","first-page":"30","DOI":"10.1109\/TAP.1986.1143727","article-title":"An overview of near-field antenna measurements","volume":"34","author":"Yaghjian","year":"1986","journal-title":"IEEE Trans. Antennas Propag."},{"key":"ref_45","doi-asserted-by":"crossref","first-page":"2711","DOI":"10.1109\/TAP.2012.2194666","article-title":"Planar near-field measurement of digital phased arrays using near-field scan plane reconstruction","volume":"60","author":"Sayers","year":"2012","journal-title":"IEEE Trans. Antennas Propag."},{"key":"ref_46","first-page":"783","article-title":"Design of robust near-field multi-beam forming based on improved LCMV algorithm","volume":"6","author":"Liao","year":"2015","journal-title":"J. Inf. Hiding Multimed. Signal Process."},{"key":"ref_47","first-page":"712","article-title":"Near-field robust adaptive beamforming based on worst-case performance optimization","volume":"1","author":"Lin","year":"2006","journal-title":"Int. J. Electr. Comput. Eng."},{"key":"ref_48","doi-asserted-by":"crossref","first-page":"3231","DOI":"10.1109\/TVT.2007.900522","article-title":"Adaptive robust DOA estimation for a 60-GHz antenna-array system","volume":"56","author":"Lee","year":"2007","journal-title":"IEEE Trans. Veh. Technol."},{"key":"ref_49","doi-asserted-by":"crossref","unstructured":"Tsang, Y.M., Poon, A.S., and Addepalli, S. (2011, January 5\u20139). Coding the beams: Improving beamforming training in mmwave communication system. Proceedings of the IEEE Global Telecommunications Conference (GLOBECOM 2011), Houston, TX, USA.","DOI":"10.1109\/GLOCOM.2011.6134486"},{"key":"ref_50","doi-asserted-by":"crossref","first-page":"1595","DOI":"10.1109\/TWC.2014.2370637","article-title":"Iterative Eigenvalue Decomposition and Multipath-Grouping Tx\/Rx Joint Beamformings for Millimeter-Wave Communications","volume":"14","author":"Xiao","year":"2015","journal-title":"IEEE Trans. Wirel. Commun."},{"key":"ref_51","doi-asserted-by":"crossref","first-page":"831","DOI":"10.1109\/JSTSP.2014.2334278","article-title":"Channel estimation and hybrid precoding for millimeter wave cellular systems","volume":"8","author":"Alkhateeb","year":"2014","journal-title":"IEEE J. Sel. Top. Signal Process."},{"key":"ref_52","doi-asserted-by":"crossref","first-page":"1592","DOI":"10.1109\/LCOMM.2015.2456872","article-title":"An Enhanced Channel Estimation Method for Millimeter Wave Systems with Massive Antenna Arrays","volume":"19","author":"Peng","year":"2015","journal-title":"IEEE Commun. Lett."},{"key":"ref_53","doi-asserted-by":"crossref","first-page":"2155","DOI":"10.1109\/TSP.2010.2040413","article-title":"A general criterion for analog Tx-Rx beamforming under OFDM transmissions","volume":"58","author":"Elvira","year":"2010","journal-title":"IEEE Trans. Signal Process."},{"key":"ref_54","doi-asserted-by":"crossref","unstructured":"Kokshoorn, M., Wang, P., Li, Y., and Vucetic, B. (2015, January 8\u201312). Fast channel estimation for millimetre wave wireless systems using overlapped beam patterns. Proceedings of the 2015 IEEE International Conference on Communications (ICC), London, UK.","DOI":"10.1109\/ICC.2015.7248503"},{"key":"ref_55","doi-asserted-by":"crossref","first-page":"3534","DOI":"10.1109\/TMTT.2009.2033302","article-title":"Single and four-element-Ka-band transmit\/receive phased-array silicon RFICs with 5-bit amplitude and phase control","volume":"57","author":"Kang","year":"2009","journal-title":"IEEE Trans. Microw. Theory Tech."},{"key":"ref_56","doi-asserted-by":"crossref","first-page":"1714","DOI":"10.1109\/JSAC.2013.130906","article-title":"Transmit Solutions for MIMO Wiretap Channels using Alternating Optimization","volume":"31","author":"Li","year":"2013","journal-title":"IEEE J. Sel. Areas Commun."},{"key":"ref_57","doi-asserted-by":"crossref","first-page":"1688","DOI":"10.1109\/JSAC.2014.2330131","article-title":"On rate region analysis of half-and full-duplex OFDM communication links","volume":"32","author":"Li","year":"2014","journal-title":"IEEE J. Sel. Areas Commun."}],"container-title":["Sensors"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.mdpi.com\/1424-8220\/16\/7\/1130\/pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2025,10,11]],"date-time":"2025-10-11T19:26:41Z","timestamp":1760210801000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.mdpi.com\/1424-8220\/16\/7\/1130"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2016,7,21]]},"references-count":57,"journal-issue":{"issue":"7","published-online":{"date-parts":[[2016,7]]}},"alternative-id":["s16071130"],"URL":"https:\/\/doi.org\/10.3390\/s16071130","relation":{},"ISSN":["1424-8220"],"issn-type":[{"type":"electronic","value":"1424-8220"}],"subject":[],"published":{"date-parts":[[2016,7,21]]}}}