{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,10,27]],"date-time":"2025-10-27T16:07:52Z","timestamp":1761581272298,"version":"build-2065373602"},"reference-count":38,"publisher":"MDPI AG","issue":"1","license":[{"start":{"date-parts":[[2015,1,16]],"date-time":"2015-01-16T00:00:00Z","timestamp":1421366400000},"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>Interference alignment (IA) has been put forward as a promising technique which can mitigate interference and effectively increase the throughput of wireless sensor networks (WSNs). However, the number of users is strictly restricted by the IA feasibility condition, and the interference leakage will become so strong that the quality of service will degrade significantly when there are more users than that IA can support. In this paper, a novel joint spatial-code clustered (JSCC)-IA scheme is proposed to solve this problem. In the proposed scheme, the users are clustered into several groups so that feasible IA can be achieved within each group. In addition, each group is assigned a pseudo noise (PN) code in order to suppress the inter-group interference via the code dimension. The analytical bit error rate (BER) expressions of the proposed JSCC-IA scheme are formulated for the systems with identical and different propagation delays, respectively. To further improve the performance of the JSCC-IA scheme in asymmetric networks, a random grouping selection (RGS) algorithm is developed to search for better grouping combinations. Numerical results demonstrate that the proposed JSCC-IA scheme is capable of accommodating many more users to communicate simultaneously in the same frequency band with better performance.<\/jats:p>","DOI":"10.3390\/s150101964","type":"journal-article","created":{"date-parts":[[2015,1,16]],"date-time":"2015-01-16T10:23:36Z","timestamp":1421403816000},"page":"1964-1997","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":10,"title":["A Novel Joint Spatial-Code Clustered Interference Alignment Scheme for Large-Scale Wireless Sensor Networks"],"prefix":"10.3390","volume":"15","author":[{"given":"Zhilu","family":"Wu","sequence":"first","affiliation":[{"name":"School of Electronics and Information Engineering, Harbin Institute of Technology,  Harbin 150001, China"}]},{"given":"Lihui","family":"Jiang","sequence":"additional","affiliation":[{"name":"School of Electronics and Information Engineering, Harbin Institute of Technology,  Harbin 150001, China"}]},{"given":"Guanghui","family":"Ren","sequence":"additional","affiliation":[{"name":"School of Electronics and Information Engineering, Harbin Institute of Technology,  Harbin 150001, China"}]},{"given":"Nan","family":"Zhao","sequence":"additional","affiliation":[{"name":"School of Information and Communication Engineering, Dalian University of Technology,  Dalian 116024, China"}]},{"given":"Yaqin","family":"Zhao","sequence":"additional","affiliation":[{"name":"School of Electronics and Information Engineering, Harbin Institute of Technology,  Harbin 150001, China"}]}],"member":"1968","published-online":{"date-parts":[[2015,1,16]]},"reference":[{"key":"ref_1","doi-asserted-by":"crossref","first-page":"7033","DOI":"10.3390\/s130607033","article-title":"Performance analysis of cooperative virtual MIMO systems for wireless sensor networks","volume":"13","author":"Rafique","year":"2013","journal-title":"Sensors"},{"key":"ref_2","doi-asserted-by":"crossref","first-page":"9887","DOI":"10.3390\/s111009887","article-title":"Cooperative MIMO communication at wireless sensor network: An error correcting code approach","volume":"11","author":"Islam","year":"2011","journal-title":"Sensors"},{"key":"ref_3","doi-asserted-by":"crossref","first-page":"291","DOI":"10.1109\/TWC.2010.01.090221","article-title":"Linear precoder designs for K-user interference channels","volume":"9","author":"Sung","year":"2010","journal-title":"IEEE Trans. Wirel. Commun."},{"key":"ref_4","doi-asserted-by":"crossref","first-page":"3425","DOI":"10.1109\/TIT.2008.926344","article-title":"Interference alignment and degrees of freedom of the K-user interference channel","volume":"54","author":"Cadambe","year":"2008","journal-title":"IEEE Trans. Inf. Theory"},{"key":"ref_5","doi-asserted-by":"crossref","first-page":"6040","DOI":"10.1109\/TIT.2010.2080830","article-title":"Degrees of freedom of the K user M \u00d7 N MIMO interference channel","volume":"56","author":"Gou","year":"2010","journal-title":"IEEE Trans. Inf. Theory"},{"key":"ref_6","doi-asserted-by":"crossref","first-page":"4309","DOI":"10.1109\/TVT.2010.2082005","article-title":"The feasibility of interference alignment over measured MIMO-OFDM channels","volume":"59","author":"Peters","year":"2010","journal-title":"IEEE Trans. Veh. Technol."},{"key":"ref_7","doi-asserted-by":"crossref","first-page":"351","DOI":"10.1049\/iet-com.2013.0178","article-title":"New interference alignment schemes with full and half-duplex relays for the quasi-static X channel","volume":"8","author":"Jin","year":"2014","journal-title":"IET Commun."},{"key":"ref_8","doi-asserted-by":"crossref","first-page":"879","DOI":"10.1109\/TVT.2013.2279761","article-title":"Stackelberg game for cognitive radio networks with MIMO and distributed interference alignment","volume":"63","author":"Xu","year":"2014","journal-title":"IEEE Trans. Veh. Technol."},{"key":"ref_9","doi-asserted-by":"crossref","first-page":"1628","DOI":"10.1049\/iet-com.2013.0222","article-title":"On the performance of asynchronous ad-hoc networks using interference alignment with renewal process","volume":"7","author":"Luo","year":"2013","journal-title":"IET Commun."},{"key":"ref_10","doi-asserted-by":"crossref","first-page":"189","DOI":"10.1109\/JOE.2013.2293932","article-title":"Region of feasibility of interference alignment in underwater sensor networks","volume":"39","author":"Pandey","year":"2014","journal-title":"IEEE J. Ocean. Eng."},{"key":"ref_11","doi-asserted-by":"crossref","first-page":"4771","DOI":"10.1109\/TSP.2010.2050480","article-title":"On feasibility of interference alignment in MIMO interference networks","volume":"58","author":"Yetis","year":"2010","journal-title":"IEEE Trans. Signal Process"},{"key":"ref_12","unstructured":"Halima, S.B., and Saadani, A. (2012, January 1\u20134). Joint clustering and interference alignment for overloaded femtocell networks. Shanghai, China."},{"key":"ref_13","doi-asserted-by":"crossref","first-page":"2613","DOI":"10.1109\/TVT.2013.2292897","article-title":"Clustering for interference alignment in multiuser interference network","volume":"63","author":"Chen","year":"2014","journal-title":"IEEE Trans. Veh. Technol."},{"key":"ref_14","doi-asserted-by":"crossref","first-page":"910","DOI":"10.1016\/j.aeue.2013.05.002","article-title":"Decentralized multiuser diversity with opportunistic packet transmission in MIMO wireless sensor networks","volume":"67","author":"Soy","year":"2013","journal-title":"AEU-Int. J. Electron. Commun."},{"key":"ref_15","doi-asserted-by":"crossref","first-page":"856","DOI":"10.1109\/TVT.2006.873837","article-title":"Virtual MIMO-based cross-layer design for wireless sensor networks","volume":"55","author":"Yuan","year":"2006","journal-title":"IEEE Trans. Veh. Technol."},{"key":"ref_16","doi-asserted-by":"crossref","first-page":"3956","DOI":"10.1109\/TVT.2010.2063719","article-title":"Improving energy efficiency in a wireless wensor network by combining cooperative MIMO with data aggregation","volume":"59","author":"Gao","year":"2010","journal-title":"IEEE Trans. Veh. Technol."},{"key":"ref_17","doi-asserted-by":"crossref","first-page":"4647","DOI":"10.1109\/TWC.2013.072313.121949","article-title":"Performance analysis and optimization for energy-efficient cooperative transmission in random wireless sensor network","volume":"12","author":"Li","year":"2013","journal-title":"IEEE Trans. Wirel. Commun."},{"key":"ref_18","doi-asserted-by":"crossref","first-page":"976","DOI":"10.1587\/transcom.E96.B.976","article-title":"Energy-efficient adaptive virtual MIMO transmission in a transmit-side correlated wireless sensor network","volume":"E96B","author":"Park","year":"2013","journal-title":"IEICE Trans. Commun."},{"key":"ref_19","doi-asserted-by":"crossref","first-page":"4069","DOI":"10.1109\/TVT.2012.2213620","article-title":"Multihop hybrid virtual MIMO scheme for wireless sensor networks","volume":"61","author":"Chung","year":"2012","journal-title":"IEEE Trans. Veh. Technol."},{"key":"ref_20","doi-asserted-by":"crossref","first-page":"191","DOI":"10.1049\/iet-wss.2011.0013","article-title":"Implementation and application of a multi-radio wireless sensor networks testbed","volume":"1","author":"Zhao","year":"2011","journal-title":"IET Wirel. Sens. Syst."},{"key":"ref_21","unstructured":"Tresch, R., Guillaud, M., and Riegler, E. (September, January 31). On the achievability of interference alignment in the K-user constant MIMO interference channel. Cardiff, Wales, UK."},{"key":"ref_22","doi-asserted-by":"crossref","first-page":"2896","DOI":"10.1109\/TIT.2012.2184909","article-title":"Linear transceiver design for interference alignment: Complexity and computation","volume":"58","author":"Razaviyayn","year":"2012","journal-title":"IEEE Trans. Inf. Theory"},{"key":"ref_23","unstructured":"Gomadam, K., Cadambe, V.R., and Jafar, S.A. (December, January 30). Approaching the capacity of wireless networks through distributed interference alignment. New Orleans, LA, USA."},{"key":"ref_24","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_25","doi-asserted-by":"crossref","first-page":"1","DOI":"10.1186\/1687-6180-2012-137","article-title":"Low complexity interference alignment algorithms for desired signal power maximization problem of MIMO channels","volume":"2012","author":"Sun","year":"2012","journal-title":"EURASIP J. Adv. Signal Process"},{"key":"ref_26","first-page":"424","article-title":"A leakage-based solution for interference alignment in MIMO interference channel networks","volume":"8","author":"Shrestha","year":"2014","journal-title":"KSII Trans. Internet Inf. Syst."},{"key":"ref_27","doi-asserted-by":"crossref","first-page":"5008","DOI":"10.1109\/TWC.2013.090413.121731","article-title":"A novel interference alignment scheme based on sequential antenna switching in wireless networks","volume":"12","author":"Zhao","year":"2013","journal-title":"IEEE Trans. Wirel. Commun."},{"key":"ref_28","doi-asserted-by":"crossref","first-page":"43","DOI":"10.1109\/MWC.2013.6472198","article-title":"CSI sharing strategies for transmitter cooperation in wireless networks","volume":"20","author":"Gesbert","year":"2013","journal-title":"IEEE Wirel. Commun."},{"key":"ref_29","doi-asserted-by":"crossref","first-page":"6561","DOI":"10.1109\/TSP.2012.2214214","article-title":"Feedback-topology designs for interference alignment in MIMO interference channels","volume":"60","author":"Cho","year":"2012","journal-title":"IEEE Trans. Signal Process"},{"key":"ref_30","doi-asserted-by":"crossref","first-page":"626","DOI":"10.1109\/TWC.2011.122211.101814","article-title":"Interference aignment with analog channel state feedback","volume":"11","author":"Ayach","year":"2012","journal-title":"IEEE Trans. Wirel. Commun."},{"key":"ref_31","doi-asserted-by":"crossref","first-page":"2878","DOI":"10.1109\/TVT.2012.2198838","article-title":"Interference alignment with differential feedback","volume":"61","author":"Zhang","year":"2012","journal-title":"IEEE Trans. Veh. Technol."},{"key":"ref_32","doi-asserted-by":"crossref","first-page":"4192","DOI":"10.1109\/TWC.2012.092412120588","article-title":"On the overhead of interference alignment: Training, feedback, and cooperation","volume":"11","author":"Lozano","year":"2012","journal-title":"IEEE Trans. Wirel. Commun."},{"key":"ref_33","unstructured":"Nan, Z., Yu, F.R., Hongjian, S., Hongxi, Y., and Nallanathan, A. (2012, January 3\u20137). Interference alignment based on channel prediction with delayed channel state information. Anaheim, CA, USA."},{"key":"ref_34","doi-asserted-by":"crossref","unstructured":"Abu-Rgheff, M.A. (2007). Introduction to CDMA Wireless Communications, Academic Press. [1st ed.].","DOI":"10.1016\/B978-075065252-0.50002-8"},{"key":"ref_35","unstructured":"Sklar, B. (2001). Digtal Communications: Fundamentals and Applications, Prentice Hall. [2nd ed.]."},{"key":"ref_36","doi-asserted-by":"crossref","first-page":"643","DOI":"10.1109\/TMC.2009.161","article-title":"Fault-tolerant relay node placement in heterogeneous wireless sensor networks","volume":"9","author":"Han","year":"2010","journal-title":"IEEE Trans. Mob. Comput."},{"key":"ref_37","doi-asserted-by":"crossref","first-page":"2579","DOI":"10.1109\/TWC.2005.853969","article-title":"On energy provisioning and relay node placement for wireless sensor networks","volume":"4","author":"Hou","year":"2005","journal-title":"IEEE Trans. Wirel. Commun."},{"key":"ref_38","doi-asserted-by":"crossref","first-page":"1423","DOI":"10.1109\/LSP.2014.2338132","article-title":"A quadratically convergent method for interference alignment in MIMO interference channels","volume":"21","author":"Gonzalez","year":"2014","journal-title":"IEEE Signal Process. Lett."}],"container-title":["Sensors"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.mdpi.com\/1424-8220\/15\/1\/1964\/pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2025,10,11]],"date-time":"2025-10-11T20:41:42Z","timestamp":1760215302000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.mdpi.com\/1424-8220\/15\/1\/1964"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2015,1,16]]},"references-count":38,"journal-issue":{"issue":"1","published-online":{"date-parts":[[2015,1]]}},"alternative-id":["s150101964"],"URL":"https:\/\/doi.org\/10.3390\/s150101964","relation":{},"ISSN":["1424-8220"],"issn-type":[{"type":"electronic","value":"1424-8220"}],"subject":[],"published":{"date-parts":[[2015,1,16]]}}}