{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,10,12]],"date-time":"2025-10-12T04:01:23Z","timestamp":1760241683641,"version":"build-2065373602"},"reference-count":40,"publisher":"MDPI AG","issue":"8","license":[{"start":{"date-parts":[[2018,7,24]],"date-time":"2018-07-24T00:00:00Z","timestamp":1532390400000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"funder":[{"DOI":"10.13039\/501100010198","name":"Ministerio de Econom\u00eda, Industria y Competitividad, Gobierno de Espa\u00f1a","doi-asserted-by":"publisher","award":["BIA2017-87573-C2-2-P"],"award-info":[{"award-number":["BIA2017-87573-C2-2-P"]}],"id":[{"id":"10.13039\/501100010198","id-type":"DOI","asserted-by":"publisher"}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Entropy"],"abstract":"<jats:p>Aiming at the limitations of the existing Limited Feedback Interference Alignment algorithms, this paper proposes a direct codeword selection scheme that maximizes the lower-bound of the user rate and reduces the sum rate loss by integrating the Bit Allocation algorithm. The target signal is decoded using the maximum signal to interference plus noise ratio (MAX-SINR) algorithm. Moreover, low complexity and global searching mechanisms are deployed to select the optimized codewords from the generated sets of codewords that approach the ideal precoder. Simulation results show that the proposed algorithm effectively improves the rate lower-bound of the system user as compared with the existing state-of-the-art algorithms.<\/jats:p>","DOI":"10.3390\/e20080546","type":"journal-article","created":{"date-parts":[[2018,7,24]],"date-time":"2018-07-24T11:51:38Z","timestamp":1532433098000},"page":"546","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":4,"title":["A Novel Codeword Selection Scheme for MIMO-MAC Lower-Bound Maximization"],"prefix":"10.3390","volume":"20","author":[{"given":"Waleed","family":"Shahjehan","sequence":"first","affiliation":[{"name":"Department of Electrical Engineering, University of Engineering &amp; Technology, Peshawar P.O. Box 814, Pakistan"}]},{"given":"Syed Waqar","family":"Shah","sequence":"additional","affiliation":[{"name":"Department of Electrical Engineering, University of Engineering &amp; Technology, Peshawar P.O. Box 814, Pakistan"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-0862-0533","authenticated-orcid":false,"given":"Jaime","family":"Lloret","sequence":"additional","affiliation":[{"name":"Integrated Management Coastal Research Institute, Universitat Politecnica de Valencia, Gandia, 46730 Valencia, Spain"}]},{"ORCID":"https:\/\/orcid.org\/0000-0003-3190-3635","authenticated-orcid":false,"given":"Ignacio","family":"Bosch","sequence":"additional","affiliation":[{"name":"Institute of Telecommunications and Multimedia Applications (iTEAM), Universitat Polit\u00e8cnica de Val\u00e8ncia, Camino Vera n\/n, 46022 Valencia, Spain"}]}],"member":"1968","published-online":{"date-parts":[[2018,7,24]]},"reference":[{"key":"ref_1","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":"Cadambre","year":"2008","journal-title":"IEEE Trans. Inf. 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Proceedings of the IEEE International Conference on Communications (ICC), Budapest, Hungary.","DOI":"10.1109\/ICC.2013.6655493"},{"key":"ref_8","unstructured":"Sara, T., Ad\u00e3o, S., Ruid, R., and Gameiro, A. (2015, January 6\u201310). Robust iterative interference alignment with limited feedback. Proceedings of the IEEE Global Telecommunications Conference (GLOBECOM), San Diego, CA, USA."},{"key":"ref_9","doi-asserted-by":"crossref","unstructured":"Lee, N., Shin, W., and Clerckx, B. (2012, January 28\u201331). Interference alignment with limited feedback for two-cell interfering MIMO-MAC. Proceedings of the International Symposium on Wireless Communication Systems, Paris, France.","DOI":"10.1109\/ISWCS.2012.6328431"},{"key":"ref_10","doi-asserted-by":"crossref","first-page":"882","DOI":"10.1109\/TWC.2014.2361335","article-title":"Robust iterative interference alignment for cellular networks with limited feedback","volume":"14","author":"Jan","year":"2015","journal-title":"IEEE Trans. Wirel. Commun."},{"key":"ref_11","doi-asserted-by":"crossref","unstructured":"Li, Y., Diao, X., Dong, Q., and Tang, C. (2017). Interference alignment based on rank constraint in MIMO cognitive radio networks. Symmetry, 9.","DOI":"10.3390\/sym9070107"},{"key":"ref_12","doi-asserted-by":"crossref","first-page":"4019","DOI":"10.1109\/TVT.2014.2366470","article-title":"Limited feedback design for interference alignment on two-cell interfering MIMO-MAC","volume":"64","author":"Kim","year":"2015","journal-title":"IEEE Trans. Veh. Technol."},{"key":"ref_13","doi-asserted-by":"crossref","first-page":"8775","DOI":"10.1109\/TVT.2015.2509501","article-title":"Throughput analysis of interference alignment for a general centralized limited feedback model","volume":"65","author":"Wang","year":"2016","journal-title":"IEEE Trans. Veh. Technol."},{"key":"ref_14","doi-asserted-by":"crossref","first-page":"540","DOI":"10.1109\/LCOMM.2014.021214.132762","article-title":"Limited feedback-based interference alignment for interfering multi-access channels","volume":"18","author":"Gao","year":"2014","journal-title":"IEEE Commun. Lett."},{"key":"ref_15","doi-asserted-by":"crossref","first-page":"8107","DOI":"10.1109\/TWC.2016.2612628","article-title":"Interference Alignment for Downlink Multi-Cell LTE-Advanced Systems with Limited Feedback","volume":"15","author":"Mosleh","year":"2016","journal-title":"IEEE Trans. Wirel. Commun."},{"key":"ref_16","doi-asserted-by":"crossref","first-page":"1","DOI":"10.3390\/electronics6030063","article-title":"Massive MIMO wireless networks: An overview","volume":"6","author":"Hassan","year":"2017","journal-title":"Electronics"},{"key":"ref_17","doi-asserted-by":"crossref","first-page":"1842","DOI":"10.3390\/e14101842","article-title":"A Survey on interference networks: Interference alignment and neutralization","volume":"14","author":"Jeon","year":"2012","journal-title":"Entropy"},{"key":"ref_18","doi-asserted-by":"crossref","unstructured":"Dong, A., Shu, H.Z.M., and Yuan, D. (2017). Simultaneous wireless information and power transfer for MIMO interference channel networks based on interference alignment. Entropy, 19.","DOI":"10.3390\/e19090484"},{"key":"ref_19","doi-asserted-by":"crossref","unstructured":"Kakar, J., and Sezgin, A. (2017). A survey on robust interference management in wireless networks. 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Netw., 180.","DOI":"10.1186\/s13638-015-0409-z"},{"key":"ref_23","doi-asserted-by":"crossref","unstructured":"Pitaval, R.A., Tirkonen, O., and Blosteing, S.D. (2011, January 5\u20139). Low complexity MIMO precoding codebooks from orthoplex packings. Proceedings of the IEEE International Conference on Communications (ICC), Kyoto, Japan.","DOI":"10.1109\/icc.2011.5963214"},{"key":"ref_24","doi-asserted-by":"crossref","unstructured":"Khan, I., Zafar, M.H., Jan, M.T., Lloret, J., Basheri, M., and Singh, D. (2018). Spectral and energy efficient low-overhead uplink and downlink channel estimation for 5G massive MIMO systems. Entropy, 20.","DOI":"10.3390\/e20020092"},{"key":"ref_25","doi-asserted-by":"crossref","unstructured":"Khan, I., Singh, M., and Singh, D. (2018). Compressive sensing based sparsity adaptive channel estimation for 5G massive MIMO systems. Appl. Sci., 8.","DOI":"10.3390\/app8050754"},{"key":"ref_26","doi-asserted-by":"crossref","first-page":"3309","DOI":"10.1109\/TIT.2011.2142270","article-title":"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_27","doi-asserted-by":"crossref","first-page":"181","DOI":"10.1016\/j.aeue.2018.03.038","article-title":"Efficient Compressive Sensing Based Sparse Channel Estimation for 5G Massive MIMO Systems","volume":"89","author":"Khan","year":"2018","journal-title":"Int. J. Electron. Commun."},{"key":"ref_28","doi-asserted-by":"crossref","first-page":"358","DOI":"10.1109\/TWC.2011.111211.110810","article-title":"A new channel quantization strategy for MIMO interference alignment with limited feedback","volume":"11","author":"Kim","year":"2012","journal-title":"IEEE Trans. Wirel. Commun."},{"key":"ref_29","doi-asserted-by":"crossref","first-page":"6481","DOI":"10.1109\/TSP.2012.2218238","article-title":"Grassmannian differential limited feedback for interference alignment","volume":"60","author":"Ayach","year":"2012","journal-title":"IEEE Trans. Signal Process."},{"key":"ref_30","unstructured":"Thukral, J., and Olcskei, H.B. (July, January 28). Interference alignment with limited feedback. Proceedings of the IEEE International Symposium on Information Theory, Seoul, Korea."},{"key":"ref_31","unstructured":"Guillaud, R.M. (2012, January 3\u20137). Limited feedback for interference alignment in the K-user MIMO interference channel. Proceedings of the IEEE Information Theory Workshop, Lausanne, Switzerland."},{"key":"ref_32","doi-asserted-by":"crossref","unstructured":"Zhou, R., Lv, T., Gao, H., Long, W., and Lu, Y. (2012, January 9\u201312). A new limited feedback scheme for interference alignment in two-cell interfering MIMO-MAC. Proceedings of the IEEE 23rd International Symposium on Personal Indoor and Mobile Radio Communications, Sydney, Australia.","DOI":"10.1109\/PIMRC.2012.6362610"},{"key":"ref_33","doi-asserted-by":"crossref","unstructured":"Zhou, R., Lv, T., Long, W., Gao, H., Lu, Y., and Liu, E. (2013, January 9\u201313). Limited feedback schemes based on ICI alignment in two-cell interfering MIMO-MAC. Proceedings of the IEEE International Conference on Communications (ICC), Budapest, Hungary.","DOI":"10.1109\/ICC.2013.6655413"},{"key":"ref_34","doi-asserted-by":"crossref","first-page":"960","DOI":"10.1109\/LCOMM.2012.050112.120316","article-title":"Interference alignment for uplink cellular systems with limited feedback","volume":"16","author":"Cho","year":"2012","journal-title":"IEEE Commun. Lett."},{"key":"ref_35","doi-asserted-by":"crossref","unstructured":"Krishnamachari, R.T., and Varanasi, M.K. (2010, January 12\u201318). Interference alignment under limited feedback for MIMO interference channels. Proceedings of the IEEE International Symposium on Information Theory (ISIT), Austin, TX, USA.","DOI":"10.1109\/ISIT.2010.5513544"},{"key":"ref_36","doi-asserted-by":"crossref","first-page":"1785","DOI":"10.1109\/TSP.2014.2304926","article-title":"Performance analysis and optimization for interference alignment over MIMO interference channels with limited feedback","volume":"62","author":"Chen","year":"2014","journal-title":"IEEE Trans. Signal Process."},{"key":"ref_37","doi-asserted-by":"crossref","first-page":"2616","DOI":"10.1109\/TCOMM.2011.070511.100313","article-title":"Downlink interference alignment","volume":"59","author":"Suh","year":"2011","journal-title":"IEEE Trans. Commun."},{"key":"ref_38","doi-asserted-by":"crossref","first-page":"1108","DOI":"10.1109\/TIT.2007.915691","article-title":"Quantization bounds on Grassmann manifolds and applications to MIMO communications","volume":"54","author":"Dai","year":"2008","journal-title":"IEEE Trans. Inf. Theory"},{"key":"ref_39","doi-asserted-by":"crossref","unstructured":"Selvaprabhu, P., Chinnadurai, S., Sarker, M.A.L., and Lee, M.H. (2018). Joint interference alignment and power allocation for k-user multicell MIMO channel through staggered antenna switching. Sensors, 18.","DOI":"10.3390\/s18020380"},{"key":"ref_40","doi-asserted-by":"crossref","first-page":"1456","DOI":"10.1109\/TWC.2015.2490223","article-title":"Interference alignment with quantized grassmannian feedback in the k-user constant MIMO interference channel","volume":"15","author":"Mohsen","year":"2016","journal-title":"IEEE Trans. Wirel. 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