{"title":"Worst- and average-case complexity of LLL lattice reduction in MIMO wireless systems","authors":"J. Jaldén, D. Seethaler, G. Matz","doi":"10.1109/ICASSP.2008.4518202","DOIUrl":null,"url":null,"abstract":"Lattice reduction by means of the LLL algorithm has been previously suggested as a powerful preprocessing tool that allows to improve the performance of suboptimal detectors and to reduce the complexity of optimal MIMO detectors. The complexity of the LLL algorithm is often cited as polynomial in the dimension of the lattice. In this paper we argue that this statement is not correct when made in the MIMO context. Specifically, we demonstrate that in typical communication scenarios the worst-case complexity of the LLL algorithm is not even finite. For i.i.d. Rayleigh fading channels, we further prove that the average LLL complexity is polynomial and that the probability for an atypically large number of LLL iterations decays exponentially.","PeriodicalId":333742,"journal":{"name":"2008 IEEE International Conference on Acoustics, Speech and Signal Processing","volume":null,"pages":null},"PeriodicalIF":0.0000,"publicationDate":"2008-05-12","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"106","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"2008 IEEE International Conference on Acoustics, Speech and Signal Processing","FirstCategoryId":"1085","ListUrlMain":"https://doi.org/10.1109/ICASSP.2008.4518202","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"","JCRName":"","Score":null,"Total":0}
引用次数: 106
Abstract
Lattice reduction by means of the LLL algorithm has been previously suggested as a powerful preprocessing tool that allows to improve the performance of suboptimal detectors and to reduce the complexity of optimal MIMO detectors. The complexity of the LLL algorithm is often cited as polynomial in the dimension of the lattice. In this paper we argue that this statement is not correct when made in the MIMO context. Specifically, we demonstrate that in typical communication scenarios the worst-case complexity of the LLL algorithm is not even finite. For i.i.d. Rayleigh fading channels, we further prove that the average LLL complexity is polynomial and that the probability for an atypically large number of LLL iterations decays exponentially.