A Matrix-Algebraic Approach to Successive Interference Cancellation In CDMA

A Matrix-Algebraic Approach to Successive Interference Cancellation In CDMA
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  IEEE TRANSACTIONS ON COMMUNICATIONS, VOL. 48, NO. 1, JANUARY 2000 145 A Matrix-Algebraic Approach to SuccessiveInterference Cancellation in CDMA Lars K. Rasmussen  , Member, IEEE  , Teng J. Lim  , Member, IEEE  , and Ann-Louise Johansson  , Member, IEEE   Abstract— In this paper, we describe linear successive inter-ference cancellation (SIC) based on matrix-algebra. We showthat linear SIC schemes (single-stage and multistage) correspondto linear matrix filtering that can be performed directly on thereceived chip-matched filtered signal vector without explicitlyperforming the interference cancellation. This leads to an analyt-ical expression for calculating the resulting bit-error rate whichis of particular use for short-code systems. Convergence issuesare discussed, and the concept of -convergence is introduced todetermine the numberof stages required for practical convergencefor both short and long codes.  Index Terms— Code-division multiaccess, linear algebra, mul-tiuser channels, signal detection. I. I NTRODUCTION I N A MOBILE communications system, multiple access tothe common channel resources is vital. In a system basedon spread-spectrum transmission techniques, code divisionprovides simultaneous access for multiple users. By selectingmutually orthogonal codes for all users, they each achieveinterference-free single-user performance. It is however notpossible to maintain orthogonal spreading codes at the re-ceiver in a mobile environment, and thus multiple-accessinterference (MAI) arises. Conventional single-user detectiontechniques are severely affected by MAI, making such systemsinterference-limited [1]. Traditional matched filter receiversfor code-division multiple-access (CDMA) also require strictpower control in order to alleviate the near–far problem wherea high-powered user creates significant MAI for low-poweredusers.More advanced detection strategies can be adopted to im-prove performance. In [2], Verdú developed the optimal (0,1)-constrained maximum-likelihood (ML) detector for multiuserCDMA. The inherent complexity however increases exponen-tially with the number of users, rendering the optimal ML de-tector impractical. Paper approved by B. Aazhang, the Editor for Spread Spectrum Networks of the IEEE Communications Society. Manuscript received June 9, 1997; revisedJuly1,1998.ThispaperwaspresentedinpartattheIEEEVehicularTechnologyConference, Phoenix, AZ, May 1997, and in part at the Multiaccess, Mobility,and Teletraffic Workshop, Melbourne, Australia, December 1997.L. K. Rasmussen is with the Telecommunication Theory Group, Departmentof Computer Engineering, Chalmers University of Technology, SE-412 96Gothenburg, Sweden (e-mail: J. Lim is with the Centre for Wireless Communications, Teletech Park,Singapore 117674 (e-mail: Johansson is with Nokia Svenska AB, SE-164 25 Kista, Sweden(e-mail: Item Identifier S 0090-6778(00)00517-1. For practical implementation, parallel and successive inter-ference cancellation (SIC) schemes have been subject to mostattention. These techniques rely on simple processing elementsconstructed around the matched filter concept. The first struc-ture based on the principle of interference cancellation was themultistage detector in [3]. Here, the cancellation is decision-di-rected (i.e., nonlinear) and is done in parallel. In [4], Dent et al. proposed a serial approach, a single-stage nonlinear SICscheme, while Kawabe et al. suggested a multistage nonlinearSIC technique in [5]. A closely related scheme was suggestedby Sawahashi et al. in [6]. Linear SIC detectors have been con-sidered in detail for both single-stage and multistage cases in[7] and [8], while Jamal and Dahlman have compared the per- formance of the linear and the nonlinear SIC approaches in [9].An algebraic approach to SIC was initially introduced in[10] and further developed in [11]. Closely related work by Elders-Boll et al. was presented in [12] and [13], where they suggest linear detectors based on the application of classic iter-ative techniques for solving linear systems. The Gauss–Seideliteration was here identified as SIC. Iterative methods for lineardetector design have also been proposed by Juntti et al. in [14].The equivalence to interference cancellation was however notrecognized.Inthispaper,wedescribethelinearSICschemebasedonma-trix-algebra. We show that the linear SIC schemes (single-stageand multistage) correspond to linear matrix filtering that can beperformed directly on the received chip-matched filtered signalvector without explicitly performing the interference cancella-tion. This leads to an analytical expression for calculating theresulting bit-error rate (BER), which is of particular use forshort-code systems. Convergence issues are discussed, and theconceptof -convergenceisintroducedtodeterminethenumberof stages required for practical convergence for both short andlong codes.The paper is organized as follows. In Section II, the uplink model is described, and the techniques for SIC are briefly sum-marized. In Section III, we introduce a matrix-algebraic ap-proach for describing linear SIC, which allows for new insightinto the behavior of the schemes. The equivalent matrix filtersfor linear SIC are derived, and convergence issues are discussedfor multistage schemes, including the concept of -convergencefor both short and long codes. Numerical examples are pre-sented in Section IV, and conclusions are drawn in Section V.The following notation is used for the product of matricesif if (1) 0090–6778/00$10.00 © 2000 IEEE
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