5th Workshop on Signal Processing Advances Wireless Comunicatons Box-constrained multiuser detection based on multiplication-free coordinate descent optimisation Æ  Deparment ofElectronics York  or, l Email: zl@ohm..ac.  - Multiuser detection can ofen be decribed as a constraine quadratic optimisation problem. Many it erative tÎ nique are a,'ailable to sol'e this problem; however, due to high complexity tcannot be efetivey implemented in real· tmÏ We propose a nOl'cl iterative technique, the DCD (Dichotomous Co ordinate Decent} algorithm which guarante connrgence in the box-constrained quadratic op timisation problem. We inl'estigate application of the DCD algorithm t multiuser detection and show that it provide a high detection performance and complexity lowC than other known box-constrained multiuser detectors. Moreover, the proposed algorith is mltiti and division.free; make it atractive for real·time implementation in hardware ( C) or fxed point (DSP) sofware. IÌ  In multiple-acces CDMA ste, multiuser detection is caable of providing high detection perormance (1], Multiu�er detection c be describd as a solution of an optimiation poblem: in ost cases it ithe aratc optimisation problem. Unconstrained quadratic opti misation  knon to result  decorelaing 2J and MMSE multiuser e3.The tighter te constraints, the better the detectionperfo mance a be achieve. The optimal multiuser detection is equiv. alent to the solution of a (-1,+ I)-contrained maimum-likelihood (ML)roblem 4J. However, ch detection  complex for prati cal systems. Many subpti mal detection chee have been proe, ossin lower computational loa, b alo havig poorer detecti on eaceaoptimal detector. A "closed cone et"onstrained ML detetor has bᵫenintrodud n [5] a acompet llrting alterative to the (-1, +1)-contrained opti ma etcor; kwn successive snd parallel cancellation schemes ae special case of the algorithm. Sphere-cnstrained quadrdtic op      possess a e  a o  tat of the MMSE detetor 5,61. Bter detecto p ormance i ache b box-constrained optimisation [5,7, 8).Hower, the com· plexity  schemes   high. In paricular,  ee u tilicatio ad division oration, hich are difcult for hardae or e-ont otare immentatio, In thi s paper. we rooe a new multiuser detection algoihm wich possesses a lo coputational load ad high detect ion perfor. mance. algorithm s based on box-consrained coordinate-descent quadratic optimiatio. Multiuser tectrs based on cordinae de scent otimation were aso proposed n 9; hoeer, thee receives arecopleormementation. We ntduce a novel multipcatio free and division-free i tera tivetechue,  Dchtmous Coordinate Dcet (D) algorithm which guarantees convergence in t  cntraied adratic optimi sat ion obe. We i nvestigate applica tion ofthe DCD alothm to multur tcton. We sho that the '() a 5 .  C.  Department of Electronics University of York Yor, YOO 5DD, UK Eail: tct@hm.ok.ac.u DCD-based multiuser detctor provides high detection perance ad loer umber of ope!dtions compared to known box-constrained uË More imporantly, a ed b shifts onl.  akes he roposed algorith attract or rea -t me implementation inhardare (FPGA, ASIC)o -pont (DSP) ot ware. IÍ M M We consider a basband uplink achroou  system with K active user  the resec AWGN. Use  tansmitsa block of  BPSK mbos (n)  -I,+1,  = 0. ..  -  spread b a real-aled coe ) = k(  + 1), . .. ,N + N)J. The nss delas k aTe s be integer mult iples o the chip interval and iihinone symbol interval of a lent N.The aution on he modul ation lype, real-valued spreading code, ad tansmission delays a d for clarity only. The resultin g i ted discrete-time baseband signal a bol int erval  d()Ck(n) ee k) = N+ k1) (L-)-.  coninuo tie received signa l is down-converted o baseban, aed through a filter matched  he chipulse-sh ape and sampled. The received base band  L- K X = 2 L ()()+n (I) =O =) e  is an N.-dimensional vector. N. = N(L + 1), of indepen dent, identically distributed rand aiabs of zer o mean and ari ane (2. e assue perfect er control  hae scro nisaion or aÈ The received sigal can be writea  = d+n () whre  the NÅ  atri ofeceied readi codes,  =   i thtota nuber symbols tranmted in he block, and d is thedaa er a siz N.Atrcoati mache to  sprea codes, we obtain (3) where y ithematched flterut ctor asize  and  "  i e N   correlaton matri ospeadig codes. We assume here hs symmetric positive teÊ É  Œ  The neral constrained  pr oblem f asynchronous CDMA is escbed as(ee, e.g. [5])  = i {J(h)} = i {hTRh - 2hTY} (4) EU EU Weconsidethe otimisation problem under e contain E=(h, ...  )  l  j  . .. ,N (5) 0-7803-8337 - 004/20.00©2004 IEEE 43