Partial Template Based Receiver in Impulse Radio Ultra-Wideband Communication Systems

Partial Template Based Receiver in Impulse Radio Ultra-Wideband Communication Systems Cao Yang School of Electronics and Informati on Engi neer ing Harbin In stitute of Techn ology Harbin, China xiaoyang _cao@126.com Luo Chao School of Electronics and Informati on Engi neer ing Harbin In stitute of Technology Harbin, China chlu ochao@163.com Wu Xuanli School of Computer S cience and Te chnol ogy School of Electronics and Informati on Engi neer ing Harbin In stitute of Technology Harbin, China xlwu 2002@hit. edu.cn Abstract — For hig h s peed ultr a- wi deba nd (U WB ) co mmuni cati on systems, the multipath interf erence exhibits a pri mary obstacl e to improve tra nsmissio n perfor mance. In o rder to enh ance the signal to i nterference plus noi se ratio (S INR) in the recei ver, a partial template recei ver is propose d in this paper. Instead of using the conven tional template, the m odel in this pa per adopts a partial template to demodulate signals. To analyze the perfor mance of the propos ed receive r, bit error rate (B ER) formulation of IR-UWB sy stems in the presen ce of multipath interference, multiuser i nterference an d addictive w hite Gaus sian noise (AW GN) is derived in IEEE 802.15.4a c hannel m odels. Simulation results show that, com pared w ith the conventional correlatio n receiv er, the pro posed recei ver ca n achieve a better BER perfor mance for hig h E b / N 0 , which fa lls in the convention al used E b / N 0 range. Keywords-Ultra -Wideba nd; Partial Templa te Receiver; Multipath Interference; BER Analysis; I. I NTRODUCTION As an en ergy efficien t and l ow- complexity wireless access technol ogy, ultra-wide band (UWB ) has attracted more and more re searcher s’ attention i n w ire less sensor net works (WSN) and w irel ess body are a net w ork (WBA N) [1-3 ]. U WB is selecte d as on e of the enabling techn ologies f or wirel ess sen sor networks i n 2007 [1-2]. Ho wever, in cer tain specific enviro nments, espec ially reside ntial and indoor o ffice environm ents, the d ense m ultipath chann el of UWB becomes a big challen ge to c ollect ene rgy efficiently with huge m ultipath interfe rence. G enerally, th ere are two ty pes of multip ath interfe rences: One is cau sed b y the in terferenc e of tw o adjac ent data sym bols, which is called in ter-sym bol interferen ce (IS I). Anoth er is cau sed by the inte rferen ce betw een a pulse an d its own m ultipaths, w hich is c alled intra- symbol in terferen ce (IASI) . And both of them will have a significan t impact on the BER perf orm ance of U WB sy stems , especially wh en the dat a transm ission rate is h igh. In recent years , m any research ers have do ne a lot of researc h on wavefo rm desi gning to max imize pow er effi ciency of puls e res trict ed by FCC spectra l mas k. Undoub tedly, an ef fectiv e use of pow er effic iency c an impro ve SNR in the r eceiver; ho wever, it cannot ensure the recei ver can also obtai n a high SINR, which includ es both noise a nd i nterfere nce. T herefor e, higher power effi ciency canno t guara ntee a better BER p erformance . And [4] and [ 5] discussed the system transmission performance with different wavefor ms and fina lly they dre w the concl usion that a good corre lation proper ty of wavefor m should also be taken into consid eration i nstead o f only foc using on maxi mizing p ower efficien cy of puls e. On th e oth er hand , in order to ma ke an effective us e of multipath com ponents, diff erent ty pes o f receive rs a re pr oposed [6- 8]. [9 ] analy zed th e perf orm ance of RAKE re cept ion an d com pared two com bining stra tegies- equal gain co mbining (EGC ) and maximal rat io combini ng (MRC). In te rms of h ardw are comple xity, TR receive r has a obvi ous adva ntage over RAKE r ecei ver. However , [10] po inted out that the noise can seve rely dec rease th e perform ance of TR recei ver because r eferenc e pulse m ust be t ransmitted in noise channe l. However, simulati on in th is pape r show s that c orrelation rece iver ca nnot ac hieve a d esirabl e BE R perfor mance i n presence of addictiv e white Gaussi an noise, multipath interfe rence an d m ultiuser int erferenc e. Th erefore , to en hance the perf orm ance of c orrela tion receive r, a n ovel recei ver algorithm -partial template receive r is intr oduced and a detail ed analy sis of h ow it can im prove s ystem perf orman ce is presen ted. II. S YSTEM M ODE L O F U LTR A -W IDE B AN D C OMMU NICA TI ONS In a TH-B PSK UWB system, the tr ansmitted signal of the n -th user ca n be given by: 1 (, ) (, ) () , 0 () ( ) . s N ni ni n p fi j c j s td E p t j T C T − = =− − ∑ (1) where, () p t is the un it ene rgy pu lse w aveform , whose en ergy is E p and m ean pulse repetiti on peri od is T f . () , {1 , 2 , 3 } n ij h CN = ……, is the tim e hopping s equence of the i - th bit of the n -th user with c T corres ponding t o the tim e hoppi ng slot time. (, ) {1 , 1 } ni d ∈− repres ents th e bina ry dat a sequen ce an d on e dat a sy mbol is c ompos ed of s N pulses . Thi s work is supp orted b y Speci ali zed Res earch Fund for the Doct oral Program of High er Ed ucati on (New Teachers ) (Gran t No. 2009 23021 20001) , China P ostdo ctor al Scie nce F ound ation ( Grant No. 20100 4710 80), an d Heil ongjiang Post docto ral G rant (G rant N o. L BH-Z 09153) . Accor ding IEEE 802 .15. 4a , the impu lse res ponse of UWB system can be w ritten as f ollow s: ,, 11 () ( ) . LK kl l kl lk ht t T αδ τ == =− − ∑∑ (2) where, , kl α corre sponds to the tap weight o f k -th ray o f l -th cluste r, and , kl τ is the k - th ray ’s arriv al tim e relative to the l -th cluster’ s arriva l time T l . L an d K denot e th e nu mber of obse rvable clu ste rs and ray s, respect ively . Finally the receiv ed signal can b e demonstra ted a s: (, ) () 11 () ( ) () () . u I N N ni n f ni r t s t i T ht nt τ == =− + ∗ + ∑∑ (3) where, () n τ is the n -th user’s delay rela tive to the fir st user due to asynchronous transmission, assuming (1) 0 τ = . I N represents the n umber of inte rfering pulses f rom th e previ ous peri ods, max max / If b s NT R N ττ ⎡⎤ == ⎡⎤ ⎢⎥ ⎢⎥ , b R is transmission bit rate, max τ is maxim um multipath delay. A nd n(t ) denot es addictive wh ite Gaussian no ise. For the tap w eight , kl α , it f ollow s a Nakag ami-m distribu tion w ith param eters ( , m Ω ) accord ing to ,, 21 ,, 2 ,, , ,, , 2 ( ) ( ) exp( ). () kl kl mm kl kl kl kl kl kl kl kl mm pdf m αα α − =− ΓΩ Ω (4) where, ( ) Γ⋅ repr esents th e Gamm a function, m is the Nakaga mi-m factor which is mode led as a lognormal ly dist ribu tion ran dom varia ble, a nd 2 ,, [] kl kl E α =Ω . The mean power of differ ent rays is given b y 11 , 11 ,, 12 11 exp( / ) and [] . [( 1 ) 1 ] 0o r lk l l kl k l l kk l l E kkl l τγ αα γ β λ β λ Ω− ⎧ == ⎪ =− + + ⎨ ⎪ ≠≠ ⎩ (5) where, l Ω corresp onds to th e integ rated ene rgy of th e l -th cluste r, and l γ is the in tra-c luster decay tim e con stant, wh ich is linearly depended on the arriv al time of the clu ster, 0 ll kT γ γγ ∝+ . (6) and th e m ean energ y of l -th clust er is given by: 10 lo g( ) 10 log(e xp( / )) . ll c l u s t e r TM Ω= − Γ + (7) A ssum e that w e ar e going to re ceive s ignals of th e firs t ra y and ha ve achie ved perfec t synchro nizat ion. For the convent ional c orrel ation r eceiver , the tem plate f or dem odulat ion i s [4] : 1 (1) 11 , 1 0 () ( ) . s N fj c j vt p t j T C T T τ − = =− − − − ∑ (8) The sig nal t o inte rference plus n oise (SINR ) can be expre ssed as: 22 2 2 SI NR . b nI A S II S IM U I E σσ σ σ = ++ + (9) where, b E repr esent s the energy for the de sired signa l, and 22 2 2 ,, , nI A S II S I M U I σσ σ σ d enote th e va riance for a ddictive wh ite Gaussian noise , intra-s ymbol in terfe rence , inter-s ymbol interfe rence an d mu ltiuser inte rference , respec tively. F or B PSK sy stem , the B ER ex pressi on is g iven by 1S I N R () . 22 BER erfc = (10) The ener gy for d esired signal b E and th e v arian ce for white Gaussian noise 2 n σ are ex pres sed as : 22 0 22 0 () . () / 2 . bu s nn s EE Z N EZ NN Ω σ == == (11) where, 0 Ω is the energy of the first r ay in the first cluster , which can be exp ressed as : 0 01 2 1 . [( 1 ) 1 ] Ω γβ λ β λ = −+ + (12) The va riance for in tra-sy mbol interfe rence 2 IASI σ is gi ven b y 22 2 0 0 2 e x p ( / ) () () . m K T IASI s p k Ny f y R y d y σΩ γ = =− ∑ ∫ (13) where, y denot es , kl τ . And th e varian ce fo r inter-sy m bol interfe rence ( ISI) 2 ISI σ is give n by 22 2 / 2 2 () e ( ) ( ) . m m K T y ISI ISI s p T k E ZN f y R y d y γ Σ σΩ − − = == ∑ ∫ (14) where, Σ Ω can be ex presse d as max 1 1 1 () / / 0 0 11 11 [] 1 ee 2 () ( ) . Is Is sf c o d e fc o d e l l sf c o d e NN s s NN L Ts T sT T T Ts T ls s c l c l l l code E T fT fT d T d T d ττ τγ τ τ − Σ = − + −+− −Γ −+ == ++ Ω= Ω =Ω × ∑ ∑∑ ∫∫ ∫ (15) where, s Ω represen ts the s -th in terferi ng pulse ’s ener gy. Suppose that there exists 1 u N + user s in the system, the varian ce for m ultiu ser interf eren ce 2 MUI σ is 22 /2 2/ 2 00 /2 2 /2 2/ 2 0 /2 2 () () e ( ) ( ) () e ( ) ( ) fm f fm f MUI MUI K TT z y bs u p Tz k K TT z y bs u p Tz k EZ F R N N f y R y z dydz F RN N f y R y z d y d z γ γ σ ω ω − − −− = − − Σ −− = = =Ω + +Ω + . ∑ ∫∫ ∑ ∫∫ (16) where, y represen ts , kl τ and z represen ts u t . III. P ART IAL T EMPLATE R ECEI VER For conven tional correlati on receive r, the template for demodu lat ion is ex press ed by (8) . How ever, from the simu lation results w e figure out that such t emplate can not achieve a desire d perfo rmance in dense m ultipath envir onments such as IEEE 802.15. 4a indoo r office enviro nment. I n dense multipath environm ent, sev eral ad jacent m ultipaths m ay overla p with each oth er an d resu lt in int ra-sym bol inte rferen ce, which make s the cor relation r eceiver cannot de modulate signals eff ectively . In this cas e, w e propose a partial template correlati on rec eiver t o m itigate intra-sym bol inte rferenc e. Th e partial tem plate origin ates from conventional c orrelation receive r tem plate, w hich can be ob tained by settin g the right par t of the co nve ntio na l templa te to be zero while keep th e left part as it is. For inst ance, if we ado pt the sec ond order derivati on of Gaussian pulse t o transm it info rmation and N s is chosen to be 1, th e conventio nal template an d partial tem plate is sho wn in Fig. 1 (a) and (b), respective ly. -0.25 -0. 2 -0. 15 -0.1 -0. 05 0 0.0 5 0.1 0.15 0. 2 0.25 -6 -4 -2 0 2 4 6 8 10 12 x 10 4 Time(ns) Am plitude (a) Convent ional templa te -0.25 -0.2 -0. 15 -0.1 -0. 05 0 0.0 5 0. 1 0.15 0.2 0.25 -6 -4 -2 0 2 4 6 8 10 12 x 10 4 Time(ns) Am pl itu de (b) Part ial tem plate Fig ure1.T he conv ention al templ ate and part ial te mplate In the m eantim e, the SINR fo rmu lation for pa rtial tem plate rece iver is given by 22 2 2 SI NR . b nI A S I I S I M U I E σσ σ σ ′ ′ = ′′ ′ ′ ++ + (17 ) wher e b E ′ corres ponds to n ew en ergy for the desi red s ignal , an d 22 2 2 ,, , nI A S I I S I M U I σσ σ σ ′′ ′ ′ represe nt the ne w variance for white Gaussian noise, intra-symbol inter ference, inter-symbol interfe rence an d m ultiuser interfer ence, respectively . The expressio ns for b E ′ , 22 2 2 ,, , nI A S I I S I M U I σσ σ σ ′′ ′ ′ are sim ilar to the conve ntional te mplate recei ver discussed in sect ion Ⅱ , wh ic h can be deri ved by cha nging the co nventional temlp late ( ) vt to partial template ( ) vt ′ . IV. P ERFOR MAN CE C OMPARS ION B ETWEEN P AR T IA L T EM PLATE R ECEIVER A ND C ONVEN TI ONAL T EMPLATE R ECEI VER In Fig . 2, the s econ d or der de riva tion of Ga ussian pul se w aveform w ith time durat ion T m ＝ 0 .5ns is adopted in the simu lation and 10dB bandwidth is 5.6GHz . Without loss of gener ali t y, we consider N s equal s 1. Moreo ver , we set th e time hoppi ng width T c equals to T m and the number of time hopping N h is chose n to be 16. Supposing tha t ther e exist s 4 users in the system with data transmission rate of 15Mbp s for each user. We do simulati on in indoor offi ce LOS envir onment defi ned by IEEE80 2.15.4 a. 0 2 4 6 8 10 12 14 16 10 -4 10 -3 10 -2 10 -1 10 0 E b /N 0 (dB) BER Conve nti onal templ a te , si mul a ti on C o n v en t i on al t em p l at e, th eo r et i cal an al y s i s P a r t ia l t e m p la t e , s im u la t io n P a r t ia l t e m pla t e , t h e o r e t ic a l a n a lys is Figure 2 .Sim ulat ion resu lts for c onventi onal temp lat e receiver a nd pa rtial templ ate re ceive r As is sh own in Fig .2, partial template receive r dem onstrates a be tter BE R perfor mance co mpare d with c onve ntional template receiv er. Du ring l ow E b / N 0 values, the partial template rece iver shows a worse BER per formance t han convent ional template receiv er, w hile for the hi gh E b / N 0 value s range s, it has a much better BER perform ance . More im portantly , as th e increase of E b / N 0 , the parti al template receiver show s a more ob vious BER adva ntage over the co nvent ional templat e receive r. Accord ing to equ ation ( 17), w hen us ing part ial tem plate to demod ulate signa ls, the values o f desired signal energy, noi se and all types of in terfe rences w ill decre ase. How ever, during high E b / N 0 val ues, 2 IASI σ ′ has a m ore signi fican t decr ease th an the oth er fou r decis ion v ariabl es. Th eref ore, the s ign al to inter ferenc e plus noise r atio ( SINR) i s enha nced i ndirectl y duri ng high E b / N 0 va lu e s. Ne ver t he le s s, whe n E b / N 0 is lo w, the addictive white Gau ssian noi se bec omes the m ajor fact or of SINR. T hus, SINR decrea ses during lo w E b / N 0 range s. Fig. 3 and Fig. 4 present the BE R performance compar ison between partial tem plate rec eiver and conv entional template rece iver in reside ntial LOS enviro nment and indoor offic e LOS envir onments , res pectively . The param eters f or th e tw o chann el m odels are sh ow n in Table 1. Furt herm ore, diff eren t wavefor ms (the firs t, third, fifth orde r deriva tion of Gaussian pulse) a re taken into consi deration in th e figures. TABLE I. IEEE 802. 15.4 A CHANNEL PARAMETERS Resi den tial L OS environmen t Indoor offi ce LOS environmen t L 3 5.4 Λ [1/ns ] 0.04 7 0.01 6 λ 1, λ 2, [1/ ns] β 1.54,0 .15,0. 095 0.19,2.9 7,0.0 184 Г [ns] 22.61 14.6 γ 0 [ns] 12.53 6.4 0 2 4 6 8 10 12 14 16 10 -4 10 -3 10 -2 10 -1 10 0 E b /N 0 (dB) BER Conve ntional te mpla te , Ga uss 1t h P a r t ia l t e mp la t e , G a u s s 1 t h Conve ntional te mpla te , Ga uss 3r d P a r t ia l t e mp la t e , G a u s s 3 r d Conve ntional te mpla te , Ga uss 5t h P a r t ia l t e mp la t e , G a u s s 5 t h Fig ure3. BE R per form ance comp ariso n betw een par tial template rece ive r and conven ti onal t emplat e receiver i n residential LOS environment 0 2 4 6 8 10 12 14 16 10 -3 10 -2 10 -1 10 0 E b /N 0 (dB) BER Conve ntiona l te mpla te , Ga us s 1t h P a r t ia l t e m p la t e , G a u s s 1t h Conve ntiona l te mpla te , Ga us s 5t h P a r t ia l t e m p la t e , G a u s s 5t h Fig ure4. BE R per form ance comp ariso n betw een par tial template rece ive r and whole tem plat e receiver i n ind oor off ice LOS enviro nments From Fig. 3 and Fig. 4, w e notice that for differ ent channel models and w avef orms, the parti al tem plate receiver can improv e sys tem BER perf orma nce in con trast w ith conve ntional te mplate rece iver during hi gh E b / N 0 values. How ever, the im provem ent of sy stem perfo rmance v aries with diffe rent wavefo rms. It t urns out tha t the first and third ord er of Gau ssian pulse demon strat e a mor e obvi ous im prov emen t in BER per formance than the fifth der ivati ve of Gaussian p ulse. V. C ONC LUSION In this paper a p artial tem plate base d receiv er for U WB commu nication sy stems is int roduced. S imulation results show that it can i mprove system per formance dur ing high E b / N 0 values in contrast with co nventio nal templat e receiver. Mor eover , the prop osed re ceiver is a gener ic re ceiver , whic h can be empl oyed in dif feren t chann el m odels an d di ffer ent w aveforms. Neve rtheless , it s hould be note d that f or the l ow E b / N 0 values, the pa rtial tem plate re ceiver can not pres ent an im provem ent on sys tem perf orm ance. R EFERENCES [1] I EEE std 802.1 5.4a-2007, “ Part 15. 4: W ireless Me dium Access Control (MAC) and Ph ysical Layer(PHY) Specifi cations for Low-Rat e Wireless Per sonal Are a Netw orks(W PA Ns),” 200 7. [2] N. R iaz an d M. G havam i, “A naly tical per form ance ev aluatio n of ultr a- wideb and m ultip le access schem es for diffe rent w ireless se nsor netwo rk appli cati on environ ments ,” IET Comm. , vol. 9 , pp. 1473–148 7, March. 2009 . [3] B. Mar ek , T . Dav id, G . Ben , T. N ick an d M. J im, “A schem a for the selectio n of ne twor k topology for wirele ss body are a netw orks,” I EEE Radi o and Wireles s Symp osiu m, Ma rch. 201 1. [4] X. L. W u, D. Lin and X . Z. Yan g, “P erform ance compar ison wit h diffe rent pulse wav efor ms in ul tra- wide band base d w irele ss se nsor netw orks ,” Perv asive Computi ng Sig nal Pr oces sing an d Appl icatio ns, pp. 6 92- 695, 20 10. [5] X. Y . NI NG , “Multi path i nterfe re nce analy sis fo r im pulse ultra- wide band s ystems, ” Journ al of Jilin Univers ity (En gineeri ng an d Techn ology Edit ion), vol. 39(6 ). Novemb er. 2009 . [6] Y. L . Chao and R. A . Schol tz, “O ptim al an d subo ptiaml rece iver s for ultra-w ideband tr ansmitte d refe rence sy stems,” I EEE Global Telecomm un icat ions Conferen ce, vol. 2, pp . 759-76 3, Janu ary. 20 04. [7] S. F ranz an d U. Mi tra, “O n opt imal d ata dete ction f or UW B tra nsmitted refer ence syste ms,” IEEE Gl obal Tele communicatio ns Confe rence, v ol. 2, pp. 744- 748, January . 2004. [8] R. Ho ctor a nd H. T oml inson, “ De lay-hoppe d tra nsmi tted-re fer ence RF communicat ions,” I EEE Ultr a Wideband Sy stems and Te chnolog ies, pp. 265 -269, Au gust. 2002. [9] M. Z. Win, G. Chri sikos and N. R. Sollen berg er, “P erfor man ce of RAK E Rece ptionin D ense Multip ath Cha nnel s:Im plicatio ns of Spreading B andwidth andSele ction Dive rsity Order,” IEEE Jo urnal on Select ion Areas i n Commu nicati ons , vol. 18 (8), pp . 1516–1 525,2 000. [10] J. D. Choi a nd W. E . Stark , “Pe rform ance of ultra-w ideban d commun ica tion s with su bopti mal rec eivers i n mu ltipa th cha nnels, ” I EEE Journ al on Selec ted Areas in C ommuni cation s, vol. 20(9), pp. 1754- 1766 , Decemb er. 2002 .