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  1. 1. G S Krishnam Naidu Y, CH.Raghava Prasad, Subba Reddy Vasipalli / International Journal ofEngineering Research and Applications (IJERA) ISSN: 2248-9622 www.ijera.comVol. 3, Issue 3, May-Jun 2013, pp.625-629625 | P a g eAnalysis of Code Tracking Technique in CDMANon CoherentReceiver1G S Krishnam Naidu Y,2CH.Raghava Prasad, 3Subba Reddy Vasipalli123Assistant professor, Department of ECE, KL University, Guntur, A.P, India-522502.ABSTRACTIn this paper, we propose and analyse anew non coherent receiver with PN code trackingfor direct sequence code division multiple access(DS-CDMA) communication systems inmultipath channels. We employ the decision-feedback differential detection method to detectMDPSK signals. An "; error signal"; is used toupdate the tap weights and the estimated codedelay. Increasing the number of feedbacksymbols can improve the performance of theproposed non coherent receiver. For an infinitenumber of feedback symbols, the optimumweight can be derived analytically, and theperformance of the proposed non coherentreceiver approaches to that of the conventionalcoherent receiver. Simulations show goodagreement with the theoretical derivation.Keywords -Optimum weights, pn code, DS-CDMAI. INTRODUCTIONCode division multiple access is used totransmit many signals on the same frequency at thesame time. A non coherent receiver with PN codetracking is used for direct sequence code divisionmultiple access (DS-CDMA) communicationsystems. In spread spectrum communicationsynchronization is necessary for transmitting andreceiving ends.If it is out of synchronizationinsufficient signal energy will reach the receiver.Forbetter synchronization of the system code trackingtechnique is used pn code tracking is applied forcoherent and noncoherent cases.In coherent case atthe demodulator,the coherent carrier reference isgenerated.It is difficult to generate coherentreference at low s/n ratio.The loss of noncoherent detection comparedwith conventional coherent detection is limited andcan be adjusted by the generation of the referencesymbolfor the decision feedback differentialdetection. The performance of noncoherent receivercan approach the performance of conventionalcoherent receiver when infinite number of feedbacksare used.At first we have generated the spread spectrumsignal. The original binary sequence is taken andbinary phase shift keying is done to the signal and tomake the calculations easier we are using fastfourier transform.The BPSK signal is multipliedwith pn code to get the respective spread spectrumsignal.The signal is received at the receiver throughAGWN channel.Then the signal is transferredthrough adaptive filter as shown in figure 1.1.Adaptive filter minimizes the error between somedesired signal and some reference signal.It designsitself based on the characteristics of input signal,byadjusting the tap weightsII. ADAPTIVE FILTERAn adaptive filter is a filter that self-adjusts its transfer function according to anoptimization algorithm driven by an error signal.Because of the complexity of the optimizationalgorithms, most adaptive filters are digital filters.Fig 1.1:adaptive filterTo start the discussion of the block diagram we takethe following assumptions:i. The input signal is the sum of a desiredsignal d(n) and interfering noise v(n)x(n)=d(n)+v(n)ii. The variable filter has a Finite ImpulseResponse (FIR) structure. For such structuresthe impulse response is equal to the filtercoefficients. The coefficients for a filter oforder p are defined as      Tnnnn pwwww ,...,1,0 .The error signal or cost function is the differencebetween the desired and the estimated signal)()()( ndndneThe variable filter estimates the desired signal byconvolving the input signal with the impulseresponse. In vector notation this is expressed asD^(n)=wn*x(n)Where, X(n) = [ x(n),x(n-1),------x(n-p)]Tis an inputsignal vector.Moreover, the variable filter updates the filtercoefficients at every time instantWn+1= Wn + ΔWn
  2. 2. G S Krishnam Naidu Y, CH.Raghava Prasad, Subba Reddy Vasipalli / International Journal ofEngineering Research and Applications (IJERA) ISSN: 2248-9622 www.ijera.comVol. 3, Issue 3, May-Jun 2013, pp.625-629626 | P a g eWhere, ΔWn is a correction factor for the filtercoefficients.The adaptive algorithm generates this correctionfactor based on the input and error signals. LMS andRLS define two different coefficient updatealgorithms.Fig 1.2:The conventional coherent receiver-jointdetection and pn code trackingAs compared with the fig 1.2 and 1.3,there exists achange that reference symbol is added on the feedback side for non coherent receiver.Fig 1.3:The proposed noncoherent differentialdetection receiver with pn code trackingAs at the receiver the demodulation process is doneand that signal is multiplied with the reference pnsignal to get the original signal.III. ANALYSISIn the CDMA system, the base stationtransmits K data vectors of active users. Each user,k,transmits a data symbol sequence {bk(n)},k = 1,....,K, which consists of independent and identicallydistributedM-ary PSK symbols at symbol intervalTs, i.e.,bk(n) ∈ {ej2πν/M | ν ∈(0, 1, .....,M − 1)}. Thedata symbol sequences of different users areindependent. The actual data rate may be varied dueto the service provided or the actual transmissionconditions. Each data symbol bk(n) of user k is firstoversampled by a spreading factor Lcand theresulting vector is multiplied element-by-element bythe elements of PN spreading code sequence {pk(l)},k = 1, ....,K, which consists of Lcin general complexchips at chip interval Tcand satisfies the relationTc=Ts/Lc. The transmitted baseband spreadspectrumsignal is defined asS(t)= 10KKn)()( skk nTtPNnb (1)where bk(n) is the information-bearing symbol ofthe k-th user, and PNk(t) is a wideband PN sequencedefined by PNk(t) = _Lc−1 l=0 pk(l)Ψ(t − lTc)where pk(l) ∈ {•}1}is the l-th element of the PNcode of user k, and Ψ(t) is the chip waveform. TheCDMA downlink signal is then transmitted througha multipath channel. In the digital DSCDMAreceiver, the incoming waveform is downconvertedin quadrature and sampled at the Nyquist rate. Thebandwidth of PN code is approximately 1/Tc. TheNyquist sampling interval is Td,Td = Tc/D, where Dis the number of samples during one chip duration inthe receiver. Therefore, the number of samples inone symbol duration is DLc. In general, the discrete-time channel is modeled relative to the bandwidth ofthe DS waveform.A multipath channel can be represented bya tapped-delay-line with spacing equal to 1/DB,where B is the signal bandwidth. Thus, the channelcan be modeled as an FIR filter of length Ln whoseimpulse response is {hi}Ln−1 0 . ISI arises for Lngreater than one, and MAI arises due to channeldistortion or non-orthogonal spreading code or both.We assume that the channel order Ln _ DLcsince themaximum delay spread of the channel is usuallyinsignificant in relative to the symbol period Ts. Thereceived sample sequence {ri} can be expressed asji er  10nLl ilil vShje 10nLliodl vTTliSh  ))(( (2)Where S(t − τ0) means that S(t) suffersfrom timing offset, Θ denotes a constant phase shiftintroduced by channel, and τ0 denotes the true codedelay. The noise term {υi} is an i.i.d. Gaussianrandom sequence with the variance σ2n. The PNcode samples generated in the receiver arerepresented by {ci} which is obtained by samplingPNk(t) and ci = PNk(iTd−τ ) where τ is the codedelay which can be adapted to track the true codedelay τ0. Our problem is to design an adaptive filter{wi} that estimates (or predicts) the desired signal.In the same time, we estimate the code delay τ0 toachieve code synchronization.The conventional coherent receiver withPN code tracking is shown in Fig. 1.2. The constantphase shift Θ is assumed to be known perfectly. Thetap weight vector isHLwo nwnwnwnw )](1)...()([)( 1  (3)WhereLwis the number of taps of the transversalfilter used in the receiver. The local PN code vectorisC(n)=[cDLc(n-1)+1 CDLc(n-1)+2..CDLcn]T(4)Where [・]Tdenotes Transposition and [・]HdenotesHermitian operation.
  3. 3. G S Krishnam Naidu Y, CH.Raghava Prasad, Subba Reddy Vasipalli / International Journal ofEngineering Research and Applications (IJERA) ISSN: 2248-9622 www.ijera.comVol. 3, Issue 3, May-Jun 2013, pp.625-629627 | P a g eDefine the sample matrix,)1()...3()1()2()1(.........1...1)1()1(...2)1(1)1(=U(n)weweweeeeeeeLnrDLLnrDLLnrDLnrDLnrDLnrDLnrDLnrDLnrDL(5)The estimated signal )(_nY=Tenee DLYnDLYnDLYdefnY ]...2)1(1)1([)(_= )()( nWnUH(6)Note that C(n) has the property C(n)TC(n) = βwhere β is a constant that can be determined. Thatis, with sampling time Tc/D and without filtering,the maximum correlation of PN sequence is DLc.After filtering, β is no longer an integer, but stillselected by maximum correlation value in general.The value β depends on the sampling of the chipwaveform Ψ(t), that is, )(max1 2dDole lTxL  dTwhere  0 (7)If Ψ(t) is time-limited. It is desired that the output ofthe adaptive filter is the estimation of the desiredsignal, so that the normalized de-spreader output isand the output behaves like an MPSK signal.  /)()()( nCnUnWndHeoh (8)In other words, we want that the signal at the de-spreader output to have the same statistic as that ofan ideal MPSK demodulator output. To achieve thisgoal we can use the cost functionJcoh = E[ddif(n) –d dif(n)]2(9)Where dcoh(n) is the hard decision result ofdcoh(n).Let ecoh(n) = dcoh(n) −d coh(n) be the error signal,the cost function Jcohcan be written asJcoh=E[dcoh(n)d*coh(n)-[dcoh(n)CT(n)UT(n)W(n)/β-d*coh(n)WH(n)U(n)C(n)/β+C(n)U(n)WH(n)CT(n)UH(n)W(n)/β2](10)Where (・)∗denotes complex conjugation. When theLMS algorithm is used to minimize the costfunction Jcoh, we need to compute∂Jcoh ∂W = −2 β e∗coh(n)U(n)C(n) and∂Jcoh/∂τ = -dcoh(n) ∂CT(n)/∂τUH(n)W(n)/(β-d*coh(n)U(n)WH(n)∂C(n)/∂τ)β+WH(n)U(n)(∂C(n)/∂τCT(n)+C(n)∂CT(n)/∂τ)×UH(n)W(n)/β2) (11)The tap weight of the adaptive filter is thus updatedbyW(n+1)=W(n) -μ∂Jcoh/∂w= W(n) +μ[2/β e*coh(n)U(n)C(n) ] (12)Where, μ is the step-size. The code delay τ isupdated through τ (n+1) = τ (n)−λ∂Jcoh ∂τ where λis the step-size. The quantity −∂Jcoh ∂τ can beregarded as an “error signal”, estimating the chip-timing error of a code tracking loop.Fig. 1.3 showsthe block diagram of the proposed noncoherentreceiver that combines the differential detectionwith PN code tracking for DS-CDMA systems. Theinformation sequence {ak(n)} is first differentiallyencoded. The resulting MDPSK symbols bk(n) aregiven bybk(n)=ak(n)bk(n-1) (13)and the transmitted signal model is the same as (1).The received sample sequence {ri} is also expressedas (2). Here, the constant phase shift Θ is unknown.At the receiver, the sampled signals are first passedthrough the transversal filter and then despreaded bythe local PN sequence. The tap weight vector W(n),local PN code vector C(n), and the received samplematrix U(n) can be described as equations (3), (4),and (5), respectively. The normalized despreaderoutput q(n) is the same as (8), and can berepresented asq(n) = WH(n)U(n)C(n)/β.In the next stage, the differential detection isnecessary to recover the MDPSK informationsequence. The decision variable ddif(n) is obtainedby noncoherent processing of the despreader outputq(n),ddif(n) = q(n)q∗ref(n − 1) where the referencesymbol qref(n − 1) is generated as followsqk(n-1)=1/N-111NIq(n-1) 11jmddif(n-m) (14)whereN,N ≥ 2, is the number of despreader outputsymbols used to calculate ddif(n). ddif(n) is the harddecision result of ddif(n). Note that for N = 2, qref(n− 1) = q(n − 1), ddif(n) is the decision variable of aconventional differential detection. However, for N>2, a significant performance improvement can beobtained. We can use the cost functionJdif=E[ddif(n) -d dif(n)]2The error signal can be defined as edif(n) def=ddif(n) − ˆ ddif(n). Here, edif(n) at the n-th symboltime also depends on past tap weight vectorsW(n−ν), ν ≥ 1. For the derivation of the adaptivealgorithm, these past tap weight vectors are treatedas constants since |edif(n)|2 is differentiated onlywith respect to W(n). The cost function ofdifferential detection Jdifcan be written asJdif =E[ddif(n)d*dif(n)-ddif(n)qref(n-1)/βCT(n)UH(n)xW(n)-d*dif(n)q*ref(n-1)/βC(n)U(n)WH(n)+qref(n-1)2/β2CT(n)UH(n)W(n)C(n)U(n)WH(n) (15)The gradient of the cost function with respect to thetap weight vector is∂Jdif/∂W =-2/βq*ref(n-1)d*dif(n) U(n)C(n)+2/β2 qref(n-1)2U(n)C(n)CT(n)UH(n)W(n)=-2/βq*ref(n-1)e*dif(n)U(n)C(n) (16)and the gradient of the cost function with respect tothe code delay is∂Jdif/∂τ=-ddif(n)qref(n-1)/β ∂CT(n)/∂τ UH(n)W(n)-d*dif(n)q*ref(n-1)/β )WH(n)U(n)∂C(n)/∂τ+qref(n-1)2/β2WH(n)U(n)×(∂C(n)/∂τ CT(n)+C(n)∂ CT(n)/∂τ) UH(n)W(n) (17)
  4. 4. G S Krishnam Naidu Y, CH.Raghava Prasad, Subba Reddy Vasipalli / International Journal ofEngineering Research and Applications (IJERA) ISSN: 2248-9622 www.ijera.comVol. 3, Issue 3, May-Jun 2013, pp.625-629628 | P a g eThe gradient vector ∂C(n) ∂τ is the same as (10).The tap weight of the noncoherent adaptive filter isupdated byW(n+1)=W(n)+μ[2/βq*ref(n-1)e*dif(n)U(n)c(n)] (18)and code delay τ is updated by τ(n+1)=τ(n)-λ∂Jdif/∂τ.IV. SIMULATION RESULTSFrom the fig 4.1 I have mentioned the fft ofspread spectrum signal, which is transmitted throughAGWN channel. After the signal reaches thereceiver it passes through adaptive filter whichadjusts itself according to tap weights.Fig 4.1:FFT Of Spread Spectrum SignalTransmittedFig 4.2: Adaptive Filter OutputFig 4.3: Signal Error RateFig 4.4:Noncoherent Receiver ResponseFrom fig 4.3 it was analysed that as thenumber of iterations increased, the error ratedecreased at linear phase and remains constant.From fig 4.4 it is analysed that as E/N ratioincreases,then SER decreases accordingly.In thissimulation we are using matlab and analysingSERvs E/N, number of iterations vs error rate andalso I have shown the spread spectrum signal andthe output of adaptive filter.IV. CONCLUSIONA novel noncoherent receiver for jointtiming recovery and data detection in DS-CDMAsystems is proposed in this work. It estimates thedesired signal and code delay by LMS algorithm atthe same time. The MMSE solution of the proposedreceiver is analyzed theoretically and by computersimulations. Three different chip waveforms aresimulated in two different multipath channels withdifferent numbers of active users. It is shown thatthe timing offset can be rapidly tracked even if themismatch is up to half chip time interval. The loss ofnoncoherent detection compared with conventionalcoherent detection is limited and can be adjusted viathe generation of the reference symbol for thedecision-feedback differential detection. Theperformance of the noncoherent receiver canapproach the performance of the conventionalcoherent receiver if an infinite number of feedbacksymbols is used, as has been shown analytically.Furthermore, simulations show that the proposedreceiver in an asynchronous situation approaches theperformance as that of the receivers with perfectsynchronization.V. ACKNOWLEDGEMENTSThe authors like to express their thanks tomanagement and department of ECE KLUniversityfor their support and encouragement during thiswork.REFERENCES[1] Adaptive DS-CDMA Receiver with CodeTracking in Phase Unknown EnvironmentsFang-BiauUeng, Jun-Da Chen, and Shang-Chun Tsai, Student Member, IEEE
  5. 5. G S Krishnam Naidu Y, CH.Raghava Prasad, Subba Reddy Vasipalli / International Journal ofEngineering Research and Applications (IJERA) ISSN: 2248-9622 www.ijera.comVol. 3, Issue 3, May-Jun 2013, pp.625-629629 | P a g e[2] Special Issue on the European PathTowards UMTS, IEEE PersonalCommunications, Vol. 2, No. 1, Febr.1995.[3] M. H. Callendar, “Future Public LandMobile Telecommunication Systems,”IEEE Personal Communications, Vol. 1,No. 4, pp. 18-22, Fourth Quarter 1994.[4] T. Ottosson, A. Svensson, “Multirateschemes for multimedia applications inDS/CDMA systems,” Submitted toRVK’96, Luleå, Sweden, June 1996.[5] A. Johansson, A. Svensson, “Interferencecancellation in multirate DS/CDMAsystems,” Submitted to RVK’96, Luleå,Sweden, June 1996.[6] M. El-Tarhuni and A. Ghrayeb, “A robustPN code tracking algorithm for frequencyselective Rayleigh-fading channels,”IEEE Trans. Wireless Commun., vol. 3,no. 4, pp. 1018–1023, July 2004.[7] R. Schober, W. H. Gerstacker, and A.Lampe, “Noncoherent MMSE interferencesuppression for DS-CDMA,” IEEE Trans.Commun., vol. 50, pp. 577–587, Apr.2002.[8] R. Schober and L. H.-J. Lampe, “DF-DDfor multi-chip differentially encoded DS-CDMA,” in Proc. IEEE GLOBECOM, vol.4, pp. 2325– 2329, Dec. 2003.Author’s BibliographyG S KRISHNAM NAIDU Ywas born in 1987 atVisakhapatnam, Andhra Pradesh, India. HeGraduated in Electronics and CommunicationEngineering from Avanthi Institute of Engineering& Technology, JNTUK. Completed his M.Tech inCommunications and Radar Systems in K LUniversity.Presently he is working as assistantprofessor in K L UNIVERSITY. His researchinterests include wireless communicationsand multimedia applications.CH.RAGHAVA PRASAD was born in 1986 atVijayawada, Andhra Pradesh, India. He Graduatedin Electronics and Communication Engineeringfrom V.R.Siddartha Engineering College, ANU.Completed his M.Tech in Embedded Systems inVignan’s Engineering College, JNTUK. Presentlyhe is working as assistant professor in K. L.UNIVERSITY. His research interests includeEmbedded Systems, Image Processing and wirelesscommunications.SUBBA REDDY VASIPALLI was born in 1986 atBhimavaram, Andhra Pradesh, India. He Graduatedin Electronics and Communication Engineeringfrom Kakinada Institute Of Engineering &Technology, JNTU. Completed his M.Tech inEmbedded Systems in Joginapally B. R.Engineering College, JNTUH. Presently he isworking as assistant professor in K. L.UNIVERSITY. His research interests includeantennas, MEMS and wireless communications.