ACEEE Int. J. on Network Security, Vol. 02, No. 01, Jan 2011SIR Analysis of Overloaded CDMA System Using            Orthog...
ACEEE Int. J. on Network Security, Vol. 02, No. 01, Jan 2011increase the overloading performance. The example             ...
ACEEE Int. J. on Network Security, Vol. 02, No. 01, Jan 2011B. Weighted LPIC                                              ...
ACEEE Int. J. on Network Security, Vol. 02, No. 01, Jan 2011conventional LPIC on flat Rayleigh fading channel andadditive ...
ACEEE Int. J. on Network Security, Vol. 02, No. 01, Jan 2011[4] H. Sari, F. Vanhaverbeke and M. Moeneclaey, “Multiple     ...
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SIR Analysis of Overloaded CDMA System Using Orthogonal Gold Codes

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This paper introduces a direct-sequence codedivision
multiple access (DS/CDMA) concept which
accommodates a higher number of users than the spreading
factor N. This new multiple access concept makes use of two
sets of orthogonal signal waveforms, one for the first set of
users and the other for the additional users. The two sets of
users are scrambled by a set specific pseudonoise sequence. A
two stage and three stage conventional and weighted parallel
detection technique is proposed to cancel interference between
the two sets of users. The signal to interference ratio of the
two sets of users is derived. The proposed technique thus
accommodates N users without any mutual interference and a
number of additional users at the expense of a small signal-tonoise
ratio penalty.

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SIR Analysis of Overloaded CDMA System Using Orthogonal Gold Codes

  1. 1. ACEEE Int. J. on Network Security, Vol. 02, No. 01, Jan 2011SIR Analysis of Overloaded CDMA System Using Orthogonal Gold Codes Sasipriya S1, Ravichandran C.S2 1 Karpagam college of Engineering/ IT Department, Coimbatore, India Email: ksmrityunjay@yahoo.com 2 SSK college of Engineering & Technology/Principal, Coimbatore, India Email: eniyanravi@gmail.comAbstract— This paper introduces a direct-sequence code- iteration consisting of two steps, one to detect the signalsdivision multiple access (DS/CDMA) concept which transmitted by the first set of users and the other to detectaccommodates a higher number of users than the spreading the signals transmitted by the second set of users. Thefactor N. This new multiple access concept makes use of two introduction of orthogonal/orthogonal gold codes issets of orthogonal signal waveforms, one for the first set ofusers and the other for the additional users. The two sets of justified by the fact that the set-1 users suffer fromusers are scrambled by a set specific pseudonoise sequence. A interference of the set-2 users only, while the set-2 userstwo stage and three stage conventional and weighted parallel suffer from interference of the set-1 users only resulting indetection technique is proposed to cancel interference between residual multiple-access interference present at the filterthe two sets of users. The signal to interference ratio of the output.two sets of users is derived. The proposed technique thus One approach to tackle multiuser interference problem isaccommodates N users without any mutual interference and a to employ a suitable linear transformation on the matchednumber of additional users at the expense of a small signal-to- filter outputs. Belonging to this family is the so-callednoise ratio penalty. decorrelating receiver [10]. Another popular approach is toIndex Terms— Gold codes, Linear Parallel Interference employ interference cancellation, i.e., to attempt removalCancellation (LPIC), Multiple Access (MA), Multiple Access of the multiuser interference from each user’s receivedInterference (MAI), Overloading, Signal to Interference(SIR) signal before making data decisions. In principle, the ICRatio. schemes considered in the literature fall into two categories, namely, successive and parallel cancellation. I. INTRODUCTION The advantage is that they do not require significant complexity when compared to minimum mean square Multiple access (MA) communication represents an error-MMSE detector [11], decorrelating detector [10] oractive area of current research since it is the only means of linear decision directed interference cancellation [12]. Thecommunication among users in wireless systems such as first PIC detector for code division multiple accessmobile and cellular terrestrial systems and satellite based (CDMA) communication systems was derived by Varanasisystems. One of the category of multiple access technique and Aazhang in [8] where their PIC detector was called ais orthogonal-waveform multiple access (OWMA), which multistage detector. The multistage detector was shown toincludes FDMA, TDMA, OFDMA, CDMA with have close connections to the optimum maximum-orthogonal spreading sequences (called orthogonal CDMA, likelihood detector and also to possess several desirableor OCDMA), and any other multiple access technique properties. In [5] the MAI estimates are weighted beforewhich assigns orthogonal signal waveforms. The other cancellation and the value of the weights are low at thecategory includes direct-sequence CDMA and frequency- early stages and large at the later stages. An iterative linearhopping CDMA with pseudo-noise (PN) spreading parallel interference cancellation [3] technique is adoptedsequences. This paper concentrates on direct-sequence to cancel interference in unscrambled DS/CDMA systemCDMA with PN sequences which is referred as PN- for N users.CDMA. The beauty of the multiple access concept P. Kumar et al. [1] have studied the overloadingpresented in [6] is that it combines the advantages of performance of Orthogonal / Scrambled Orthogonal (O/S-OWMA and PN-CDMA while avoiding their shortcomings O), which is a modification of S-O/O scheme. In S-O/Oand undesirable features. scheme the same set of Walsh- Hadamard sequence is A DS/CDMA scheme which can accommodate N users scrambled by a set specific pseudo-random (PN) sequence.without any mutual interference, while also A method of accommodating K=N+M users in an N-accommodating a number of additional users at the expense dimensional signal space that does not compromise theof some SNR penalty is devised. The proposed technique minimum Euclidean distance of the orthogonal signalingconsists of assigning one set of orthogonal gold codes to has been presented in [9] for AWGN channel. A tree-likethe first N users, and another set of orthogonal gold codes correlation coefficient structure of user signatures suitableto the additional users, but overlaying them with a different for optimal multiuser detection has been proposed in [7]. APN sequence, for all additional users. The signals new overloading scheme using hybrid techniques has beentransmitted by users from the same set are mutually proposed in [2], where the spreading codes andorthogonal, but there is no orthogonality between users transmission modes are different for the two sets tofrom different sets. Detection is performed iteratively, each 50© 2011 ACEEEDOI: 01.IJNS.02.01.554
  2. 2. ACEEE Int. J. on Network Security, Vol. 02, No. 01, Jan 2011increase the overloading performance. The example In eqn.(4,5), Au ,k u is the complex channel attenuationdeveloped by H. Sari, F. Vanhaverbeke, and M. th for the k user of the set-u. For AWGN channel, A u ,k u =1.Moeneclaey [4] is based on a particular combination ofTDMA and OCDMA. The phase term is φu ,k for the kth user in set-u. The u A multistage Conventional Linear Parallel Interference orthogonal Gold codes of both the sets are overlaid by aCancellation (CLPIC) and Weighted Linear Parallel set-specific pseudo-noise (PN) sequence which is the sameInterference Cancellation (WLPIC) is adopted in this paper for all users within the set. In order to split the interferenceto cancel the interference. In parallel interference power evenly over the in-phase and quadrature componentscancellation each stage uses the prior stage’s tentative of the useful signal (irrespective of the carrier phase), wedecision outputs to generate new multiple-access consider complex valued PN sequences: the chips pnuinterference estimates. These interference estimates are randomly takes their values from the set {exp(jπ/4),subtracted from the original observation to produce new exp(j3π/4), exp(j5π/4),exp(j7π/4)}.tentative decision outputs with presumably lower multiple-access interference. III. INTERFERENCE CANCELLATION This paper is organized as follows. In the next section,basic principle is described. Interference cancellation is We consider a multistage conventional and weightedpresented in section-3 and SIR analysis in section-4. LPIC at the receiver. The first stage is a conventionalSection-5 explains about the Simulation results. Finally, matched filter (MF), which is a bank of K correlators, eachconclusion of this paper is presented. matched to a different user’s spreading waveform. The (1) (1) received vector yk and yk at the output of the first stage II. BASIC PRINCIPLE 1 2 of the matched filter detector for the set-1 users and set-2 Consider a DS/CDMA system with a spreading factor of (1)N, and assume that K=N+M, (where M<N) number of users (the superscript (1) in yk1 denotes the first stage)users is to be accommodated. The following notation for respectively are given bythe discrete-time matrix model of the received BPSK Mmodulated CDMA signal after demodulating and chip y k1 = A k 1 h k 1 b k 1 + ∑ ρ k 1k 2 A k 2 h k 2 b k 2 + n k 1 (1) (6)matched filtering will be used. k 2 =1 y = b1A1h1S1 + b2A2h2S2 + n (1) N (1) y k 2 = A k 2 h k 2 b k 2 + ∑ ρ k 1k 2 A k 1 h k 1 b k 1 + n k 2 (7) Let us denote S1 and S2 as the signature matrices of the k1 =1set-1 and set-2 users respectively. The signature waveformmay be expressed as where ρ k1k 2 is the cross-correlation coefficient between the N set-1 users and set-2 users spreading waveforms, given by su,ku (t) = ∑ s u , k p c ( t − jTc ) j (2) T ρ k1k 2 = ∫ s k ( t )s k ( t )dt , ρ k1k 2 ≤ 1, and n k ’s are complex u j=1 1 2 0where s j u,ku ∈ {1, 1}, Tc is the chip duration and pc(t) is the Gaussian with zero mean and variance equal to σ 2. Thereal valued unit-energy rectangular chip pulse. In this received vector y(k1) , y(k1) is used for multiaccess 1 2paper, two different orthogonal Gold code sets for set-1 and interference(MAI) estimation and cancellation in theset-2 users are considered. Let us denote b1 and b2 as the second stage of parallel interference cancellation.data matrices of the set-1 and set-2 users respectively. Thedata signal bu,ku (t) of the kth users in set-u, may be A. Conventional LPICexpressed as In LPIC, the MAI estimate for the set-1 users in stage m, ∞ m > 1, is obtained by multiplying y(km −1) with ρ k1k 2 and 2 bu,ku (t) = ∑ b lu , k u p Tb ( t − lTb ) (3) summing them up. More specifically, an estimate of the l = −∞ MAI for a desired user in the current stage is obtainedwhere the data sequences blu , k u ∈ {-1,1} are independent using all the other user’s soft outputs from the previousand identically distributed (i.i.d.) random variables taking stage for cancellation in the current stage. Accordingly, thevalues of +1 and -1 with equal probability. In eqn.[3] Tb is bit decision for the set-1 users after interference cancellation in the mth stage is given bythe bit duration, N is the spreading factor and pTb (t) is therectangular pulse of the information data bits. Matrices A1and A2 are diagonal matrices of received signal amplitudes (m) * (1) ( b k1 = sgn (Re(h k 1 y k 1 − ∑ ρk 1 , k 2 y k 2 M ( m −1) k 2 =1 ))) (8)for two sets of users and can be expressed as Similarly, the bit decision for the set-2 users after A1 = diag[A1,1cos( φ1,1),…, A1,Ncos( φ1,N)] (4) interference cancellation in the mth stage is given by A2 = diag[A2,1cos( φ2,1),…, A2,Mcos( φ2,M)] (5) (m) k (1) ( b k 2 = sgn (Re(h * 2 y k 2 − ∑ ρk 1 , k 2 y k1 N ( m −1) k 1 =1 ))) (9) 51© 2011 ACEEEDOI: 01.IJNS.02.01.554
  3. 3. ACEEE Int. J. on Network Security, Vol. 02, No. 01, Jan 2011B. Weighted LPIC 2 ⎛ N ⎞ In a weighted LPIC, the MAI estimate for the set-1 users 2A 2 2 ⎜1 − p (k22) ∑ ρ 21 ,k 2 ⎟ k k SIR k 2 = ( 2) ⎝ k1 =1 ⎠ (16)and set-2 users in stage m, m > 1, is weighted by a factor (m) (m) σ 2( 2 ) + σ 2 ( 2 ) I Np k1 and p k 2 respectively before cancellation. The mth k2 k2stage output of the set-1 users and set-2 users respectivelyare given by B. Average SIR at 3rd Stage Output (m) (1) (m) M ( m −1) The soft values of the interference cancelled outputs of y k 1 = y k1 - p k1 ∑ ρ k1 , k 2 y k 2 (10) all the other users from the second stage are used to k2 =1 reconstruct (estimate) the MAI for the set-1 user in the (m) (1) (m) N ( m −1) third stage. The MAI estimate is then weighted by the y k 2 = y k 2 - p k 2 ∑ ρ k1 , k 2 y k 1 (11) factor p(k3) and cancelled. The third stage output of the set-1 k1 =1 1 user, y(k3) is then given byThe bit decision for the set-1 users and set-2 users after 1weighted interference cancellation in stage m is M y k 1 = y k1 - p k 1 ∑ ρ k 1 , k 2 y k 2 ( 3) (1) ( 3) ( 2) b (m) k1 = ( ( sgn Re h y * k1 m k1 )) (12) k2 =1 = sgn (Re(h )) ( 3) bk 2 (m) * k2 yk 2 m (13) = Ak1 h k1 bk1 X + I k1 + N (k3) 1 (17)In the following, we obtain exact expressions for the whereaverage SIR’s at the output of the weighted LPIC. ( 3) M ∑ ρ k1k 2 (1 − p k 2 ) + 2 ( 2) X = 1- p k 1 k2 =1 IV. SIR ANALYSIS M K ( 3) pk1 ∑ ρ k ,k p (k2 ) ∑ ρ j ,k 1 2 2 1 2 (18)A.. Average SIR at 2 Stage Output nd k 2 =1 j1 =1 The weighted interference cancelled output of the 2nd The terms I (k3) and N (k3) in (17) represent the interferencestage for the set-1 users is given by 1 1 and noise terms introduced due to imperfect cancellation in M using the soft output values from the second filter stage. ( 2) (1) (1) (1) y =y k1 k1 - p k1 ∑ ρ k1 , k 2 y k2 The average SIR of the set-1 user at the output of the k2 =1 second stage, SIR (k2) is then given by ⎛ M ⎞ = A k1 h k1 bk1 ⎜1 − p( 2 ) ∑ ρ 2 ,k ⎟ + I (k2) + N (k2 ) 1 k1 k1 2 ⎝ ⎠ 2 A 21 X 2 1 1 k 2 =1 SIR k1 = (19) ( 2) k (14) σ 2( 3 ) + σ 2 ( 3 ) I k1 N k1 The terms I (k2 ) and 1 N (k2 ) in (14) represent the 1 Likewise, the average SIR of the set-2 user at the output ofinterference and noise terms introduced due to imperfect the third stage, SIR ( 32) is then given by kcancellation in using the soft output values from thematched filter stage. Since hk’s are complex Gaussian, both 2A 2 2 X 2 SIR k 2 = (20) ( 3) kI (k2 ) and N (k2 ) are linear combinations of Gaussian random 1 1 σ 2( 3 ) + σ 2 ( 3 ) I Nvariable with zero mean and variance equal to σ I( 2 ) and 2 k2 k2 k1σ 2 N( 2 ) respectively. V. SIMULATION RESULTS k1 The average SIR of the set-1 users at the output of the This section presents the simulation results of the average SIR and Bit Error Rate (BER) performance of thesecond stage, SIR ( 2 ) is then given by k1 proposed WLPIC scheme. The results are compared with 2 those of CLPIC and matched filter detector. It is noted in ⎛ M ⎞ all graphs that the weighted LPIC clearly outperforms both 2A 21 ⎜1 − p (k2) ∑ ρ 21 ,k 2 ⎟ k k ( 2) SIR k1 = ⎝ 1 k 2 =1 ⎠ (15) the MF detector as well as the conventional LPIC. The σ 2( 2 ) + σ 2 ( 2 ) channel model used is a one sample spaced, two-ray, equal- I N k1 k1 gain Rayleigh fading and additive white Gaussian noiseSimilarly, the average SIR of the set-2 users at the output model. The data modulation is BPSK and the spreading factor N is 64. The number of set-1 users taken is 20.of the second stage, SIR ( 2 ) is then given by k2 In Fig.1, the BER performance comparison of scrambled scheme with weighted LPIC as a function of average SNR per bit with that of the MF detector as well as the 52© 2011 ACEEEDOI: 01.IJNS.02.01.554
  4. 4. ACEEE Int. J. on Network Security, Vol. 02, No. 01, Jan 2011conventional LPIC on flat Rayleigh fading channel andadditive white Gaussian noise is observed. It is found thatfor 25% overloading the 3rd stage CLPIC and WLPICapproaches the single user detector. The Fig.2 at 41%overload supports an additional 8 users at a BER of greaterthan 10-3 for the 3rd stage WLPIC. However theperformance of 2nd stage WLPIC and 3rd stage CLPICdeteriorates at a BER of 10-3. Figure 3. BER performance of scrambled system with 50% overloading and processing gain of 64. Figure 1. BER performance of scrambled system with 25% overloading and processing gain of 64. Figure 4. BER performance of scrambled system with 64% overloading and processing gain of 64. VI. CONCLUSION A new multiple access concept has been used in the direct-sequence code-division multiple access (DS/CDMA) concept to accommodate higher number of users than the spreading factor N. The BER performance was evaluated through MATLAB simulation. A two stage and three stage Figure 2. BER performance of scrambled system with 41% conventional and weighted parallel detection technique was overloading and processing gain of 64. used to cancel interference between the two sets of users. The signal to interference ratio of the two sets of users is In Fig. 3, the BER performance comparison of also derived for the second stage and third stage. It is thusscrambled scheme with weighted LPIC with that of the MF shown that the proposed technique provides 50%detector as well as the conventional LPIC is observed at overloading at a BER of 10-3 supporting an additional 1050% overloading. The 3rd stage WLPIC supports an users.additional 10 users at a BER of 10-3. Hence, complexscrambling increases the amount of overloading REFERENCESsignificantly in overloaded DS-CDMA systems. The [1] P. Kumar, M. Ramesh, and S. Chakrabarti, “Performanceperformance degradation of 2nd stage WLPIC and 2nd and evaluation of orthogonal/ scrambled-orthogonal overloaded3rd stage of CLPIC is large. DS-CDMA system,” IEEE International Conference on The BER increases at 64% overloading for both the Wireless Communications and Networks (WOCN), JulyWLPIC and CLPIC as shown in Fig. 4. It is observed in all 2007.graphs that the BER of 2nd stage CLPIC is large and the [2] P. Kumar and S. Chakrabarti, “A New Overloading Scheme for DSCDMA System,” National Conference onBER of the proposed 3rd stage WLPIC is less. Thus the Communication, pp. 285-288, 26-28 Jan.’ 2007, IIT Kanpur.proposed WLPIC scheme results in significantly better [3] V. Tikiya, S. Manohar, and A.Chockalingam, SeniorBER performance than both the matched filter detector as Member, IEEE, “SIR-Optimized Weighted Linear Parallelwell as the CLPIC scheme. The 3rd stage of the WLPIC Interference Canceller on Fading Channels,” IEEEscheme is found to have high SIR. Transactions On Wireless Communications, Vol. 5, No. 8, August 2006 53© 2011 ACEEEDOI: 01.IJNS.02.01.554
  5. 5. ACEEE Int. J. on Network Security, Vol. 02, No. 01, Jan 2011[4] H. Sari, F. Vanhaverbeke and M. Moeneclaey, “Multiple communications,” IEEE Trans. Commun., vol. 38, pp. 509– access using two sets of orthogonal signal waveforms,” IEEE 19, Apr. 1990. Commun. Lett., vol. 4, no. 1, pp. 4-6, Jan. 2000. [9] J. A. F. Ross and D. P. Taylor, “Vector assignment scheme[5] D. Divsalar, M. K. Simon, and D. Raphaeli, “Improved for M+N users in N-dimensional global additive channel,” parallel interference cancellation for CDMA,” IEEE Trans. Electronics. Letter, vol. 28, August 1992. Commun. vol. 46, no. 2, pp.258-268, Feb.1998. [10] R.Lupas and S. Verdu, “Linear multiuser detectors for[6] S. Verdu, “Multiuser Detection,” Cambridge University synchronous code division multiple-access channels”, IEEE Press, 1998. Trans. Information Theory, vol. 35,pp. 123-136, January[7] R. E. Learned, A. S. Willisky and D. M. Boroson, “Low 1989. complexity joint detection for oversaturated multiple access [11] U. Madhow and M.L. Honig, “MMSE interference communications,” IEEE Trans. Signal Processing, vol. 45, suppression for direct-sequence spread spectrum CDMA”, pp. 113-122, January 1997. IEEE Trans Communication, vol.42, pp.3178-3188,[8] M. Varanasi and B. Aazhang, “Multistage detection in December 1994. asynchronous code-division multiple-access [12] L. K. Ramussen, T. I. Lim, and A-L. Johnson, “A Matrix- Algebraic Approach to Successive Interference Cancellation in CDMA.”, IEEE Trans. Comm,. vol. 48, Jan. 2000. 54© 2011 ACEEEDOI: 01.IJNS.02.01.554

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