Research Article Multigroup Synchronization in 1D-Bernoulli Chaotic Collaborative CDMA

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1 Hindawi Wireless Communications and Mobile Computing Volume 2017, Article ID , 7 pages Research Article Multigroup Synchronization in 1D-Bernoulli Chaotic Collaborative CDMA Sumith Babu Suresh Babu and R Kumar Department of Electronics and Communication Engineering, SRM University, Chennai, India Correspondence should be addressed to Sumith Babu Suresh Babu; sumithbabusb@yahoocoin Received 6 July 2016; Revised 22 September 2016; Accepted 11 October 2016; Published 12 January 2017 Academic Editor: Álvaro Marco Copyright 2017 S B Suresh Babu and R Kumar his is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited Code-division multiple access (CDMA) has played a remarkable role in the field of wireless communication systems, and its capacity and security requirements are still being addressed Collaborative multiuser transmission and detection are a contemporary technique used in CDMA systems he performance of these systems is governed by the proper accommodation of the users and by proper synchronization schemes he major research concerns in the existing multiuser overloaded CDMA schemes are (i) statistically uncorrelated PN sequences that cause multiple-access interference (MAI) and (ii) the security of the user s data In this paper, a novel grouped CDMA scheme, the 1D-Bernoulli chaotic collaborative CDMA (BCC-CDMA), is introduced, in which mutually orthogonal chaotic sequences spread the users data within a group he synchronization of multiple groups in this scheme has been analyzed under MAI limited environments and the results are presented his increases the user capacity and also provides sufficient security as a result of the correlation properties possessed by the chaotic codes Multigroup synchronization is achieved using a 1D chaotic pilot sequence generated by the Bernoulli Map he mathematical model of the proposed system is described and compared with the theoretical model of the synchronization in CDMA, the simulation results of which are presented 1 Introduction he demand for high capacity wireless systems is increasing day by day Wireless communication system generations including the 3rd generation (3), the 4th generation (4), and the upcoming 5th generation (5) strive to achieve the ever increasing needs for faster data transfer and higher security Code-division multiple access (CDMA) has always been fulfilling these requirements and is expected to be an effective solution for future systems too An important aspect of CDMA is to increase the capacity or the number of users, with acceptable error performance Several grouped CDMA schemes are being studied intensively and are widely used to meet the capacity needs of several modern communication systems he collaborative CDMA scheme increases the capacity by grouping a small number of users that share the same pseudorandom (PN) spreading sequence and enables group spreading and despreading operations [1] It also outperforms the CDMA multiuser detection (MUD) schemes using group pseudo decorrelating detector (PD) andlayeredspacetime(las)mud[2]advancedmud techniques incorporate more users than the number of the spreading sequences but at the expense of considerable performance degradation [3, 4] Also, orthogonal spreading sequences are shared by more than one user in a groupbased collaborative spreading process [5] Various schemes with reusability of the spreading sequences have been tested under different channel scenarios [3, 6] Hence, such schemes provide a brief research outlook, to multiuser scenarios, in order to accommodate the ever increasing number of users he proposed system inherits capabilities like interference rejection, antijamming, fading reduction, and low probability of interception from the conventional direct sequence spread spectrum (DSSS) systems [7] In conventional DSSS systems, the users transmit their information using Walsh functions or wavelets [8] Chaotic sequences can also be used as spreading codes instead of PN sequences hey can be generated by simple or complex differential equations and are dependent on the initial conditions A very small change in the differential equation s initial conditions can

2 2 Wireless Communications and Mobile Computing cause a large deviation in the system states over time, which makes these systems difficult to intercept Sequences, with good cross-correlation properties, generated using chaotic mapscanbeusedincdmasystems[9]systemsusing chaotic sequences both as carrier of users data and as pilot areanalyzed[10]variousmethodshavebeenproposedto obtain binary sequences from chaotic trajectories generated by nonlinear ergodic maps [11] Synchronization within such chaos based DS-CDMA systems is an active area of research due to the lack of robust synchronization techniques [12, 13] A theoretical analysis of synchronization in DSSS using chaotic sequences has also been analyzed [14] Nonlinear dynamicchaoticsequencesprovidemessageconcealment using chaotic phase shift keying techniques [6, 15] After analyzing several such techniques, the proposed scheme addresses the synchronization of multiple groups in a highly secure and high capacity chaotic grouped CDMA system using chaotic sequences which are used as the carrier and the pilot he proposed scheme provides better synchronization and can be integrated into less complex wireless systems Section 2 describes the defects in classical multiuser schemes Section 3 explains the proposed system model and presents its principle and mathematical realization Section 4 discusses the simulation results Finally, the conclusion and future work are given in Section 5 2 he Defects in Classical Multiuser Scheme Overloading of users is a major problem as far as future communication systems are concerned aking into account thecdmasystems,anincreaseinthenumberoftheusers increases the MAI But the number of PN sequences cannot be increased in accordance with the growing number of simultaneous users Hence, the number of users per group is restricted in the grouped CDMA case he collaborative CDMA scheme is an example which achieves a maximum of 90 users only per cell sector, with three users sharing a PN sequence, in an additive white aussian noise (AWN) channelalso,itispossibleforanopponenttoimitatethe transmission by decoding the PN sequences by their bit timings Synchronizing the systems under such conditions is impractical he proposed system addresses this issue by using chaotic sequences, generated by 1D map, both as carrier and as synchronization pilot 3 he Proposed System Model 31 BCC-CDMA Multiuser ransmitter Design he baseband model for the proposed multigroup synchronization in the BCC-CDMA system is shown in Figure 1 he transmitter signal s t (t) is s t (t) = s kl (t) = k=1 l=1 k V kl (t) B Ck (t) (1) l At the transmitter side, the total number of users (K) is divided into groups, each consisting of users Users, with encoded message V 1 within a group, will use the same chaotic-spreading sequence B C Userswithinagroupusethe same chaotic sequence generated by the 1D map Sequences of length 1 Naregenerated(whereN is the order of the spread code matrix) using the 1D-Bernoulli transformation given by 2x; 0 x < 05 f (x) ={ } (2) 2x 1; 05 x<1 he piecewise linear function (2) generates the iterated function map A unique initial condition generates the chaotic sequence and is mapped onto the ijth element of the N N matrixheith row constitutes the spreading sequences for the ith group in the BCC-CDMA scheme he klth user sequence is s kl (t) =V kl (t) B Ck (t) ={ 1 B Ck (t), V kl (t) = 1, for t [(i 1) c,i c ] +1 B Ck (t), V kl (t) =+1, for t [(i 1) c,i c ] }, (3) where i denotes the ith transmitted bit Now, for the synchronization block, a chaotic pilot sequence modulated by ones is considered (generated from the same chaotic map with a special initial condition): S 00 (t) =V 00 (t) B C0 (t) =+1 B C0 (t), (4) for t [(i 1) c,i c ] he pilot sequence is a periodic sequence with finite duration and determines the starting point of the spreading of the individual user groups Hence, when the received pilot is synchronized with its stored reference, it can determine the beginning of the individual user groups 32MultigroupSynchronizationinBCC-CDMAhe data is spread and transmitted at the beginning of the pilot sequence In order to achieve this, the received pilot has to be synchronized with its locally generated replica he received pilot is a time shifted replica of the transmitted chaotic pilot and is given by B C0 (t τ) As the pilot is synchronized, the control variable B Csync is generated by the synchronization block he control variable reduces the time delay using the feedback loop his control signal will align the th user group at the instant of the th group of the transmitted sequence he received signal is r (t) =( h kl V kl B Ck ) 2A cos (ω c t+φ)+ξ t (t) =( V kl B Ck ) 2A [cos ω c t cos φ+sin ω c t sin φ] + 2ξ I t (t) cos ω c t 2ξ Q t (t) sin ω c t, where φ is a phase difference assumed between the carriers at transmitter and receiver, I= 2 cos ω c t, Q= 2 sin ω c t, (5)

3 Wireless Communications and Mobile Computing 3 D-Bernoulli chaotic sequence generator V 00 =1 S 00 B C0 h 00 Channel estimation b 11 Mapping {0 1} {1 1} V 11 B C1 S 11 h 11 b 0 ( ) t= b ĥ 1 b1 = arg min (d 1 ) 2 b11 b 1 Mapping V 1 S 1 B C1 h 1 AWN ξ1(t) I FIR I LPF B C1 Z 1 R 1 a 1 b1 b 1 Mapping {0 1} {1 1} V 1 B C S 1 h 1 B C t= b b 0 ( ) Z ĥ b = arg min (d ) 2 a b1 b b Mapping V B C S h roup despreading stage roup decorrelation stage ML joint detection stage 1D-Bernoulli chaotic sequence B Csync Chaotic pilot synchronization I LPF B C0 (t τ) r 11 (t) m (m 1)t Z 11 () 2 z r(t) B C0 (t τ) Q LPF r 12 (t) m (m 1)t Z 12 () 2 Figure 1: Baseband model for the proposed multigroup synchronization in BCC-CDMA the amplitude of the pilot is A= 2E c / c,andh kl =1is the channel gain coefficient of the klth user Now, the received signal is multiplied by the in-phase component to get r 11 (t) =r(t) 2A cos (ω c t) = {( V kl B Ck ) 2A [cos ω c t cos φ+sin ω c t sin φ] + 2ξ I t (t) cos ω c t 2ξ Q t (t) sin ω c t} 2A cos (ω c t) =( V kl B Ck )A[1+cos 2ω c t] cos φ +( V kl B Ck )Asin 2ω c t sin φ+ξ I t (t) [1 + cos 2ω c t] ξ Q t (t) sin 2ω c t he signal in (6) is now low pass filtered to get r 11 (t) =( V kl B Ck )Acos φ+ξ I t (t) (6)

4 4 Wireless Communications and Mobile Computing =V 00 B C0 A cos φ+( V kl B Ck )Acos φ k=1 l=1 +ξ I t (t) =B C0A cos φ+ξ a (t) (Since, pilot V 00 =+1), (7) where ξ a (t) contains the interuser interference and AWN Analogously, we get r 12 (t) =B C0 A sin φ+ξ b (t) (8) Now, r 11 and r 12 are multiplied by a reference sequence (mbittimeshiftedversionofthereceivedpilot)withm chips (M = / c ) and then integrated to get z 11 and z 12 as follows: t=m z 11 = r 11 (t) B C0 (t τ) dt t=(m 1) c t=m = [B C0 A cos φ+ξ a (t)]b C0 (t τ) dt t=(m 1) c t=m =Acos φ B C0 B C0 (t τ) dt t=(m 1) c t=m + ξ a (t) B C0 (t τ) dt t=(m 1) c =Acos φr (τ) +N 1 = 2E c c cos φr (τ) +N 1 he first correlation value is obtained by aligning the M chips of the pilot and multiplying and summing them with the reference sequence If the correlation value is greater than the threshold value, the process is stopped; else, the step is repeated for next chip intervals until synchronization is achieved Similarly, we get t=m z 12 =Asin φ B C0 B C0 (t τ) dt t=(m 1) c t=m + ξ b (t) B C0 (t τ) dt t=(m 1) c =Asin φr (τ) +N 2 = 2E c c sin φr (τ) +N 2, (9) (10) where N 1 and N 2 are aussian random variables with zero mean and variance /2 and can be expressed as N 1,N 2 (0, /2) herefore, z 11 and z 12 are also aussian and can be expressed as z 11 ( 2E c c z 12 ( 2E c c cos φr (τ), 2 ), cos φr (τ), 2 ) (11) he correlation and synchronization are controlled by the decision variable z and are given by (substituting the values of A and M ) z=z z2 12 = 2 [ (2 ME 2 c cos φr (τ)) [ sin φr (τ)) ] ] = 2 [4ME c +(2 ME c = 2 2 cos 2 φr 2 (τ) +4 ME c sin 2 φr 2 (τ)] 4 ME c R 2 (τ) [cos 2 φ+sin 2 φ] = λ, 2 (12) where λ = 4(ME c / )R 2 (τ) is a noncentral chi-squared random variable with two degrees of freedom hus, the probability density function (PDF) of the control variable z is P z (ψ) = { { { 1 2σ 2 e (1/2)(λ+ψ/σ 2) I 0 ( λψ σ 2 ), ψ>0 } } 0, otherwise} (13) Now,thedecisionismadewithrespecttothefollowing hypotheses Null Hypothesis H 0 : locally generated sequence is not aligned with the received sequence: H 0 : τ > c (14) R (τ) 0 Actual Hypothesis H 1 : locally generated sequence is aligned with the received sequence within one chip duration: H 1 : τ c (15) R (τ) >0 Based on the above hypotheses, the conditioned probability density functions are P z (ψ H 0 )= 1 2 2σ 2 e (1/2)(ψ/σ ) P z (ψ H 1 )= 1 2) 2σ 2 e (1/2)(λ+ψ/σ I 0 ( λψ σ 2 ) (16) herefore, the probability of false alarm for the first case (ie, m=1)is P F (m=1) =P z (ψ > H H 0 ) 1 = 2) (17) H 2σ 2 e (1/2)(ψ/σ dψ = e (1/2)(ψ/σ2),

5 Wireless Communications and Mobile Computing 5 where the threshold is set at H = ln p F (m=1) (18) Similarly, the detection probability is Performance of BCC-CDMA (with sync): spread length 31 P D (m=1) =P z (ψ > H H 1 ) 1 = 2) H 2σ 2 e (1/2)(λ+ψ/σ I 0 ( λψ σ 2 )dψ (19) Average BER 10 2 =e (1/2)(ψ/σ2) 10 3 Now, considering the transformation ψ=(xσ) 2,(19)canbe expressed as P D (m=1) = xe (1/2)(λ+x) I 0 ( λx) dx (20) H /σ 2 Equation (20) resembles Marcum s Q-Function and therefore P D can be expressed as P D (m=1) =Q M ( λ, H σ 2 ) (21) When the condition R(τ) R(0) = 1 is fulfilled, the system achieves synchronization and the upper bound is obtained as (substituting values of λ and H ) P D (m=1) Q M (2 M E c, 2 ln p F (m=1)) (22) hus, for a particular value of E c /, Q M varies with respect to the value of M enabling it to synchronize the receiver 4 Performance Analysis and Numerical Results he BER performance is investigated and compared with that of conventional collaborative CDMA scheme In Figure 2, the performance of BCC-CDMA system, with synchronization, is analyzed with a spreading length of 31 choosing =30 and = [2, 4] such that it accommodates groups of 30 2 and 30 4 users, giving a total number of K =60and120 users, respectively he performance is compared with that of conventional CDMA, with 30 1 users, and collaborative CDMA with 60 and 90 users ( =30and = [2, 3]) he BCC-CDMA and collaborative CDMA give a BER of and , respectively, accommodating 60 users, at SNR 15 db It is clearly shown that the BCC- CDMA scheme achieves a BER improvement of at 15dB with equal number of usersas K is increased, BCC- CDMA achieves a BER improvement of 38% accommodating 120 users (additional number of 30 users) he synchronization of the system is better understood by considering the detection and false alarm probabilities SNR (db) Collaborative CDMA [30 2] BCC-CDMA [30 2] Collaborative CDMA [30 3] BCC-CDMA [30 4] Conventional CDMA [30 1] Figure 2: BER performance of the proposed BCC-CDMA (with sync): spread length 31 he performance criteria are (i) probability of detection P D and (ii) probability of false alarm P F he expressions for P D and P F are obtained by taking into account the output of the acquisition part he synchronization is achieved when the decision variable z exceeds the threshold H hough z exceeds H several times, it is only once that the received signal r(t) is in synchronism with B C0 (t τ) o understand this better, the probability of false alarm is expressed by comparing it with Baye s rule as follows: P F (m=1) =P r (ψ m > H H 0 ) = P r (ψ m > H H 0 ) P r (H 0 ) (23) he numerator and denominator terms of (23) can be expressed as P r (ψ m > H H 0 )= lim D ( c D ) P r (H 0 )= lim D (D 1 D ), (24) where c is the number of times the decision variable ψ m overcomes the threshold H and D isthetotalnumberof discrete values of ψ m Substituting (22) and (23) into (21), P F (m=1) = lim D (c/d) lim D ((D 1) /D) = lim D ( c D 1 ) (25)

6 6 Wireless Communications and Mobile Computing o obtain an accurate result, the experiment has to be runalargenumber(j) oftimes,keepings limited hus, the probability of false alarm is j P F (m=1) = lim ( ) (26) j j(d n 1) n=1 Now, the probability of detection is P D (m=1) = P r (ψ m > H H 1 ) (27) P r (H 1 ) here are only two possible outcomes, that is, whether the decision variable ψ m has exceeded the threshold H or not herefore, the numerator in (27) can be expressed as P r (ψ m > H H 1 ) { lim ( 1 D = D )= 1 D, { lim { ( 0 D D )=0, c n ψ m > H } Otherwise } } he denominator term in (27) can be expressed as (28) P r (H 1 ) = lim ( 1 D D ) (29) Substituting (26) and (27) into (25), P D (m=1) = P r (ψ m > H H 1 ) P r (H 1 ) ={ 1, ψ m > H 0, otherwise } Running the experiment j number of times, P D (m=1) = lim ( { 1, ψm> H j j j n=1 0, otherwise } n (30) ) (31) he results of simulation (theoretical and empirical operating curves) for the proposed system have been plotted (in Figure 3) at E c / = 15dB he red dashed line is the theoretical simulation obtained by evaluating (22) he detection and false alarm probabilities (P D and P F ) are not independent; that is, a lower threshold increases P D but also increases P F hevalueof 15 db is chosen to represent worse E c / due to high traffic he synchronization of the proposed scheme is analyzed with four different groups of users he operating curves for = [2, 3, 4] cases are obtained taking into account the terms ( k=1 l=1 V kl B Ck )A cos φ and ( k=1 l=1 V kl B Ck )A sin φ in r 11 and r 12,respectively he simulation parameters are shown in able 1 5 Conclusions and Future Scope A highly secure and high capacity grouped scheme is proposedforthecdmasystemthataccommodatesahigher P D Receiver operating curves for BCC-CDMA at E c / = 15dB Empirical: =1, 2, 3, 4 heoretical: =1 Figure 3: Receiver operating curves for multigroup synchronization in BCC-CDMA able 1: Simulation parameters for the proposed multigroup synchronization scheme System parameters Values Message length bits Spreading length 31 bits roups, 30 E c / 15 db Collaborating users, [1,2,3,4] otal number of users, K [30, 60, 90, 120] number of full-rate users than the conventional multiuser CDMA schemes In the proposed scheme, a certain number of users are grouped together that collaborate by sharing orthogonal chaotic-spreading sequences generated by 1D chaotic map For example, using chaotic sequences of length 31, the proposed scheme supports 120 full-rate users compared to 90 and 30 users supported by collaborative CDMA and the conventional CDMA, respectively Multigroupsynchronizationisthenachievedusingachaoticpilot sequence, which is modulated by all ones, generated from the same chaotic map he simulations show that the multiple groups can be synchronized with a probability of detection of more than 85% Investigations on channel estimation in the proposed scheme are of practical importance Also, the attractive properties of chaotic sequences may lead to the implementation of three-dimensional (3D) chaotic maps and can be considered for future research Competing Interests he authors declare that they have no competing interests P F

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