A NOVEL CHAOS BASED MODULATION SCHEME (CS-QCSK) WITH IMPROVED BER PERFORMANCE

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1 A NOVEL CHAOS BASED MODULATION SCHEME (CS-QCSK) WITH IMPROVED PERFORMANCE K.Thilagam 1 and K.Jayanthi 1 Researh Sholar, Department of ECE, Pondiherry Engg. College, Puduherry, India thilagam.k@pe.edu Assoiate Professor, Department of ECE, Pondiherry Engg. College, Puduherry, India jayanthi@pe.edu ABSTRACT In reent years, various haos based modulation shemes were evolved, of whih the CS-DCSK modulation tehnique provides better performane and bandwidth effiieny, due to its ode domain approah. The QCSK modulation tehnique provides double benefit: higher data rate with similar performane and same bandwidth oupation as DCSK. By ombining the advantage of ode shifted differential haos shift keying (CS-DCSK) and Quadrature haos shift keying (QCSK) sheme, a novel CS-QCSK modulation sheme alled ode shifted Quadrature haos shift keying is proposed. The noise performane of CS-QCSK is better to most onventional modulation shemes and also provides an inreased data transmission rates with greatly improved robustness. Analytial expressions for the bit-error rates are derived for both AWGN hannel and Rayleigh multipath fading hannel. The simulation result shows that the proposed method outperforms lassial haoti modulation shemes in terms of bit error rate (). KEYWORDS Differential haos shift keying (DCSK) ; Quadrature haos shift keying (QCSK); Code shifted differential haos shift keying (CS-DCSK); ode shifted Quadrature haos shift keying ( CS- QCSK); Bit Error Rate(). 1. INTRODUCTION In the last few years, a great researh effort has been devoted, onerning haoti arrier modulation. In ontrary to the onventional modulation shemes, a wideband, non-periodi haoti signal is used as arrier, whih results in good orrelation harateristis and robustness against multipath fading effets. The basi onept of haos based modulation tehniques for oherent and non-oherent systems have been analyzed and studied in [1] &[]. For a oherent system, the reeiver needs an exat replia of the haoti signal, suh robust synhronization tehniques are still not realizable in a pratial environment [3].It is worth mentioning the evolution of various types haos based modulation shemes and their signifiane and this setion is devoted for summarizing the literature survey/ researh findings of suh shemes. The DCSK sheme, disussed in [4] represents a more robust non-oherent sheme, in whih the exat knowledge of the haoti basis funtions is not needed at the reeiver. To further enhane the DCSK sheme, frequeny-modulated DCSK (FM-DCSK) was introdued to overome the Sundarapandian et al. (Eds): CoNeCo,WiMo, NLP, CRYPSIS, ICAIT, ICDIP, ITCSE, CS & IT 7, pp , 1. CS & IT-CSCP 1 DOI : 1.511/sit.1.46

2 46 Computer Siene & Information Tehnology ( CS & IT ) varying bit-energy problem in DCSK, whih is very well explored in [5], [6]. The study of multipath performane of the frequeny-modulated DCSK (FM-DCSK) system is analyzed in [8],[1]. The analysis was simulation based and the path that suffers from random fading, to be inorporated in the hannel model was assumed an ideal onstant gain value. In [7], the role of synhronization in digital ommuniations using haos was disussed. At reeiver, the two piees of haoti signals are orrelated, then the binary symbol is deoded based on the sign of the orrelator output. The DCSK ommuniation sheme, whih exploit the repetitive nature of the haoti signal, extending from simple binary ommuniations to more sophistiated detetors, have been disussed [8]. Multipath performane of binary DCSK systems using a standard orrelation detetor was disussed in [9]-[1]. Quadrature CSK (QCSK) is a multilevel version of DCSK, based on the generation of an orthogonal of haoti funtions. It allows an inrease in data rate oupying same bandwidth with respet to DCSK [11]. In [13],[18] the performane of the DCSK system over a hannel with Rayleigh fading or Riean fading was disussed with the neessity to model the effets of multipath delay spread as well as fading. A multiple-aess tehnique with differential haos shift keying using a one dimensional iterative map to generate the haoti signals for all users and similar average data rates for the users have been disussed [14]-[15],[19]. In [16] FM-QCSK disusses the generation of inherent wideband signal with onstant energy per bit, whih an be ahieved by using the ombination of frequeny modulation with QCSK. The high-level onstellation in FM-QACSK whih an improve the speed of haos shift keying is examined in [17].The ultra wide band systems based on DCSK and FM-DCSK shemes and the implementation in both analogy and digital tehnology is disussed in [].The DCSK system inorporated with two-user ooperative diversity tehnique and multiple aessing is adopted and disussed in[1] as a result exellent rossorrelation harateristis of Walsh ode sequenes is obtained. CS-DCSK uses ode domain approah, the referene and the information bearing signals are transmitted at the same time slots, it offers better performane and bandwidth effiieny, as disussed in []. In this paper, a novel CS-QCSK modulation sheme is proposed, whih is the ombination of CS-DCSK and QCSK modulation shemes. In addition to high data rates, it offers the advantage of both the CS- DCSK and QCSK shemes [], [11]. The remaining part of the paper is organized as follows: In setion, the proposed system model and problem formulation is desribed. Setion 3, elaborates the analytial derivation for different hannel onditions. Simulation results are disussed in Setion 4. Setion 5, deals with the onlusion of the paper.. OVERVIEW ON CHAOS BASED MODULATION SCHEMES In order to explain the CS-QCSK system, a brief introdution to DCSK, QCSK and CS-DCSK methods is essential and details are given in this setion..1. Differential Chaos Shift Keying (DCSK) In DCSK system, for eah symbol period two haoti sample funtions are used to represent, one bit of information. The transmitted DCSK signal has two parts, the first part of the signal is referene signals, while the seond denotes the information-bearing signals. If the bit 1 is to transmitted, then the information bearing signal is the replia of the referene part. If the bit is to be transmitted, then the information bearing signal is the inverted opy of the referene part. The i-th symbol an be represented as, S D C SK ( t ) T x ( t ) t i t < ( ti + ) = + T x (t T / ) ( ti + ) t < ( ti + T ) (1)

3 Computer Siene & Information Tehnology ( CS & IT ) 47 where, T is the symbol duration. In the reeiver, the original information is extrated by omputing the orrelation between two reeived sample funtions. The output of the orrelator is sampled over eah symbol period and the output is finally given to the deision devie to determine the binary values 1 s or s... Quadrature Chaos Shift Keying (QCSK) Similar to DCSK method, eah symbol period of QCSK also has two parts, but the modifiation is, information-bearing signals holds two bits of information by means of quadrature haos shift keying tehnique. Sine two bits of information are transmitted, it is possible for QCSK sheme to obtain higher data rate. Quadrature haoti signals are produed by an orthonormal basis haoti sample funtions x(t) and y(t). Let, x(t) be the haoti referene signal, assuming that the signal x has zero mean value and is defined as x ( t ) = f k s in ( k ω t + ϕ k ) () k = 1 and y(t) be the quadrature haoti referene signal, obtained by hanging the phase of eah fourier frequeny omponent by π/, and is defined as, y ( t ) = f k sin( kω t + ϕ k π / ) (3) k = 1 The signals x(t) and y(t) are orthogonal in the interval I t = [,t] and is defined as, τ x y x ( t ) y ( t ) d t = (4) The transmitted QCSK signal is given by, S QCSK ( t) T E x ( t ) < t < b = T E (a1x ( t T / ) + a y (t T / )) t < T b where E b is the bit energy over T / period, satisfying the orthogonal relations. C x (t-t/) is haoti signal with duration T/ and C y (t-t/) is haoti signal orthogonal to C x (t-t/) with duration T/. (5).3. Code Shifted - Differential Chaos Shift Keying (CS-DCSK) In DCSK, the referene and the information bearing signals are transmitted in two onseutive time slots beause of its TDMA approah. This time domain approah provides two independent hannels for the transmission of referene and information bearing signals. With this, it requires a delay omponent both in the modulator and demodulator iruits and halves the data rate. To overome this drawbak, an alternative approah used is CS-DCSK, where both the referene and the information bearing signals are transmitted in the same time slot beause of its ode domain approah (i.e) the two signals are separated by walsh odes instead of time delay. The transmitted CS-DCSK signal is given by, N 1 N 1 = + ( ) + + ( ) = (6) S t W C t kt a W C t kt T NT b R,k 1 I,k 1 S C k = k =

4 48 Computer Siene & Information Tehnology ( CS & IT ) Where, W R,k+1 is the referene signal,w I,k+1 is the information signal,c(t-kt ) is the haoti signal, T s is the symbol duration and T is the hip duration. The limitation of this system is, with the inreased omplexity the Bit Error Rate obtained by this system is more or less similar when ompared with the existing system..4. System Model of CS-QCSK Modulation The aim of this setion is to illustrate the pratial importane of CS-QCSK modulation sheme, whose simplified transmitter and reeiver blok diagram are shown in figure.1and figure. respetively. A baseband system is onsidered for simpliity. But it is understood, that if the sheme is to be employed for wireless ommuniations a modulator is in need to generate the orresponding RF passband signal. Furthermore, it is assumed that the desription of the CS- QCSK sheme in the ontinuous-time domain admits an equivalent disrete-time representation. It disussed in the above, briefly about the advantage of CS-DCSK and QCSK shemes, by ombining these two tehniques a novel CS-QCSK modulation sheme an be arrived at Transmitter In CS-QCSK, the symbol S is transmitted with the referene signal and information signal in the same time slot but separated by Walsh ode sequenes. The CS-QCSK transmitted signal is given by, N 1 N 1 N 1 (7) S t = W C t kt + a W C t kt + a W C t kt T = NT b R,k+ 1 x 1 I1,k + 1 x I,k+ 1 y S C k= k= k= Where a 1 Є {-1, 1}, a Є {-1, 1} is mapped from b Є {,1} whih is the information bit to be transmitted. This sheme uses different Walsh ode for the referene and information signal,where W R,k+1 represent the Walsh ode for referene signal and W I1,k+1, W I,k+1 represent the Walsh ode for information signal, C(t) is the haoti signal with duration of T. Both the referene and the information signal are transmitted in the same time slot as given in equation (7). The orthogonality of two signals are given by, x C t kt y t kt t < ( k + 1)T x = otherwise (7.a) C t kt Let, t kt t < ( k + 1)T y = otherwise (7.b) T s = NT N 1 N 1 N 1 = W C t kt a W C t kt a W C t kt. dt (8) R,k+ 1 x 1 I1,k + 1 x I,k+ 1 y k = k = k = T s Eb = ( t) y ( t). dt (8.a) T (.) = Transporse of vetor.

5 t = C t kt ; k x x t C t kt ; y = y k Computer Siene & Information Tehnology ( CS & IT ) 49 The orthogonality of the signal is assured by walsh ode sequenes, therefore the referene and the information signal are independent of the haoti arrier. (8.b) (8.) Figure.1 Blok diagram of CS-QCSK Transmitter Referring to the above transmitter blok diagram, the CS-QCSK modulation sheme onsist of haos signalgenerator,whih generates haos signal C x (t) and its orthogonal signal C y (t).the orthogonal signal is obtained by taking the Hilbert transform of the haos signal C x (t). The transmitter blok onsists of three Walsh funtion generator, whih generates three different Walsh ode sequenes that are orthogonal in nature. It has (N-1) delay elements of T hip duration. The three Walsh funtion generator, generate Walsh odes, W R,k+1 for referene signal, and W I1,k+1, W I,k+1 for information signal. The referene signal of Walsh ode W R,k+1 is multiplied with the haos signal and the orresponding output is obtained by the swithing unit S1.It has a bit splitter, whih splits the input bit stream into odd and even sequenes. The information signal of Walsh ode WI1,k +1 is multiplied with the odd sequene of bits and the haos signal,the orresponding output is obtained by the swithing unit S. The information signal of Walsh ode W I,k+1 is multiplied with the even sequene of bits and the orthogonal haos signal, the orresponding output is obtained by the swithing unit S 3.The output obtained at the swithing unit S and S 3 are summed and it is further summed with the swithing unit S1 to obtain the final output. The CS-QCSK signal is finally obtained.

6 5 Computer Siene & Information Tehnology ( CS & IT ).4.. Reeiver ~ r Figure. Blok diagram of CS-QCSK Reeiver The above Figure. shows the blok diagram of CS-QCSK reeiver. The reeiver unit onsists of band pass filter with the bandwidth of B whih an pass the reeived signal r(t) without any distortion. The reeiver filter output with Additive White Gaussian Noise (AWGN) n(t) is obtained as, N 1 N 1 N 1 R,k+ 1 x ( ) 1 I1,k + 1 x ( ) I,k+ 1 y ( ) (9) ( t) = W C t kt + a W C t kt + a W C t kt + n(t) k= k= k= x ret t kt y 1, kt t < ( k + 1)T, otherwise = (9.a) ret t kt 1, kt t < ( k + 1)T, otherwise = (9.b) The reeiver filter output is further given to the three mixer unit M1,M and M3.In the mixer unit the filter output signal is multiplied by a retangular funtion weighted by the three Walsh ode sequenes. The transmitted signal is of Walsh odes inorporated with three terms. In order to obtain those terms A, B and C the reeiver filter output is multiplied by a retangular funtion. The output of M1, M and M3 is multiplied to obtain the signal ABC. The multiplier output is then given to the integrator unit to obtain the observation signal. The integrator output is given to the hard deision devie, where the bits are estimated by the deision rule. Using walsh ode, the transmitted signal is inorporated with three terms A, B and C. The three terms A, B and C an be obtained by multiplying equation (7) that orresponds to referene signal and information signals respetively. The terms X, Y and Z in the reeiver blok are X=W ret t kt Where, R,k+ 1 x Y=W + ret t kt, I1,k 1 x Z=WI,k + 1ret y t kt, N 1 R,k+ 1 x (1) k = A = S t W ret t kt.

7 Computer Siene & Information Tehnology ( CS & IT ) 51 N 1 I1,k + 1 x (11) k = B = S t W ret t kt N 1 I,k+ 1 y (1) k = C = S t W ret t kt Ts = NT Z = ABC. dt (13) Substituting, equation (7) in (1),(11)and(1). The equations (14), (15) and (16) are obtained. N 1 N 1 N 1 x ( ) 1 R,k+ 1 I1,k + 1 x ( ) R,k+ 1 I,k+ 1 y ( ) (14) A = C t kt + a W W C t kt + a W W C t kt k= k= k= N 1 N 1 R,k+ 1 I1,k + 1 x ( ) 1 x ( ) (15) B = W W C t kt + a C t kt k= k= N 1 N 1 R,k+ 1 I,k+ 1 x ( ) y ( ) (16) C = W W C t kt + a C t kt k= k= Substituting equation (14), (15) and (16) in (13) T s = NT N 1 N 1 N 1 Z = C x ( t kt ) + a1 W W C R,k 1 I1,k 1 x ( t kt ) + a W W C R,k 1 I,k 1 y ( t kt ) k= k= k= N 1 N 1 N 1 N 1 ( ) + ( ) ( ) + ( ) W W C t kt a C t kt W W C t kt a C t kt dt R,k+ 1 I1,k + 1 x 1 x R,k+ 1 I,k+ 1 x y k= k= k= k= The above equation (17) an be simplified as, Z a a E (18) 1 b 3. ANALYTICAL DERIVATION OF UNDER VARYING CHANNELS The analytial expression for the of CS-QCSK over AWGN and the multipath Rayleigh fading hannels are derived in the following setion Additive White Gaussian Noise (AWGN) Channel From the reeiver unit, the observation variable obtained is given by ( + ) N 1 k 1 T (17) ~ ~ R,k 1 ( t ) + I1,k 1 I,k 1 ( t) r + + r (19) Z = W. W W. dt k = kt N 1 ( + ) k 1 T W W W ( W a W a W R,k 1 I1,k 1 I,k 1 R,k 1 1 I1,k 1 I,k 1) ( t kt ) n( t)]. dt () = k= kt

8 5 Computer Siene & Information Tehnology ( CS & IT ) There are different types of haoti maps to generate the haoti signals, they are lassified as (i)logisti map (ii) ubi map (iii) Bernoulli-shift map. In the proposed method, logisti map is onsidered and is defined as, x (n+1) = 1-x (n).where, β =T f s is the number of samples in a hip time and K=T s f s =N β is the symbol duration. In the remaining part of the paper, K is referred as the spreading fator. Consider, the transmission of a1=a=+1 sequene. The logisti map is defined in the ontinuous time domain. In order to onvert into the disrete time domain, onsider C j be the samples of haoti signal and η j be the hannel noise. Then, the equation for disrete time equivalent is given as, N 1 β W W W R,k 1 I1,k 1 I,k 1 ( W a W a W R,k 1 1 I1,k 1 I,k 1). k m η k + m (1) Z = + + β + β Where, kβ + m k= m= 1 m, κβ κβ + m < ( k + 1) β =, otherwise From the equation (1),the deision variable is deomposed into three terms, where, Z () Z = Z A + Z B + ZC (3) N 1 β WR,k 1WI1,k 1W I,k 1 ( WR,k 1 a1wi1,k 1 awi,k 1) β + ) (4) = + + A k m k= m= 1 N 1 β W R,k+ 1WI1,k + 1WI,k + 1 ( WR,k + 1 a1w I1,k + 1 aw I,k+ 1) ( + )( η + ) (5) Z = + + β β Z B k m k m k= m= 1 ( N 1 β = WR,k + 1WI1,k + 1WI,k + 1 β + ) (6) C k m k= m= 1 By applying, Expetation and Variane to the above equations, (4), (5) and (6) the expetation and variane values of these variables are obtained as, { } { } { A 1 A 1 3 β j } E Z b = = E Z a = + = N E C (7) { } { } E Z b = 1 = E Z a = + 1 = (8) B { } { } B E Z b = 1 = E Z a = + 1 = (9) C C { } { } { A 1 A 1 3 β j } Var Z b= = Var Z a =+ = N Var C (3) { } { } { B 1 B 1 β j} Var Z b= = Var Z a=+ = N NVar C (31) { 1 } { 1} β Var Z b = = Var Z a = + = N N (3) C C Where, E{.} represents the expetation operator and var{.} represents the variane operator,then { 1 } { 1} 3 β { j } E Z b = = E Z a = + = N E C (33) (.

9 Computer Siene & Information Tehnology ( CS & IT ) 53 { 1 } { 1} 3 { j } { j } Var Z b= = Var Z a =+ = NβVar C + NβN Var C + NβN (34) For the transmission of a 1 =a = -1 sequene, the expetation and variane of observation variable is derived similarly. { 1 } E{ Z a 1} E Z a = = = + (35) { 1 } Var{ Z a 1} Var Z a = = = + (36) It is assumed, that the probability distribution of the observation variable an be approximated by gaussian approximation and the transmitted bits are equiprobable. Therefore, the bit error rate of CS-QCSK modulation sheme is obtained as, 1 1 = Pr( Zm < b = 1) + Pr( Zm b = ) (37) 1 1 = Pr( Zm < a = + 1) + Pr( Zm a = 1) { m a = + 1} { a = + } 1 E Z = erf Var Zm 1 Where, m=; represents the number of information bits transmitted per time slot.for logisti E C = 1/ and variane of haos signal is maps, the expetation of haos signal is { j } { j } 1/ 8 Var C = and therefore equation (37) beomes, 1 3N β E { C j } = erf ( 3N βvar { C j } + N β N Var { C } ) j + N β N C S Q C SK 1 3 ( E b / N ) = erf 3 1 K + K + E b / N Rayleigh Multipath Fading Channel Considering the rayleigh multipath fading hannels, the reeived signal is denoted as r ( t) = h( t) x( t ) + n( t) (39) and the hannel impulse response is given as h t L 1 l= (38) = αlδ ( l η) (4) Where, L is the number of propagation paths, α l gain of the lth path, τl is the delay of the l th path and δ(t) denotes the dira delta funtion. The gains α l of the propagation paths are assumed to be independent idential distributed Rayleigh random variables. The measured in Rayleigh multipath hannel is an approximation developed from the noise performane of AWGN hannel. The onditional measured for the multipath is given by,

10 54 Computer Siene & Information Tehnology ( CS & IT ) (α, α 1 α L-1 ) = (γ b ) (41) Where, γ b = (E b /N o ) (α, α 1 α L-1 ) = ( γ + γ γ L-1 ) The probability density funtion (PDF)of γ i is an exponential distribution given by, f ( x) 1 x = exp (4) γ γ k The probability density funtion (pdf) of γ b is obtained as, = f γ f γ f γ. f γ L b 1 1 k Where, f(γ k ) is the pdf of instantaneous (SNR) measured in the ith path. By averaging the onditional bit error rates in the multipath hannels, the total measured is obtained as, = γ f γ dγ (44) b b b In this paper, it is assumed to have two multipath hannels with three propagation paths, then the error rate expressions are CS QCSK 1 3( γ b ) = erf 3 1 K + K + 4 ( γ ) In order to validate the analytial approah of the proposed sheme, an attempt is made through simulations. The next setion presents the simulation analysis of the proposed sheme and it is finally ompared with the analytial results. 4. SIMULATION ANALYSIS The performanes of CS-QCSK modulation shemes for different hannel onditions are also analyzed through Matlab simulation. Simulation parameters taken for the analysis are hip duration(t)=milliseond,symbol duration(ts)= miro seond, transmission power(p)=43dbm, noise power spetral density(no)=1,spread fator(k)=4, the hannel types are AWGN and Rayleigh. Firstly, the performane of AWGN hannel is disussed, followed by multipath Rayleigh fading hannel Performane over AWGN Channel b (43) (45) Theoretial Simulated Eb/No (db) Figure. 3 performane of CS-QCSK modulation sheme for AWGN hannel.

11 Computer Siene & Information Tehnology ( CS & IT ) 55 From the figure.3, it is inferred that performane of CS-QCSK sheme is plotted with the theoretial and simulated values.the values alulated from the analytial expression and the simulation are very similar and both the graph merge with eah other.for the value of 1-6, the required (Eb/No) value is 1dB(approximately) k A =4 k A =6 k A = Eb/No Figure.4 performane of the CS-QCSK modulation sheme over AWGN hannel for various spread fator. performane of CS-QCSK modulation sheme for various spreading fators (K=4, K=8,K=1) were plotted. It is inferred from the above graph that, as the K value inreases the noise performane beome worse. In general, smaller Spreading fator orresponds to minimum noise level. Therefore, for smaller values of K the performane is better DCSK QCSK CS-DCSK CS-QCSK Eb/No(dB) Figure. 5 performane omparison for different modulation shemes with CS- QCSK modulation sheme Over AWGN hannel. In the above graph, the performane of different modulation shemes were ompared. For the value of 1-1, the required Eb/No value for CS-DCSK, DCSK, QCSK and CS-QCSK is 18.4 db, 17.8dB,17.dB and 1.dB respetively. On inferring these Eb/No values, the performane of proposed CS-QCSK modulation sheme is better ompared to the DCSK, CS- DCSK and QCSK modulation shemes.

12 56 Computer Siene & Information Tehnology ( CS & IT ) 4.. Performane over Rayleigh Multipath Channel Theoretial Simulated Eb/No (db) Figure. 6 performane of CS-QCSK modulation sheme for Rayleigh multipath hannel. From the above figure, it is inferred that performane of CS-QCSK sheme is plotted with the theoretial and simulated values.the values alulated from the analytial expression and the simulation are very similar and both the graph merge with eah other.for the value of 1-6, the required (Eb/No) value is13.1db(approximately) k R =4 k R =6 k R = Eb/No Figure.7 performane of the CS-QCSK modulation sheme over Rayleigh hannel for various spread fator. performane of CS-QCSK modulation sheme for various spreading fators (K=4, K=8,K=1) were plotted. It is inferred from the above graph that, as the K value inreases the noise performane beome worse. In general, smaller Spreading fator orresponds to minimum noise level. Therefore, for smaller values of K the performane is better.

13 Computer Siene & Information Tehnology ( CS & IT ) DCSK QCSK CS-DCSK CS-QCSK Eb/No(dB) Figure. 8 performane omparison for different modulation shemes with CS- QCSK modulation sheme Over AWGN hannel. In the above graph, the performane of different modulation shemes were ompared. For the value of 1-1, the required Eb/No value for CS-DCSK,DCSK,QCSK and CS-QCSK is 18.8 db,18db,17.4db and 13.1dB respetively. On inferring these Eb/No values, the performane of proposed CS-QCSK modulation sheme is better ompared to the DCSK, CS- DCSK and QCSK modulation shemes Spread fator Figure. 9 Effet of spreading fator on performane of the CS-QCSK modulation sheme. Eb/No has been fixed at 1 db. is plotted against the spreading fator by fixing Eb / No at 1 db.it is inferred that, larger the spreading fator, worse the performane. 5. CONCLUSION In the field of haos-based ommuniation, M-ary DCSK sheme seems to be the best known modulation sheme. But, the drawbak is, it requires (N-1) number of of delay lines both in the transmitter and the reeiver units. In this paper, an improved haos-based ommuniation method

14 58 Computer Siene & Information Tehnology ( CS & IT ) using CS-QCSK tehnique is reommended. The proposed CS-QCSK sheme, avoids the use of delay lines in the reeiver units. It transmits the referene and information signals in the same time slot and offers an inrease in data rate, better performane and bandwidth effiieny. The performane of the proposed modulation sheme is analyzed in ontext of AWGN and multipath hannels. Analytial expressions for of CS-QCSK are derived and verified with matlab simulation. Simulation results, shows that the CS-QCSK has better performane in AWGN and Rayleigh fading hannels, when ompared with the onventional modulation shemes. This proves the suitability of the proposed modulation tehnique for a mobile radio senario, whih is the need of the hour. REFERENCES [1] Abel and W. Shwarz, Chaos ommuniations Priniples, shemes, and system analysis, Pro. IEEE,vol. 9,pp , May [] G. Kolumbán, M. P. Kennedy, Z. Jako, and G. Kis, Chaoti ommuniations with orrelator reeivers: Theory andperformane limits, Pro.IEEE, vol. 9, pp , May. [3] H. Dedieu, M. P. Kennedy, and M. Hasler, Chaos shift keying: Modulation and demodulation of a haoti arrier using self-synhronizing Chua s iruits, IEEE Trans. Ciruits Syst. II, vol. 4, pp , Ot [4] G. Kolumbán, B. Vizvári,W. Shwarz, and A. Abel, Differential haos shift keying: A robust oding for haos ommuniation, Pro. Int.Workshop Nonlinear Dynamis of Eletroni Systems, pp. 87 9, June [5] G. Kolumbán, G. Kis, M. P. Kennedy, and Z. Jáko, FM-DCSK: A new and robust solution to haos ommuniations, in Pro., Int. Symp. Nonlinear Theory Appl., HI, 1997, pp [6] M. P. Kennedy and G. Kolumbán, Digital ommuniation using haos, in Controlling Chaos and Bifuration in Engineering Systems, G. Chen, Ed. Boa Raton, FL: CRC,, pp [7] G. Kolumbán and M. P. Kennedy, The role of synhronization in digital ommuniations using haos Part III:Performane bounds for orrelation reeivers, IEEE Trans. CiruitsSyst. I, Fundamental. Theory Appl.,vol. 47, no. 1, pp , De.. [8] G.Kolumban, Z. Jákó, and M. P.Kennedy, Enhaned versions of DCSK and FM-DCSK data transmissions systems, in Pro. IEEE ISCAS 99,vol. IV, Orlando, FL, May/Jun. 1999, pp [9] M. P. Kennedy, G. Kolumbán, G. Kis, and Z. Jákó, Performane evaluation of FM-DCSK modulation in multipath environments, IEEE Trans.Ciruits Syst. I, Fundam. Theory Appl., vol. 47, no. 1, pp , De.. [1] G. Kolumbán, Theoretial noise performane of orrelator-based haoti ommuniations shemes, IEEE Trans. Ciruits Syst. I, Fundam. Theory Appl., vol. 47, no. 1, pp , De.. [11] Z. Galias and G. M. Maggio, Quadrature haos-shift keying: Theory and performane analysis, IEEE Trans.Ciruits Syst. I, Fundam.Theory Appl., vol. 48, no. 1, pp , De. 1. [1] G. Kolumbán and G. Kis, Multipath performane of FM-DCSK haoti ommuniations system, in Pro. IEEE Int. Symp. Ciruits and Systems, Geneva, Switzerland, May, pp [13] S. Mandal and S. Banerjee, Performane of differential haos shift keying over multipath fading hannels, in Pro. Indian Nat. Conf. Nonlinear Systems and Dynamis, Kharagpur, India, De. 3. [14] G. Kolumbán, P. Kennedy, and G. Kis, Multilevel differential haos shift keying, in Pro. Int. Workshop, Nonlinear Dynamis of Eletronis Systems, NDES 97, Mosow, Russia, 1997, pp [15] F. C. M. Lau, M. M. Yip, C. K. Tse, and S. F. Hau, A Multiple-Aess Tehnique for Differential Chaos-Shift Keying IEEE Trans.Ciruits Syst. I, Fundam.Theory Appl., vol. 49, no. 1, January. [16] YiWei Zhang, Xubang Shen and Yi Ding, Design and performane analysis of an FM- QCSK haoti ommuniation system, International Conferene on Wireless Communiations, Networking and Mobile Computing, China, pp: 1-4, Sept. 6. [17] Jiamin Pan, He Zhang, Design of FM-QACSK Chaoti Communiation System IEEE trans. Wireless Communiations & Signal Proessing, 9. [18] Xia, Y.,Tse,C.K.& Lau, F.C.M, Performane of differential haos shift keying digital ommuniation systems over a multipath fading hannel with delay spread, IEEE Trans. Ciruits Syst.-II 51,68-684,4. [19] Yao,J.& Lawrane, A.J, Performane analysis and optimization of multi-user differential haosshift keying ommuniation systems, IEEE Trans.ir. Syst.-I 53, pp.75-91, 6.

15 Computer Siene & Information Tehnology ( CS & IT ) 59 [] Wang,L.,Zhang,C.& Chen, G. Performane of an SIMO FM-DCSK ommuniation system, IEEE Trans.Ciruits Syst.-II, 55, ,8. [1] Min,X.,Xu,W.,Wang, L. & Chen, G., Promising performane of an FM-DCSK UWB system under indoor environments, J. IET Commun. 4, pp , 1. [] G.Koluban,W.K.Xu and L.Wang, A Novel differential haos shift keying modulation sheme, International journal of Bifuration and haos,11,vol.1,no.3,pp Authors K.Jayanthi reeived B.E degree from University of Madras in 1997 and M.Teh degree in Eletronis and Communiation Engineering and Ph.D from Pondiherry University in 1999 and 7 respetively. She has 13years of experiene in teahing / researh. She is urrently serving as Assoiate Professor in Department of Eletronis and Communiation Engineering, Pondiherry Engineering College, Puduherry. To her redit, she has around 1 journal papers and presented 18 papers in International onferenes. Her other areas of interest inludes satellite ommuniation, Wireless multimedia networks, Spread spetrum ommuniation, Image proessing, et. She has authored a book on Qos Provisioning in Cellular Mobile Networks. K.Thilagam reeived her B.Teh and M.Teh degrees in Eletronis and Communiation Engineering from Pondiherry Engineering College in 4 and 7 respetively. She has 5 years of experiene in teahing /researh. She is urrently pursuing Ph.D in the area of Wireless Communiation. Her researh ativities are foussed on Cooperative Communiation in Cellular Networks, mainly on Modulation and oding tehniques,et