CDMA. Performance Analysis of Chaotic Spread Spectrum CDMA Systems. LI Xiao - chao, GUO Dong - hui, ZENG Quan, WU Bo - xi RESEARCH & DEVELOPMENT

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1 RESEARCH & DEVELOPME X(2003) CDMA Ξ,, (, 36005), roecker Delta, CDMA, DS - CDMA, CDMA, CDMA CDMA, CDMA, Gold asami DS - CDMA CDMA ; ; ; ;O45. 5 A Performace Aalysis of Chaotic Spread Spectrum CDMA Systems LI Xiao - chao, GUO Dog - hui, ZEG Qua, WU Bo - xi (Departmet of Physics, Xiame Uiversity, Xiame 36005,Chia) Abstract Chaotic sequece is cosidered as a good cadidate for spread spectrum sequece i CDMA systems because it is characterized by good radomess, roecker Delta autocorrelatio ad orthogoal crosscorrelatio. hrough asychroous CDMA system model, the authors aalyze the key poits of chaotic spread spectrum CD2 MA system performaces,choose Chebyshev map to istatiate the virtue of chaotic sequeces ad compare with the classic Gold ad asami sequeces. ey words Asychroous CDMA ;Chaotic sequece ;Direct sequece spread spectrum ;Chebyshev map,,, CDMA 3, DS - CDMA,, [ CD2 ] MA(DS - CDMA),, 2 DS - CDMA,, [2, ],, DS - CDMA Ξ ( ) ; (A00009) ; 3

2 RESEARCH & DEVELOPME,,,, CD2 [36 MA ] DS - CDMA CDMA, DS - CDMA DS - CDMA, CDMA [7 ], DS - CDMA Gold asami DS - CDMA DS - CDMA DS - CDMA DS - CDMA - c k, k = mod( k,), 0 Φ k < [7 ], (t) r (t), t =,a k (t) b k (t),a j (k) k Z i = j, c ; b k, l k l, a k (t) = / C, a (k) 0,a (k),,a (k) + - ( t) a i ( t) cos c tdt (3) 0 i i = 0, i = a k (t) b k (t), 0,< i = 0,i PS,k k ( t) = 2 Psi ( c t + k + ( / 2) a k ( t) b k ( t) ) = 2 Pa k ( t) b k ( t) cos ( c t + k ) () + b, k,0 ^R k, i ( k, r( t) = ( t) + k = 2 Pa k ( t - k ) b k ( t - k ) cos ( c t + < k ) (2), (t) 0 / 2,< k = 4 k k k = P/ 2 a k ( t - k ) b k ( t - k ) a i ( t) 0 ( cos (2 c t + < k ) + cos< k ) dt Z i = P/ 2{ b i,0 + k =, k i [ b k, - R k, i ( k ) ] cos< k } + k ) ( t) a i ( t) cos c tdt 0 (4) R k,j () = 0 a k ( t - ) a i ( t ) dt, ^R k,j ( ) = 0a k (t - ) a i (t) dt = l c +,0 Φ< c,r k,i ( k ) ^R k,i ( k ) [8 C ] k,i, R k, i ( ) = C k, j (L - ) ( c - )

3 RESEARCH & DEVELOPME + C k, i ( l + - ) ^R k, i ( ) = C k, i (l) ( c - ) + C k, j ( l + ) (5), Z i k, k < k b k, - DS - CDMA b k,0 C k,i,m, 2. DS - CDMA, (5) m b k,0 = +,i Gold asami [8 ] m P/ 2, < k k, DS - CDMA [0,2] [0,] (k i),b k,l + -, i, [7 ] Var{ Z i } = P2 2 3 [2 C 2 k, i ( l) k =, k i l =- + C k, i ( l) C k, i ( l + ) ] SR i = { k =, k i l =- (6) [2C k, i 2 (l) + C k, i ( l) C k, i ( l + ) ] P } - / 2 (7) [3 C ] k,i C x,y ( l ) C x,y ( l + ) l = - = C x,x ( l ) C y,y ( l + ) l =- SR i = { 6 3 k =, k i {2 C k (0) C i (0) + 4 C k ( l) C i ( l) + l = l =0 [ C k ( l) C i ( l + ) + C k ( l + ) C i ( l) ]} P } - / 2 (8) C k C i, 3 [9 ],(4) 2 Lyapuov, (p 50, 0 000) (2) p Ε 2, i Pe [2 ],, Pe = Q ( SR i ) = - ( SR i ) (9) Birkhoff (3), [0 ]. (Chebyshev Map), x + = p ( x ) = cos ( pcos - x ), - Φ x Φ (),p () p Ε 2, Lyapuov [2 ] ( 2 ),, [ -, ] x 0 5

4 RESEARCH & DEVELOPME i ( x) j ( x)( x) dx = + i,0 i, j - 2,(x) = / ( - x 2 ), i,j =,i = j 0,i j o l = 0,,2,,, r = 2 3 (7) (4) ( A) ( l) = P ( x j ) q ( x j + l ) j = = t p ( + x) q ( x)( x) dx = - 2 ( l) (3) ],r = 2 3, p (x), p ( x j + ) = cos ( pcos - ( cos ( pcos - ( x j ) ) ) ) 3 = cos(p 2 cos - (x j ) ) = p2 (x j ) (5), p, q ( l) = j = p ( x j ) q ( x j + l ) = i p ( + x) q ( x)( x) dx - = 0 p q l + 2 p = ql + (4) - Φ x Φ, b l ( x) {0,} (9) DS - CDMA 2. 2 (8), i -, 0 / P, r = e, 0 x < c ( 2 A ) 2 A = 6 3 {2 C k (0) C i (0) + 4 k =, k i l = C k ( l) C i ( l) + [ C k ( l) C i ( l + ) + C k ( l + ) C i ( l) ] l =0 (5), 0 %,C i ( l ) C k ( l ) C ( l ) i,k, l A 2 = - 6 [2 + 4 l = C 2 ( l) + 2 l =0 C( l) C( l + ) ] (6), 9 2 A / 9C(l) = 0, 2 A (2),(x) C ( l) = ( - ) l r l - - r - l r - - r, [3 ], y j = A G( x j) (8) G(x) = d j pj (x) = ( - r) j pj (x),x [ -, j = j =,, [5 ],, x = 0, b ( x) b 2 ( x) b l ( x) b m ( x), i b i ( x) = c = ( - ) r- r ( x), 2 i x Ε c (c Ε 0) x 0 p (x), m {b i ( p (x) ) } = 0 3 (a) (b) i = 5 i = 5 i = 6, Gold asami,,, 6

2003 6 RESEARCH & DEVELOPME 3 i = 5 i = 5 6 DS - CDMA, DS - CDMA Gold asami DS - CDMA asami 5 = 63,8 E

5 RESEARCH & DEVELOPME 3 i = 5 i = 5 6 DS - CDMA, DS - CDMA Gold asami DS - CDMA asami 5 = 63,8 E b / 0, 6 E b / 0 = 22 db 8 30,, 4 = 3,9 E b / 0 = P/ 0, C(0) = 4 3, Gold, Gold,, 6 = db, 5 63, 7

6 RESEARCH & DEVELOPME, C( l) / A = I A G( x i ) G( x i + l ) i = l, = - l, Gold A m = 0 %5 % DS - CDMA, [ ] Esmael H,Dia,Bija Jabbari. Spreadig codes for direct se2 quece CDMA ad widebad CDMA cellular etworks [J ]., roecker Delta IEEE Commuicatios Magazie,998,(9)., DS - CDMA [2 ] Heiz Georg Schuster. Determiistic Chaos A Itroductio [M]. Physik - Verlag,984. [3 ] Chi - Chug Che, ug Yao, e Umeo,et al. Optimal, chaotic spread spectrum sequeces for uplik CDMA systems Gold asami () ; (2) [4 ] ohda, A sueda, Sakae. Chaotic biary sequeces by Chebyshev maps ad their correlatio properties [ A ]. IEEE, 3G secod iteratioal symposium o spread spectrum techiques ; (3), ad applicatios[ C]. Japa, 992. [5 ] ohda,a. sueda. Eve ad odd correlatio fuctios of chaotic Chebyshev bit sequeces for CDMA[A]. IEEE[C]. 994., [6 ],C [J ].,2002,42(6) [7 ] M B Pursley. Performace Evaluatio for Phase - Coded Spread - A Spectrum Multiple - Access Commuicatio - Part I System C ( l ) Aalysis[J ]. IEEE ras. Commuicatios, 977, = ( - ) l r l - - r r - - r, l = 0,,2,,,r = 2 3 [8 ] Dilip V Sarwate, Michael B Pursley Crosscorrelatio proper2 ties of pseudoradom ad related sequeces [J ]. Proc. of the CDMA IEEE,980,68(5) [9 ] Jhog Sam Lee,Leoard E Miller. CDMA y j = A G(x j),,g(x) = d j pj (x) = ( - r) j pj (x),x [M].,200. j = I j = [0 ] Yao. Error probablity of asychroous spread spectrum [ -, ],r = 2 3, p (x) multiple access commuicatio systems [ J ]. IEEE ras. C(0) Commuicatios,977, C(0) = G 2 ( x i )= [ ] M B Pursley. Evaluatig performace of codes for spread i = - G2 ( x) ( dx spectrum multiple access commuicatios[ A ]. Proc. of the = j = - d 2 j j2 p ( x) ( dx = 2 2 d j j = j = (- r) 2j = ( - r 2 ) 2 r2 - r 2 = A d m d m + l - p m+2 ( x)( x) dx = ( - ) l r l - - r - l r - - r ( A. 2), ( ) [A]. IEEE[ C] welfth Aual Allerto Coferece o Circuit ad System heory,974[ C] [2 ] R L Adler, J Rivli. Ergodic ad mixig properties of Chebyshev polyomials [ A ]. Proc. America Math. Soc. (vol. 5) [ C] (A.) C(0), (970 - ),, ( 8 )

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