1 SS 2 2 (DS) 3 2.1 DS................................ 3 2.2 DS................................ 4 2.3.................................. 4 2.4 (channel papacity)............................ 6 2.5........................................ 7 2.6 E b /N.................................... 9 3 M 11 3.1................................... 11 3.2 M......................... 11 3.3 M........................... 13 3.4 M............................... 14 3.5 M.............................. 15 4 19 4.1................................ 19 4.2.................................... 19 4.3.................................... 21 5 23 23 C 25 1
1 SS, 1,, SS, SN, SS a) (Direct Spread: DS) SS (Pseudo Noise: PN) PN PN ( ) BPF b) (Frequency Hopping: FH) PN FSK FSK 2 FH c) (Time Hopping:TH) PN FH TFH d) 2 FH/DS TFH TH/DS 2
d(t) d(t)p(t) 1-1 Data d(t) PN sequence p(t) 1: DS 2 (DS),, BPF Shannon, SS, DS 2.1 DS DS, 2. (Peseudo Noise: PN). DS 1. PN, SS ( ). B, B p PN, 2 SS. 3
2B 2B p f SS f 2.2 DS 2: 1 3 SS PN Ad(t) p(t) (1) PN p(t) p(t) 1 1 p(t) 2 =1 Ad(t) p(t) 2 = Ad(t) (2) 2.3 I(t) (BPF) 4(A) PN SS SS SS 4(B) 4
BPF p(t) LPF d(t) PN 3: DS F [I(t)] F [d(t)] 2B p SS F [d(t)p(t)] f F [I(t)p(t)] 2B f F []: 4:. B PN B p. 5
2.4 (channel papacity) [[1] ] 6
2.5 [[2] ] P S = N W, (3) W (4.212) 7
8
Fig 5.2-17 Comparison of several modulation methods at 1 5 symbol error probability.[3] 2.6 E b /N n(t), 5 G(f)., G(f) N 2 f 5: G(f) 2. n(t) =x 9
S... T b t p W (x) ([4] p.29). 6: 1 E b p W (x) = 1 σ 2π e (x mx) 2 2σ (4) σ 2, m x n(t), m x =. ψ(t), n(t) ˆn, ˆn = Ts. σ 2 N, [4] pp.744 745 n(t)ψ(t)dt (5) σ 2 = E{ˆn} m x = N 2 (6) E{ }., 1 E b., E b., E b = Tb ( S) 2 dt = ST b (7) T b : S :, E b /N S/N, ([4] p.158). E b N = ST b N = S RN = SW RN W = S R 1 N/W (8) R = 1 T b ( ) W : (Hz) N :, N = N W 1
h =1 h 1 h 2 h 3 h k 1 h k =1 SR 1 SR 2 SR 3 SR k o 3 M 3.1 7: M SS,. 1),. 2),. 3),., SS (M )., M. 3.2 M M, 2 (Linear Feedback Shift Register : LFSR) n LFSR N =2 n 1. h(x) =h k X k + + h 3 X 3 + h 2 X 2 + h 1 X 1 + h, GF(2). LFSR h i (i =, 1, 2,,k), 7, h i 1., h(x) =X 4 + X +1 8, N =2 4 1=15 M., 1. M,, Peterson [5]. Peterson GF(2 9 ) 2. Peterson 8, 2 (45) ( ) 8 1 11 2, X 4 + X +1. 4 5 ( a) 8 X 4 + X +1. 1. 11
SR 1 SR 2 SR 3 SR 4 8: M ( 15 ) 1: M ( 15 ) SR 1 SR 2 SR 3 SR 4 1 1 2 1 3 1 1 4 1 1 1 5 1 1 1 1 6 1 1 1 7 1 1 1 8 1 1 9 1 1 1 1 1 1 11 1 1 12 1 1 13 1 1 14 1 15 1 1 1 12
M 2: (8 ) 2 3 1 (7) 8 3 7 2 (13) 8 4 15 2 (23) 8 5 31 6 (45) 8, (75) 8, (67) 8 6 63 6 (13) 8, (147) 8, (155) 8 7 127 18 (211) 8, (217) 8, (235) 8, (367) 8, (277) 8, (325) 8, (23) 8, (313) 8, (345) 8 8 255 16 (435) 8, (551) 8, (747) 8, (453) 8, (545) 8, (543) 8, (537) 8, (73) 8 9 511 48 (121) 8, (1131) 8, (1461) 8, (1423) 8, (155) 8, (1167) 8, (1541) 8, (1333) 8, (165) 8, (1751) 8, (1743) 8, (1617) 8, (1553) 8, (1157) 8, (1715) 8, (1563) 8, (1713) 8, (1175) 8, (1725) 8, (1225) 8, (1275) 8, (1773) 8, (1425) 8, (1267) 8 3.3 M M h(x) α. u i = Tr(θα i ) i =, 1,,N 1 (9) u,u 1,,u i,,u N 1 : M {, 1} Tr(α) =α + α 2 + α 22 +,, +α 2n 1 : GF(2 n ) GF(2) θ : GF(2 n ) (1, 2,, 2 n 1 ), θ =1,. u i = Tr(α i ) (1), N =2 n 1 M u =(u,u 1,,u N 1 ), q, (Decimation: ), v =(v,v 1,,v N 1 )..,, v = u[q] (11) v i = Tr(θα iq )=Tr(θ(α q ) i )=Tr(θβ i ) (i =, 1,,N 1) (12)., β = α q, v M, GF(2 n ) α q (q:gcd(n,q)=1 q), M u, N M 13
3: M (15 2 ) 1 1 11111111 7 8-1 15 2 11111111., M, u = u[2]. Tr(α 2i )=Tr((α i ) 2 )=Tr(α i ) (13) ( b)? 3.4 M, n M, 1 (2 n 1 1), 1 2 n 1., 1, 1 1/2,,.,, SS,,.,, M, 2. M,., p(t), t p(t) τ p(t + τ),. R pp (τ) = 1 T p(t)p(t + τ)dt (14) T T : p(t) 1,, 2. 1,,., 1 15 2 3. M, 1, 1 1/N. M 1 N +1 τ R pp (τ) = N T b 1 N lt T b τ lt + T b (l 1)T + T b τ lt T b (15) 14
1 R pp (τ) T b 1/N T τ 9: M T : p(t) 1 T b :1 N : N = T /T b l =, ±1, ±2,. M 9., M,., M 1., M,.,, M,., SS. 1, L =7 M., M,., T, 1., M. M,., M 2,,. 3.5 M Wiener-Khintchine, F (ω) 2 R pp (τ). F (ω) 2 = R pp (τ)e jωτ dτ (16) R pp (τ) =2π F (ω) 2 e jωτ dω (17) M. (15) R pp (τ) = C n e jnω τ n= (18) 15
(1) (2) M (3) (1) (2) (4) M (5) (3) (4) (1) (6) (2) 1 (7) (3) (6) (1) (8) (3) (2) = (1) 1: M SS. (L=7) 16
Correlator Channel (1) Received signal (3) (2) Local PN-sequence generator Low-pass filter Decision stage Output data +1 (1) Received signal -1 (a) (2.a) PN sequence (correctly synchronized) +1-1 +1 (3.a) Product signal of (1) and (2.a) -1 (b) (2.b) PN sequence (not synchronized) (3.b) Product signal of (1) and (2.b) +1-1 +1-1 (c) (2.c) PN sequence (different sequence) (3.c) Product signal of (1) and (2.c) +1-1 +1-1 11: DS/SS demodulator. 17
ω, ω =2π/T. C n 1 T /2 R pp (τ)e jnωτ dτ (n =1, 2, ) C n = T T /2 1 T /2 R pp (τ)e jnωτ dτ (n = 1, 2, ) T T /2 (19). n =1, 2, C n C n = 1 T T /2 T /2 R pp (τ)e jnω τ dτ T /2 = 1 Tb (1 N +1 τ )e jnωτ dτ 1 T N T b NT T b + 1 (1 + N +1 τ )e jnωτ dτ 1 T T b N T b NT = 2 T /2 cosnω τdτ + 2 Tb (1 N +1 NT T b T N = 2 [ ] sinnω τ T /2 + 2 [ ] sinnω τ Tb NT nω T b T nω 2(N +1) NT Tb, 3, Tb τ T b cosnω τdτ =. (21). C n = 2sinnω T b NT nω + 2sinnω T b T nω Tb e jnω τ dτ T /2 e jnω τ dτ τ )cosnω τdτ (2) T b τ T b cosnω τdτ (21) [ τ Tb sinnω τ nω = sinnω T b nω ] Tb 1 T b [ Tb cosnω τ n 2 ω 2 1 sinnω τ dτ T b nω = sinnω T b 1 ( cosnω nω T b n 2 ω 2 T b +1) = sinnω T b 2 sin 2 (nω nω T b n 2 ω 2 T b /2) (22) { 2(N +1) NT ] Tb } sinnω T b 4(N +1) sin 2 (nω nω NT T b n 2 ω 2 T b /2) = (N +1)T b sin 2 (nω T b /2) NT (nω T b /2) 2 = N +1 Sa 2 (nω N 2 T b /2) (23) n = 1, 2, C n C n = N +1 N 2 Sa 2 (nω T b /2) (24). Sa(x) =(sinx)/x,. n = C = 1 T T /2 T /2 R pp (τ)dτ 18
., (15), T /2 = 2 Tb (1 N +1 τ )dτ 2 dτ T N T b NT T b = 2 (T b N +1 Tb 2 ) 2 ( T T N 2T b NT 2 T b) = 2 N N +1 1 N 2 N + 2 N 2 = 1 N 2 (25) R pp (τ) = 1 N + N +1 2 N 2 n= n Sa 2 (nω T b /2)e jnω τ (26) F (ω) 2 = F[ = = 2π n= n= n= C n e jnω τ ] C n F[e jnω τ ] C n δ(ω nω ) = 2π N +1 δ(ω)+2π N 2 N 2 n= n. 12, M. Sa 2 (nω T b /2)δ(ω nω ) (27) 4 4.1,,,.,,. 13.,, PN,, ±T c /2 (T c : )., (Delay Lock Loop ;DLL). 4.2, PN,... 19
F (ω) 2 2π/T b 2π/T b ω 2π/T 12: > < PN DLL 13: 2
,.., PN.,. 4.3, (delay lock loop : DLL). DLL, (voltage controlled oscillator : VCO), PN. 14. DLL,,,,. 14 DLL. 2, PN (early) (late) PN,, 2. ( ) τ,,. R pp (τ) = 1 T p(t)p(t + τ)dt (28) T p(t) t, p(t + τ) τ. T, p(t) 1., 2. 1,,. M, 1, 1 1 T. 15 (1), (2). T c, (< t c ). 2 15 (3). S. T, T. DC. DC. LPF, DC., DC 15 (3) τ, (V ). S, DC. DC VCO. VCO PN.,. 21
Late Code (1) (2) + (3) F(s) Early Code PN VCO 14: DLL 1 -T c -T c - (1) Early Code (2) Late Code T c 1 T c 1 t -T c T c t -1 t (3) S 15: S 22
K frequency 1,2,...,K: Channel time FDMA 1 2 TDMA FDMA: frequency-division multiple access ( ) TDMA: time-division multiple access ( ) CDMA: code-division multiple access ( ) K 2 1 CDMA frequency power code K code 2 code 1 frequency 16: Comparison of multiple access schemes. 5 [1] pp.165-167, 1988 [2],,, ( ), pp.7-9, ISBN 488552153X, 1998. [3] John Proakis, Digital Communications, 4th edition, McGrow Hill, ISBN 72321113, 2. [4] B.Sklar: Digital Communications, Prentice-Hall, p.29, p.158, pp744 745 (1988). [5] W.W.Peterson, Error Correcting Codes,M.I.T. Press, Cambridge, Mass., pp.251 254, 1965. [6],, :,, IN83-67, pp.25-3(1983-11). [7] :,, pp.3-24(1987). [8] :,, vol.15, No.1, pp.45-48(1985-1). 23
[9] :, 3. [1] : SS, 3. [11] :, 5. 24
C (1) DS,. PN PN = { 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1} ( 15 M ). (2) M. (3) (2) M. (4) M, DFT( FFT )., (27)., SS C. ((4) DFT ),. 25