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1 1 SS 2 2 (DS) DS DS (channel papacity) E b /N M M M M M C 25 1

2 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

3 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

4 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

5 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

6 2.4 (channel papacity) [[1] ] 6

7 2.5 [[2] ] P S = N W, (3) W (4.212) 7

8 8

9 Fig 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

10 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 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

11 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) ( ) , X 4 + X ( a) 8 X 4 + X

12 SR 1 SR 2 SR 3 SR 4 8: M ( 15 ) 1: M ( 15 ) SR 1 SR 2 SR 3 SR

13 M 2: (8 ) (7) (13) (23) (45) 8, (75) 8, (67) (13) 8, (147) 8, (155) (211) 8, (217) 8, (235) 8, (367) 8, (277) 8, (325) 8, (23) 8, (313) 8, (345) (435) 8, (551) 8, (747) 8, (453) 8, (545) 8, (543) 8, (537) 8, (73) (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) 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

14 3: M (15 2 ) , 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,,., 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

15 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

16 (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

17 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) (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) (c) (2.c) PN sequence (different sequence) (3.c) Product signal of (1) and (2.c) : DS/SS demodulator. 17

18 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

19 ., (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

20 F (ω) 2 2π/T b 2π/T b ω 2π/T 12: > < PN DLL 13: 2

21 ,.., 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 ) (3). S. T, T. DC. DC. LPF, DC., DC 15 (3) τ, (V ). S, DC. DC VCO. VCO PN.,. 21

22 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

23 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 , 1988 [2],,, ( ), pp.7-9, ISBN X, [3] John Proakis, Digital Communications, 4th edition, McGrow Hill, ISBN , 2. [4] B.Sklar: Digital Communications, Prentice-Hall, p.29, p.158, pp (1988). [5] W.W.Peterson, Error Correcting Codes,M.I.T. Press, Cambridge, Mass., pp , [6],, :,, IN83-67, pp.25-3( ). [7] :,, pp.3-24(1987). [8] :,, vol.15, No.1, pp.45-48(1985-1). 23

24 [9] :, 3. [1] : SS, 3. [11] :, 5. 24

25 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

UWB a) Accuracy of Relative Distance Measurement with Ultra Wideband System Yuichiro SHIMIZU a) and Yukitoshi SANADA (Ultra Wideband; UWB) UWB GHz DLL

UWB a) Accuracy of Relative Distance Measurement with Ultra Wideband System Yuichiro SHIMIZU a) and Yukitoshi SANADA (Ultra Wideband; UWB) UWB GHz DLL UWB (DLL) UWB DLL 1. UWB FCC (Federal Communications