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1 24 Investigation on HC/MC-CDMA Signals with Non-Uniform Frequency Intervals

2 CDMA (high-compaciton multicarrier codedivision multiple access: HC/MC-CDMA),., HC/MC-CDMA,., 32.,, 64. HC/MC-CDMA, HC-MCM, i

3 Abstract Investigation on HC/MC-CDMA Signals with Non-Uniform Frequency Intervals YOSHII Aira We discuss the cross-correlation between two sets of proposed high-compaction multicarrier code-division multiple access (HC/MC-CDMA) signals. The proposed HC/MC-CDMA signals having sawtooth wave carrier density are generated. We compare the cross-correlation value of the proposed HC/MC-CDMA signals with the crosscorrelation value of the conventional HC/MC-CDMA signals. As a result, it is shown that the proposed HC/MC-CDMA signals obtains low cross-correlation values when the set size is smaller than 32. The proposed HC/MC-CDMA signals can be used to reduce the interference of multiplex signals. ey words HC/MC-CDMA, HC-MCM, average cross-correlation value ii

4 1 1 2 [2][3] OFDM MC-CDMA HC/MC-CDMA[4][5][6][7] HC/MC-CDMA A 20 iii

5 A A B R ρ 23 iv

6 MC-CDMA HC/MC-CDMA HC/MC-CDMA MC-CDMA HC/MC-CDMA v

7 vi

8 1,,.,,,.,, [1].,,.,, (intersymbol interference: ISI).,, (orthogonal frequency division multiplexing: OFDM), CDMA OFDM MC-CDMA (multicarrier code-division multiple access),. MC-CDMA (high-compaction multicarrier modulation: HC-MCM) HC/MC-CDMA, MC-CDMA,., HC/MC-CDMA,,, (multiple access interference: MAI)., HC/MC-CDMA,,. 1

9 , HC/MC-CDMA.,. 2

10 2 [2][3],., OFDM, MC-CDMA , - serial-to-parallel: S/P N,, cos(2πf 0 t) cos(2πf 0 t) Data cos(2πf 1 t) cos(2πf 1 t) Data!h cos(2πf N-1 t) cos(2πf N-1 t) 2.1 3

11 2.2 OFDM. N,. S/P,.,,.,,.,. 2.2 OFDM (orthogonal frequency division multiplexing: OFDM),., PSK (phase shift eying) QAM (quadrate amplitude modulation). OFDM. n ( f n ) z n (= a n + jb n ), z n s n (t) =Re[z n exp(j2πf n t)]. n n + 1, s n (t) s n+1 (t) 0. f, z n T,. 4

12 2.2 OFDM E [s n (t)s n+1 (t)] = = 1 2 = 1 2 T 0 T 0 T 0 s n (t)s n+1 (t)dt [Re [z n z n+1 exp{j2π(2f n + f)t}] Re{z nz n+1 exp(j2π ft)}] dt {(a n a n+1 + b n b n+1 )cos2π ft (a n b n+1 a n+1 b n ) sin 2π ft}dt (2.1) (2.1) 0, f = /T ( = 1, 2,...), ft = 1. OFDM,. N, OFDM s(t). s(t) = N 1 n=0 s n (t) = N 1 n=0 Re{z n exp(j2πf n t)} = Re{z n exp(j2πnt/t ) exp(j2πf 0 t)} (2.2) f n. f n = f 0 + n f = f 0 + n/t (2.3), (2.2) OFDM N 1 n=0 z n exp(j2πnt/t ) (2.4)., OFDM IDFT(inverse discrete Fourier transform). 5

13 2.3 MC-CDMA 2.3 MC-CDMA CDMA(MC-CDMA) CDMA OFDM. OFDM, MC-CDMA,. MC-CDMA 2.2. MC-CDMA,. 2.2,. MC-CDMA. Frequency Frequency Time Message Symbol Spread code Frequency Time MC-CDMA Signals 2.2 MC-CDMA 6

14 3 HC/MC-CDMA[4][5][6][7], HC/MC-CDMA,., HC/MC-CDMA. 3.1 K HC/MC-CDMA [2]. x(t) = K x (t; T ) = =1 K b c(t; c ρ, T ), 0 < t < T (3.1) =1 T [s], x (t; T ) = b c(t; c ρ, T ) ( = 1, 2,..., K), c ρ,, b c(t; c ρ, T ) c(t; c ρ, T ) = g(t; T ), j = 1, g(t),. L l=1 c,l e j 2π T 0 (l 1 2 )t (3.2) g(t) = { 1 (0 < t < T ) 0 (otherwise) (3.3) c,l (l = 1, 2,..., L) L l, 1/T 0 [Hz]. ρ. 7

15 3.2 ρ = T 0 T (3.4) HC/MC-CDMA , c,l l. HC/MC-CDMA, IDFT L 0, IDFT L + L 0 M (y(m)(m = 1, 2,..., M)), L + L 0 M. ρ = (L + L 0 )/M. y(m) P/S D/A, HC/MC-CDMA y(t). c (1) c (2) c (3) y 1 y 2 y 3 P/S D/A y(t) c (L) (L+L 0 )point y M IDFT Add 0s. L 0 -point Remove (L+L 0 -M) samples 3.1 HC/MC-CDMA 8

16 3.3 HC/MC-CDMA HC/MC-CDMA , n(t) y(t) + n(t) A/D S/P. T M., L + L 0 M, DFT. ẑ l., ẑ l (Decision),. ^ y(1) ^z(1) y(t)+n(t)= r(t) A/D S/P y(2) ^ DFT z(2) ^ Decision ^ y(m) ^ z(l+l 0 ) (L+L 0 -M) point 3.2 HC/MC-CDMA 3.3 HC/MC-CDMA,, c(t; c, T ) c(t; c, T ) Φ T (c, c ). Φ T (c, c ). Φ T (c, c ) = T 0 c (t; c, T )c(t; c, T )dt (3.5) 9

17 3.3 HC/MC-CDMA,. (3.5) (3.2). Φ T (c, c ) = T 0 = T 0 L ( L l=1 l=1 m=1 c 2π j T (l,le 1 )t)( 0 2 L m=1 c,me j 2π T 0 (m 1 2 )t) dt L c,lr l,m c,m (3.6), r l,m 2 f l (t; T ) = g(t; T ) 1 T0 exp(j 2π(l 1/2) T 0 t) f m (t; T ) = g(t; T ) 1 T0 exp(j 2π(m 1/2) T 0 t). r l,m = = T 0 f l (t; T )f m (t; T )dt r l,m (l, m) L L R ρ { 1/ρ (l = m) 1 sin((l m)π/ρ) ρ (l m)π/ρ e j(l m)π/ρ (l m) ] R ρ = [r l,m (3.7) (3.8), (3.6). Φ T (c, c ) = T 0 c H R ρ c (3.9), H. R ρ R ρ v ρ,i = λ ρ,i v ρ,i λ ρ,i v ρ,i (i = 1, 2,..., K ; K R ρ K L). R ρ = λ ρ,i v ρ,i vρ,i H (3.10) K i=1, λ ρ,i 0 λ ρ,i 1 λ ρ,1 λ ρ,2... λ ρ,k, v ρ,i (= [υ ρ,i,1 υ ρ,i,2... υ ρ,i,l ] T ) v H ρ,i v ρ,i = {1(i = i ), 0(i i )}. (3.10) (3.9) Φ T (c, c ) = T 0 c H ( K ) λ ρ,i v ρ,i vρ,i H c (3.11) i=1 10

18 3.4., c ( = 1, 2,..., K; K K ) c ρ, = 1 λρ, v ρ, = c (3.12), (3.12) (3.11), 1 ( K ) Φ T (c ρ,, c ρ, ) = T 0 vρ, H λ ρ,i v ρ,i vρ,i H 1 v ρ, λρ, λρ, = { T0 ( = ) 0 ( ) i=1 (3.13). (3.13) c(t; c ρ,, T )( = 1, 2,..., K; K K ). 3.4, HC/MC-CDMA, 3.3,. f 3.3. K K x(t) = x (t; T ) = b c (t; T ), 0 < t < T (3.14) =1 =1 11

19 3.4, c (t; T ). c (t; T ) = g(t; T ) L l=1 c,l e j 2π T 0 (a l 1 2 )t (3.15), a l l (1 a l L), 1/T 0 [Hz]., ρ. (3.15), a l 3.3, HC/MC-CDMA MC-CDMA. MC-CDMA, T [s], 1/T [Hz]. MC-CDMA f[hz] T, ft (= 1/ρ) = 1. MC-CDMA 3.4. MC-CDMA, T,., HC/MC-CDMA, MC-CDMA., ρ > 1. HC/MC-CDMA 3.5., MC-CDMA., HC/MC-CDMA,

20 3.4 f 3.4 MC-CDMA f 3.5 HC/MC-CDMA f

21 4 4.1 ĉ (t; T ) č (t; T ) Φ(, ). Φ(, ) = 1 T T 0 ĉ (t; T )č (t; T )dt (4.1), *. Φ(, ) 2,. HC/MC-CDMA, 1/2, Φ(, ) K. L = 362, ρ = , K = , K = ,,. 14

22 4.2 Average cross-crrelation value Set size, K Nonuniform uniform Frequency [Hz]

23 Frequency [Hz]

24 5, HC/MC-CDMA. HC/MC-CDMA,.,

25 ,,,,.,., M2.,. 18

26 [1] L. Hanzo, M. Munster, B. J. Choi, and T. Keller, OFDM and MC-CDMA for broadband multi-user communications, WLANs and broadcasting, Wiley [2],, [3] Ramjee Parasad CDMA [4],, MC-CDMA,, WBS , pp.13-18, [5] M. Hamamura and J. Hyuga, Spectral efficiency of orthogonal set of truncated MC-CDMA signals using discrete prolate spheroidal sequences, IEEE WCNC 2008, March 2008 [6] MC-CDMA, WBS pp ( ). [7], FDM, WBS pp ( ). 19

27 A A.1 x(t; c ρ,, T ) 100λ [%] W = L/T 0 B = [0, L/T 0 ]. x (t; T ) X (f; T ), X (f; T ) = x (t; T )e j2πft dt T = b c(t; c ρ,, T )e j2πft dt 0 L = b T 0 c ρ,,l rl (f) l=1 (A.1). rl (f). r l (f) = 1 T 0 T = 1 ρ 0 e j2πft e j 2π T 0 (a l 1 2 )t dt sin ( (T 0 f a l )π/ρ) (T 0 f a l )π/ρ e j(t 0f a l )π/ρ (A.2) x(t; c ρ,, T ) E (in) E (in) = X (f; T ) 2 df B = b 2 T 2 0, (A.1). L/T0 0 L c ρ,,l rl (f) 2 df l=1 (A.3) 20

28 A.1 (A.3) (A.4). Ẽ (in) = b 2 T 2 0 L m=1 L l=1 c ρ,,l r l (f) f= m 1/2 T 0 2 f (A.4) Ẽ(in) f (= 1/T 0 ) 0, ρ(= T 0 /T ),. r l (f), f = m/t 0 (3.7) r l,m r l,m., (A.4). L l=1 r l (f) f= m 1/2 T 0 = r l,m (A.5) c ρ,,l r l (f) f= m 1/2 T 0 = L c ρ,,l rl,m l=1 = r H mc ρ, (A.6), r m R ρ (= [r 1 r 2... r m... r L ]; R ρ = R H ρ ) m., (A.6) (A.4). Ẽ (in) = b 2 T 2 0 L m=1 r H mc ρ, 2 f = b 2 T0 2 R H ρ c ρ, 2 f (A.7),., R ρ (3.10), c ρ, (3.12), E (in) Ẽ(in). = b 2 T0 2 Ẽ (in) ( K ) λ ρ,i v ρ,i vρ,i H 2 c ρ, f i=1 = b 2 T0 2 λ ρ, v ρ, 2 f = b 2 T 0 λ ρ, (A.8) Parseval, X(f; c ρ,, T ) E (total), 21

29 A.2 x(t; c ρ,, T )., E (total) = = = T 0 T 0 X(f; c ρ,, T ) 2 df x(t; c ρ,, T ) 2 dt c (t; c ρ,, T )c(t; c ρ,, T )dt = b 2 Φ T (c ρ,, c ρ, ) (A.9). (3.13), E (total) = b 2 T 0 (A.10)., (A.4) (A.10), 100E (in) /E (total). 100Ẽ(in) /E (total) = 100λ ρ, [%] A.2 B. x(t; c ρ,, T ) E (out) E (in),., E (total), 100(1 λ 2 ρ,. E (out) = E (total) E (in) E (total) Ẽ(in) = b 2 T 0 (1 λ ρ, ) (A.11) )[%](= E(out) /E (total) 100[%]) 22

30 B R ρ f l (t; T ) f m (t; T ) f ρ,l = [f l,1 f l,2... f l,mt ] T f ρ,m = [f m,1 f m,2... f m,mt ] T f l,n = 1 f m,n = 1 ρmt expj 2πm(n 1) ρm T ρmt expj 2πl(n 1) ρm T (n = 1, 2,..., M T ) f ρ,l f ρ,m R ρ (l, m) r l,m f H ρ,l f ρ,m( = ˆr l,m ) ˆF ρ ˆF ρ = [f ρ,1 f ρ,2... f ρ,l ] R ρ ˆF H ˆF ρ ρ ( = ˆR ρ ) ˆF ρ ˆF ρ = Ûρ ˆΛ 1 2 ρ ˆVH ρ ˆΛ 1 2 ρ ˆF ρ ˆλρ,i (i = 1, 2,..., ˆK ; ˆK ˆR ρ (= ˆF ρ ) K min(l, M T )) ˆΛ 1 2 ρ = diag( ˆλρ,1, ˆλρ,2,..., ˆλρ, ˆK ) ˆK ˆK ) Ûρ ˆV ρ Ûρ = [û ρ,1 û ρ,2... û ρ, ˆK ] M T ˆK ˆV ρ = [ˆv ρ,1 ˆv ρ,2... ˆv ρ, ˆK ] L ˆK û H ρ,iûρ,i = {1(i = i ), 0(i i )}, ˆv H ρ,iˆv ρ,i = {1(i = i ), 0(i i )} ˆF ρ = Ûρ ˆΛ 1 2 ρ ˆVH ρ ÛH ρ Ûρ = 1 K K ˆΛ 1 2 ρ ˆΛ 1 2 ρ = ˆΛ ρ ˆR ρ ˆR ρ (= ˆF H ρ )= (Ûρ ˆΛ 1 2 ρ ˆVH ρ ) H (Ûρ ˆΛ 1 2 ρ ˆVH ρ ) = ˆV ρ ˆΛ 1 2 ρ ÛH ρ Ûρ ˆΛ 1 2 ρ ˆVH ρ = K i=1 ˆλ ρ,iˆv ρ,iˆv H ρ,i = ˆV ρ ˆΛρ ˆVH ρ (B.1) (A.1) (3.9) ˆF ρ ˆR ρ ˆλ ρ,i ˆv ρ,i M T = 4L 23

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