GD152
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- さなえ いちぞの
- 5 years ago
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1 GD152
2 MUSIC T T CdmaOne 2 i
3 Beamformer MUSIC T ii
4 iii
5 1 1.1: 1.1 CDMA 1
6 1.2: 2
7 1.2(a) [1, 2] 1.2(b) [3, 4, 5] MUSIC(MUltiple SIgnal Classification) [6] ESPRIT(Estimation of Signal Parameters via Rotational Invariance Techniques) [7] [8] [9] Forward/Backward(F/B) [8] MUSIC ESPRIT F/B 1.2(c) 2 [10] MUSIC ESPRIT [11] MUSIC 1 3
8 L T L T 1.3: 1.3 T MUSIC 900MHz 2 Beamformer MUSIC 3 T 4 T 4
9 5 6 5
10 2 Beamformer MUSIC Beamformer 5 MUSIC MUSIC MUSIC ESPRIT MUSIC ESPRIT MUSIC x x y y M N(= K) L 2.2 θ l (l =1,,L) m n x R m,n(t) 6
11 y x y x antenna element 2.1: y x θ i i-th incident wave 2.2: x R m,n(t) = L F l (t)e j{φ 1,m(θ l )+φ 2,n (θ l )} + n m,n (t) (2.1) l=1 φ 1,m (θ l ) = 2π λ (m 1) x cos θ l (2.2) φ 2,n (θ ll ) = 2π λ (n 1) y sin θ l (2.3) F l (t) i 1 1 n m,n (t) λ x R m,n (t) X R (t) = A R F (t)+n (t) (2.4) X R (t) = [x R 11(t),...,x R 1,N(t),x R 21(t),...,x R 2,N(t),...,x R M,1(t),...,x R M,N(t)] T (2.5) A R = [ a R (θ 1 ),...,a R (θ l ),...,a R (θ L ) ] (2.6) 7
12 a R (θ l ) = [ e j{φ 11(θ l )+φ 21 (θ l )},...,e j{φ 1,M (θ l )+φ 21 (θ l )}, e j{φ 11(θ l )+φ 22 (θ l )},...,e j{φ 1,M (θ l )+φ 2,N (θ l )} ] T (2.7) F = [F 1 (t),,f L (t)] (2.8) [ ] T X R (t) a R (θ l ) r M L 2.2 θ l (l =1,,L) k x C k (t) r y x antenna element 2.3: L x C m (t) = F l (t)e jφm(θl) + n k (t) l=1 8
13 φ k (θ l ) = 2π λ r cos ( θ l 2π K (k 1) ) (2.9) (2.10) F l (t) l n k (t) λ x C k (t) X C (t) = A C F (t)+n(t) (2.11) X C (t) = [x C 1 (t),...,x C K(t)] (2.12) A C = [ a C (θ 1 ),...,a C (θ L ) ] (2.13) a C (θ l ) = [ e jφ 1(θ l ),...,e jφ K(θ l ), ] (2.14) X C (t) a C (θ l ) 2.2 Beamformer Beamformer X(t) a(θ l ) l k φ k (θ l ) X (t) = X R (t) (2.15) a(θ l ) = a R (θ l ) (2.16) φ k (θ l ) = φ 1,m (θ l )+φ 2,n (θ l ) (2.17) ( k = M (m 1) + n k (1, 1) (m, n) ) X (t) = X C (t) (2.18) a(θ l ) = a C (θ l ) (2.19) φ k (θ l ) = φ k (θ l ) (2.20) R xx R xx = E [ X (t)x H (t) ] (2.21) = ASA H + σ 2 I (2.22) 9
14 S S = E [ F (t)f H (t) ] (2.23) θ w k = e jφ k(θ) (2.24) θ P out = 1 2 ah (θ)r xx a(θ) (2.25) Beamformer P BF (θ) = P out a H (θ)a(θ)/2 = ah (θ)r xx a(θ) a H (θ)a(θ) (2.26) θ P BF 2.3 MUSIC MUSIC Beamformer S = E [ F (t)f H (t) ] E[ F 1 (t) 2 ] E[ F 1 (t)f2 (t) ]... E[ F 1 (t)f2 (t) ]) E[ F 2 (t)f1 (t) ] E[ F 2 (t) 2 ]... E[ F 2 (t)f L(t) ] S = (2.27) E[ F L (t)f1 (t) ] E[ F L (t)f2 (t) ]... E[ F L (t) 2 ] S L A L R xx = ASA H L µ i (i =1, 2,...,K) e i (i =1, 2,...,K) ASA H e i = µ i e i (i =1, 2,...,K) (2.28) 10
15 µ 1 µ 2... µ L >µ L+1 = = µ K = 0 (2.29) e H i e k = δ ik (i =1, 2,...,K) (2.30) δ ik R xx e i = (ASA H + σ 2 I)e i = ASA H e i + σ 2 e i = µ i e i + σ 2 e i = (µ i + σ 2 )e i (i =1, 2,...,K) (2.31) λ i = µ i + σ 2 (i =1, 2,...,K) (2.32) R xx λ 1 λ 2... λ L >λ L+1 = = λ K = σ 2 (2.33) σ 2 L AIC(Akaike Information Criteria) MDL(Minimum Description Length) R xx e i =(ASA H + σ 2 I)e i = λ i e i = σ 2 e i (i = L +1,...,K) (2.34) ASA H e i =0 (i = L +1,...,K) (2.35) 11
16 A S A H e i =0 (i = L +1,...,K) (2.36) a H (θ l )e i =0 (l =1, 2,...,L; i = L +1,...,K) (2.37) {e L+1,...,e K } (K L) {e L+1,...,e K } σ 2 (K L) {e 1, e 2,...,e K } K K S = span{e 1, e 2,...,e L } (2.38) N = span{e L+1, e L+2,...,e K } (2.39) S N (2.37) S = span{a(θ 1 ), a(θ 2 ),...,a(θ L )} (2.40) N L S S L N S = S (2.41) L {e 1,...,e L } L {a(θ 1 ),...,a(θ L )} S N (signal subspace) (noise subspace) (K L) 12
17 P MN1 (θ) = P MN2 (θ) =. P MNK L (θ) = 1 e H L+1a(θ) 2 (2.42) 1 e H L+2a(θ) 2 (2.43) 1 e H Ka(θ) 2 (2.44) (K L) MUSIC (2.45) P MN1 P MN2 P MNK L (2.45) a H (θ)a(θ) P MU (θ) = 1 Ki=L+1 e H i a(θ) 2 ah (θ)a(θ) = a H (θ)a(θ) a H (θ)e N EN H a(θ) (2.46) E N = [e L+1,...,e K ] (2.47) MUSIC θ L {θ 1,...,θ L } S =(A H A) 1 A H (R xx σ 2 I)A(A H A) 1 (2.48) S i i (2.33) K L +1 MUSIC signal 13
18 copy signal reconstruction ˆF (t) =(A H A) 1 A H X(t) (2.49) ˆF (t) F (t) W H =(A H A) 1 A H [w 1, w 2,...,w L ] H (2.50) W l w l l 14
19 3 T T 2 SN, MUSIC N [10] 15
20 3.1: 3.1 M M N MUSIC 3.2 (N +1) (N ) T T A/D x 1 K T x 1 3.2: T 16
21 3.3: T X t 1 =[x t 11,x t 12,,x t 1,(N +1)] x 1 =[x 11, x 12,, x 1,(N +1) ] x 1n =[x 1n (T ),x 1n (2T ),,x 1n (KT)] T x 1n (n =1,,N +1) n x 1n (kt) (k = 1,,K) n k 3.3 x 2 =[x 21, x 22,, x 2,(N +1) ] x 2n =[x 2n (T ),x 2n (2T ),,x 2n (KT)] T x 1,N +1 x 2,(N +1)/2 x 2,(N +1)/2 x 1,N +1 x 1 x 2 2 N x t 1,N +1 xt 2,(N +1)/2 (3.1) C(p) (p =1,,K P ) P C(p) = x 1,(N +1) ((ˆp 01 + i 1)T )x 2,(N +1)/2((i + p 1)T ) (3.1) i=1 P (P K) [ ] ˆp 01 1 C(p) 17
22 p ˆp 12 Y x 1 x 2 X 1 X 2 [12] X 1 = [ˆx 11, ˆx 12,, ˆx 1,(N +1) ] x 11 (ˆp 01 T )... x 1N (ˆp 01 T ) x 11 ((ˆp 01 +1)T )... x 1N ((ˆp 01 +1)T ) =..... x 11 ((ˆp 01 + Y 1)T )... x 1N ((ˆp 01 + Y 1)T ) R Y N (3.2) X 2 = [ˆx 21, ˆx 22,, ˆx 2,(N +1) ] x 21 (ˆp 12 T )... x 2N (ˆp 12 T ) x 21 ((ˆp 12 +1)T )... x 2N ((ˆp 12 +1)T ) =..... x 21 ((ˆp 12 + Y 1)T )... x 2N ((ˆp 12 + Y 1)T ) (3.3) ˆp (m 1),m x = [ X1,..., X m,..., X ] M = [ˆx 11,...,ˆx 1N, ˆx 21,...,ˆx 2N,...,ˆx M1,...,ˆx MN ] R Y MN X m = x m1 (ˆp (m 1),m T )... x mn (ˆp (m 1),m T ) x m1 ((ˆp (m 1),m +1)T )... x mn ((ˆp (m 1),m +1)T )..... x m1 ((ˆp (m 1),m + Y 1)T )... x mn ((ˆp (m 1),m + Y 1)T ) (3.4) x T x M N x MUSIC ESPRIT 3.2 Beamformer MUSIC ESPRIT (2.8) 18
23 MUSIC θ, θ 0 (2.2),(2.3) 2π λ x cos θ = 2π λ x cos θ 0 +2πm 2π λ y sin θ = 2π λ y sin θ 0 +2πn θ 0 (θ 0 θ) x y (3.5) cos θ = cos θ 0 + λ x m sin θ = sin θ 0 + λ y n 1 sin θ, cos θ 1 θ 0 λ x, λ y > 2 x, y < λ 2 19
24 4 4.1 T T (28) 8 MUSIC 4.1: The T character-type array antenna The rectangular array Element interval of rectangular and virtual rectangular array Circular array Radius of circular array 7+1 elements (7 4 elements) 7 4 elements 0.4-wavelength 8 elements 0.5-wavelength 20
25 4.2: The number of arrival waves wave form SN ratio The number of snapshots 6( 140deg, 40deg, 10deg,70deg,100deg,160deg) sinusoidal wave 0 20dB 300times F/B [8] T 3 3 F/B T SN SNR = 10 log SN 10dB MUSIC 4.1 T 4.2 T T 3 T SN MUSIC T SN MUSIC 21
26 SN MUSIC 0 Magnitude [db] Rectangular array Virtual rectangular array Circular array Angle [degree] 4.1: MUSIC (SNR = 10[dB]) 22
27 Rectangular array Virtual Rectangular array Circular array Power Wave Number 4.2: 0 Magnitude [db] Angle [degree] SNR 0[dB] SNR 5[dB] SNR 10[dB] SNR 20[dB] 4.3: MUSIC 23
28 0-10 Magnitude [db] Angle [degree] 4.4: MUSIC SNR 0[dB] SNR 5[dB] SNR 10[dB] SNR 20[dB] 0 Magnitude [db] Angle [degree] 4.5: MUSIC SNR 0[dB] SNR 5[dB] SNR 10[dB] SNR 20[dB] 24
29 5 T , , PC 5.1 0dBd AGC 60dBm RF 60dBm 8 I,Q 5.3 RF, 900MHz 70MHz 2 [9] 70MHz ±90 ±5dB 0.5ppm 400Hz(Max) 3dB 35MHz IQ 5MHz 12bit A/D PC MUSIC 25
30 5.1: IF Frequency Gain RF Input Range Phase Control Range Gain Control Range RF In Connector IF Output Connector 70MHz 50 3dB 110dBm 30dBm 90degree 5dB SMA-Female BNC-Female 5.1: 26
31 5.2: One Board Demodulator Mixer LPF Op-AMP I Power LED Fault LED LNA Parts AMP AMP AGC Parts Atten. BPF Mixer Atten. BPF AMP AMP 90 RF IN AGC TP BPF AMP AMP Deteotor PIC (+7dBm) LPF Mixer LO (+10dBm) LPF Op-AMP Q AMP BPF Eletrical Mode Eletrical Mode DAC Manual Mode +15V DAC Op-AMP Relay Op-AMP Phase Shifter Dual PLL Board AMP Manual Mode +15V Relay Control Board Controller RG232 Lab View 8way Splitter 10MHz Reference Clock 5.3: 27
32 1500 Output [mv] I component Q component RF IN [dbm] I/Q RF IN [dbm] 5.4: 28
33 5.5: T MHz 15dBm ADC SN 20dB /day T T 29
34 5.2: ( 1 ) Environment of experiments Inside anechoic chamber Number of arrival waves 1 Distance between transmitting and receiving antennas About 3 m Frequency 900MHz band Sampling frequency 5MHz DOA estimation algorithm MUSIC method 5.3: ( 1 ) The T character-type array antenna The rectangular array Element interval of rectangular and virtual rectangular array Circular array Radius of circular array 3+1 elements (3 4 elements) 3 2 elements 0.4-wavelength 6 elements 0.4-wavelength ˆx ˆx = x cos θ x T F/B MUSIC MUSIC 5.8 MUSIC T 30
35 7dB 180 T T 2.06 Transmitter 900MH band 0.4λ θ Receiver 1 MHz ADC sampling frequency 5 MHz PC SG 5.6: ( 1 T ) 31
36 0.4λ θ Transmitter 900MH band Receiver 1 MHz ADC sampling frequency 5 MHz PC SG 5.7: ( 1 ) 0 T-type Rectangular Circular Magnitude [db] Angle [degree] 5.8: MUSIC (DOA=0 ) 32
37 5 Error [degree] Angle [degree] 5.9: T-type Rectangular Circular T F/B T , MHz 15dBm ADC SN 20dB /day T F/B A/D 8 6 I 33
38 5.4: ( 2 ) Environment of experiments Inside anechoic chamber Number of arrival waves 2 Distance between transmitting and receiving antennas About 3 m Frequency 900MHz band Sampling frequency 5MHz DOA estimation algorithm MUSIC method 5.5: ( 2 ) The T character-type array antenna The rectangular array Element interval of rectangular and virtual rectangular array Circular array Radius of circular array 5+1 elements (5 4 elements) 3 2 elements 0.4-wavelength 6 elements 0.4-wavelength Q 6 I A/D PC PC Q F/B MUSIC H(z) = 1+αz 1 α + z 1 α ( ) α sin H(z) = ω 0 T + 2 tan 1 ω0 T = π 1+αcos ω 0 T 2 ω 0 T 1 2 ±15 MUSIC
39 T 2 T The virtual rectangular arrays 0.4λ Transmitter 900MH band θ1 θ2 Receiver 1 MHz ADC sampling frequency 5 MHz PC SG 5.10: ( 2 T ) 35
40 The rectangular arrays 0.4λ Transmitter 900MH band θ1 θ2 Receiver 1 MHz ADC sampling frequency 5 MHz PC 5.11: ( 2 ) SG 0 Magnitude [db] Angle [degree] 5.12: ( ±15 ) 36
41 5.13: (DOA=0,30 ) 5.14: (DOA= 30,0 ) 37
42 Magnitude [db] Angle [degree] 5.15: (DOA= 15,15 ) Magnitude [db] Angle [degree] 5.16: (DOA=30,60 ) 38
43 5.6: ( ) Environment of experiments Distance between transmitting and receiving antennas Frequency Sampling frequency DOA estimation algorithm Outside anechoic chamber About 7 m 900MHz band 5MHz MUSIC method , MHz 15dBm /day T F/B I Q MUSIC Beamformer Beamformer Beamformer MUSIC Beamformer MUSIC Beamformer 1 MUSIC MUSIC MUSIC Beamformer 1 39
44 The virtual rectangular arrays 0.4λ Transmitter 900MH band Receiver 1 MHz ADC sampling frequency 5 MHz PC SG 5.17: ( T ) The rectangular arrays 0.4λ 1 MHz Receiver ADC sampling frequency 5 MHz PC Transmitter 900MH band SG 5.18: ( ) Beamformer MUSIC 40
45 T Beamformer MUSIC T 0 Magnitude [db] MUSIC -20 Beamformer Angle [degree] 5.19: ( ) 41
46 0 Magnitude [db] -10 MUSIC -20 Beamformer Angle [degree] 5.20: (T ) SG 5.21: ( ) 42
47 0 Magnitude [db] MUSIC Beamformer Angle [degree] 5.22: ( ) 0 Magnitude [db] Angle [degree] MUSIC Beamformer 5.23: (T ) 43
48 SG 5.24: ( ) 5.4 T F/B CdmaOne(IS-95) A/D MUSIC Beamformer 44
49 5.7: ( ) Environment of experiments Shape of array Number of elements Frequency Sampling frequency DOA estimation algorithm Outdoor Rectangular 4 elements 900MHz band 5MHz MUSIC method 0.4λ The rectangular arrays θ Receiver ADC sampling frequency 5 MHz PC 5.25: ( ) 45
50 5.26: Beamformer MUSIC 2 4 (2.50) 46
51 0 Magnitude [db] Angle [degree] MUSIC Beamformer 5.27: ( ) The rectangular arrays 5.28: ( ) 47
52 6 T SN 10dB T MUSIC T SN T SN 1 T T T 48
53 2 49
54 Korea Maritime University Prof.Kyeong-sik Min KDDI 50
55 [1] 900MHz -, (B) vol,j-70-b no.12 pp Dec [2] RCS Jan [3] A.S.Bajwa and J.D.Parsons Small-area characteristion of UHF urban and suburban mobile radio propagation IEE Proceedings, vol.129, pt.f, no.2, pp , April [4] (B-II), vol.j72-b-ii, pp.62-71, Feb [5] H.J.Thomas, T.Ohgane and M.Mizuno, A novel antenna measurement of the angular distribution of received waves in the mobile radio environment as a function of position and delay time, Proc. IEEE Vehicular Technology Conf, pp , May [6] R.O.Schmidt, Multiple Emitter Location and Signal Parameter Estimation, IEEE Trans. Antenna & Propagat., vol.34, No.3, pp , Mar [7] R.Roy and T.Kailath, ESPRIT Estimation of Signal Parameter via Rotational Invariance Techniques, IEEE Trans. Accoust., Sppech & Signal Proc., vol.37, pp , July [8],,, [9] K.Mori, Y.Inoue, K.Ichige and H.Arai, Experiments of DOA Estimation by DBF Array Antenna at 2.6GHz, IEICE Trans. Comm., vol.e84-b, no.7, pp , July
56 [10] (B), vol.j83-b, no.9, pp , Sep [11] S.Sekizawa, Estimation of Arraival Directions Using MUSIC Algorithm with a Planar Array, ICUPC 98, pp , Oct, 1998 [12] Kyeong-sik Min Dong-chul Kim Jung-hun Kim 900MHz AP pp
57 (1) B (2) B (3) Kyeong-sik Min Dong-chul Kim Jung-hun Kim 900MHz 2002-AP (4) Akimichi Hirota, Koichi Ichige and Hiroyuki Arai, DOA Estimation by T - Type Array Antenna and Its Evaluation, Proc.URSI General Assembly, No.C2.P.4, Maastricht, The Netherlands, August (5) Kyeong-sik Min Dong-chul Kim Jung-hun Kim 900MHz B (6) Kyeong-sik Min Dong-chul Kim Jung-hun Kim 900MHz ( ) 53
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