1 Analysis for Adaptive DOA Estimation with Robust Beamforming in Smart Antenna System 指導教授：黃文傑 W.J. Huang 研究生 ：蔡漢成 H.C. Tsai

2 Outline Conception of Smart Antenna Beamforming Method DOA Estimation θ- LMS Algorithm (My Point) Local Minimum problems θ- LMS Algorithm with Robust Beamforming Conclusion

3 Conception of Smart Antenna There are constructed by some specially geometric antenna array. It changes the beam-pattern with some different methods. It increases the CINR and Capacity

4 Category -1 Switched Beam System

5 Category -2 Adaptive Beam System

6 Outline Conception of Smart Antenna Beamforming Method DOA Estimation θ- LMS Algorithm Local Minimum problems θ- LMS Algorithm with Robust Beamforming Conclusion

7 Beamforming Method Summation Beamforming Weighting DOA Estimation

8 Beamforming Tech. Array Response y(t) Output power P(w) 1.Conventional Beam-former 2.Capon’s Beam-former

9 Conv. Beamforming & Steering Vector d d θ (M-1)d X Y

10 ULA d = 0.5 λ M = 4 、 8 、 12

11 MVDR Beamforming(Capon’s)

12 Outline Conception of Smart Antenna Beamforming Method DOA Estimation θ- LMS Algorithm Local Minimum problems θ- LMS Algorithm with Robust Beamforming Conclusion

13 DOA Estimation Conventional Capon’s Subspace –MUSIC

14 Conventional DOA Estimation w(0~180) Conventional u(n) Receiving signal Pattern (0~180) DOA Est. w(n) Beamforming Weighting

15 Capon’s DOA Estimation w(0~180) Capon’s u(n) Receiving signal Pattern (0~180) DOA Est. w(n) Beamforming Weighting

16 MUSIC (MUltiple SIgnal Classification ) P MUSIC Pattern u(n) Receiving signal Eigen decomposition Noise Space V n a(0~180) DOA Est. w(n) Weighting Vector

17 Compare the three methods ULA M = 4 d = 0.5λ User’s DOA = 90° 、 120 ° SNR=10dB

18 Outline Conception of Smart Antenna Beamforming Method DOA Estimation θ- LMS Algorithm (My point) Local Minimum problems θ- LMS Algorithm with Robust Beamforming Conclusion

19 LMS (Least Mean Square )

20 w – LMS Algorithm d(n) w - LMS u(n) w(n) w(n+1) y(n) e(n) +

21 θ- LMS Algorithm + d(n) ө - LMS u(n) w(n) w(n+1) y(n) e(n) ө(n+1) ө(n) 4 x1

22 θ- LMS Algorithm u(n)w(n) w H ( n) u(n) -d(n) Cost function J(θ) find DOA θ 0 Beamforming Weighting by DOA θ 0 w(n) Weighting

23 Weighting is Instead of θ

24 Adaptive θ(n) is defined Definition =

25 ULA M = 4 d = 0.5λ DOA= 120 ° Initial DOA = 90 ° Step size = 0.01 SNR =20

26 ULA M = 4 d = 0.5λ DOA= 0 ° ~180 ° Initial DOA = 90 ° Step size = 0.01 SNR =20 DOA=90*sin(0:0.01:80*pi) + 90;

27 Steering Vector Tracking ULA M = 4 d = 0.5λ DOA= 0 ° ~180 ° Initial DOA = 90 ° Step size = 0.01 “*” steering vector “o” tracking vector DOA=90*sin(0:0.05:80*pi) + 90;

28 Beampattern Tracking ULA M = 4 d = 0.5λ DOA= 0 ° ~360 ° Initial DOA = 90 ° Step size = 0.01 “o” DOA DOA=180*sin(0:0.05:80*pi) + 180;

29 Outline Conception of Smart Antenna Beamforming Method DOA Estimation θ- LMS Algorithm Local Minimum problems θ- LMS Algorithm with Robust Beamforming Conclusion

30 Converse to Error Direction ULA M = 4 d = 0.5λ DOA= 90 ° Initial DOA = 120 ° Step size = 0.01

31 Error pattern d(n) x (n) 4 x1 d(n) x (n) w (0~180) e(0~180) 4 x1 +

32 Cost function ULA M = 4 d = 0.5λ DOA= 90 °

33 ULA M = 4 d = 0.5λ DOA= 0 ° ~180 ° DOA=90 ° Error Surface (DOA )

34 Error Surface (d ) ULA M = 4 d = 0 ~1λ DOA= 90 ° d=0.5 λ

35 Error Surface (M ) ULA M = 2 ~8 d = 0.5λ DOA= 90 ° M=4

36 2 Antsθ- LMS Algorithm d(n) ө - LMS u(n) w(n) w(n+1) y(n) e(n) ө(n+1) ө(n) 2 x1 +

37 Error Surface (M=2 d=0.5 ) ULA M = 2 d = 0.5λ DOA= 90 °

38 Error Surface (M=2 d=0.25 ) ULA M = 2 d = 0.25λ DOA= 90 °

39 Simulation (1) ULA M = 2 d = 0.25λ DOA= 5 ° Initial DOA = 175 ° SNR = 30 dB

40 ULA M = 2 d = 0.25λ DOA= 170 ° Initial DOA = 5 ° SNR = 30dB Simulation (2)

41 2 – 4 “θ-LMS” 2 antennas “θ-LMS” 4 antennas “θ-LMS” Initial θ

42 Outline Conception of Smart Antenna Beamforming Method DOA Estimation θ- LMS Algorithm Local Minimum problems θ- LMS Algorithm with Robust Beamforming Conclusion

43 Noise problem θ- LMS Algorithm needs high SNR level. High noise level brings the DOA estimation result worse. The DOA estimation error will cause the terrible performance We use the Robust Beamforming Method to conquer the estimation error problem.

44 The flow chart of Robust Beamforming Ref : Riba J., Goldberg J., Vazquez G., “Robust Beamforming for Interference Rejection in Mobile Communications”, Signal Processing, IEEE Transactions on

45 Robust Beamforming

46 BER Analysis BPSK ULA M = 4 d = 0.5 λ DOA = 90°

47 Outline Conception of Smart Antenna Beamforming Method DOA Estimation θ- LMS Algorithm Local Minimum problems θ- LMS Algorithm with Robust Beamforming Conclusion

48 Conclusion DOA is an important parameter for beamforming system. But, the MUSIC algorithm is complex. The new method “ө - LMS” is simpler to realized Robust Beamforming can repair the fault of “ө - LMS”

49 Future Work Noise and channel problem Multi-user problems SINR Analysis Multi-path & DOA distribution Moving Source analysis Performance Analysis (User # 、 DOA 、 SNR 、 Beamforming method 、 Antenna # …etc.) Adaptive Analysis (Step-size Moving DOA 、 SNR 、 other adaptive structure)

50 Capon’s Beamforming

51 Step Size

52 Cost function

53 New cost function  {J(  )} is defined partial J(  ) by 

54 The Formula Derives

55 Initial = 90 ° DOA = 0 ° ULA M = 2 d = 0.25λ DOA= 0 ° Initial DOA = 90 °

56 Initial = 90 ° DOA = 180 ° ULA M = 2 d = 0.25λ DOA= 180 ° Initial DOA = 90 °

57 Noise problem

58 Degree spreading k = 0 Ref : Riba J., Goldberg J., Vazquez G., “Robust Beamforming for Interference Rejection in Mobile Communications”, Signal Processing, IEEE Transactions on

59 Robust Beamforming

60 Complex Surface