Adaptive Antennas in Wireless Communication Networks

Transcription

1 Bulgarian Academy of Sciences Adaptive Antennas in Wireless Communication Networks Blagovest Shishkov Institute of Mathematics and Informatics Bulgarian Academy of Sciences 1

2 introducing myself Blagovest Shishkov, Dr of Sciences, Professor of Statistical Communication Theory and Signal Processing, Sofia, Bulgaria 2

3 contents introduction background ESPAR antenna signal model of the adaptive antenna; objective function the Stochastic approximation method Kiefer-Wolfowitz minimization procedure learning curves, simulation results and performance analysis further development, blind (unsupervised) algorithm conclusion 3

4 contents introduction background ESPAR antenna signal model of the adaptive antenna; objective function the stochastic approximation method Kiefer-Wolfowitz minimization procedure learning curves, simulation results and performance analysis further development. blind (unsupervised) algorithm conclusion 4

5 introduction 1/2 Radio and its impact to telecommunications Fundamental role of Antennas Phased array antennas consist of multiple stationary antenna elements coupled together and allows more precise control of the radiation pattern Such a network is usually called Beamforming Adaptive antennas as a promising way to push the frontiers of wireless communications Digital beamforming of conventional adaptive arrays sounds quite cost-effective 5

6 introduction 2/2 We propose electronically steerable passive array radiator (ESPAR) antenna that performs analog aerial beamforming which is more cost-effective than digital beamforming antennas Unlike conventional adaptive antennas, it has only a single output port for observation and performs nonlinear spatial filtering by variable parameters Wireless Ad-hoc Community Network (WACNet). Core technology to implement WACNet 6

7 contents introduction background ESPAR antenna signal model of the adaptive antenna; objective function the stochastic approximation method Kiefer-Wolfowitz minimization procedure learning curves, simulation results and performance analysis further development. blind (unsupervised) algorithm conclusion 7

8 background 1/3 An adaptive antenna in general consists of an antenna array and an adaptive processor : 1. receive a signal at each element 2. weight each and sum them up 8

9 background 2/3 two basic receiver architect. ABF-electro magn. coupling among array elements. 1., 2 DBF implies a LN RF ampl., frequency conv., A/D conv. 1. receive a signal at each element 2. weight each and sum them up are done in space, not in circuits. The weights are controlled by equival. elem. length and their coupling strength 9

10 background 3/3 ABF works upon electromagnetic coupling among array elements and ESPAR antenna is an example of a pragmatic implementation of ABF (Shishkov, Ohira, Cheng, 2001) Reactively controlled antenna arrays dates back to Harrington, 1978, Dinger, 1984, Scott, 1999 However they don t meet the demand of adaptively canceling interferences and reducing an additive noise. In this lecture adaptive beamforming of the ESPAR antenna is proposed by using normalized mean squared error as an objective function and its minimization via stochastic descent technique in accordance with stochastic approximation theory. 10

11 contents introduction background ESPAR antenna signal model of the adaptive antenna; objective function the stochastic approximation method Kiefer-Wolfowitz minimization procedure learning curves, simulation results and performance analysis further development. blind (unsupervised) algorithm conclusion 11

12 ESPAR antenna 1/3 7-element adaptive ESPAR antenna 12

13 ESPAR antenna 2/3 reactance & admittance matrix The central radiator is excited by an RF signal source with internal voltage ν s and output impedance z s. x m x min Ω to x max Ω x = [x 1,x 2,,x M ] - reactance vector X = diag[z s, jx 1,, jx M ] Y = [y kl ] y 0 I - diagonal reactance matrix - admittance matrix - first column of Y - identity matrix The voltages and currents are mutually related by electromagnetic coupling among the radiators and the following scalar circuit equations hold v 0 = v s - z s i 0 v m = jx m i m, m=1,2,,m 13

14 ESPAR antenna 3/3 Current weight vector Employing voltage and current vectors v = [ν 0,ν 1,, ν M ] and i = [i 0,i 1,, i M ] the above scalar equations are transformed into a single vector fashion as v = v s u 0 Xi i = Yv i - RF current weight vector nonlinear spatial filtering 14

15 contents introduction background ESPAR antenna signal model of the adaptive antenna; objective function the stochastic approximation method Kiefer-Wolfowitz minimization procedure learning curves, simulation results and performance analysis further development. blind (unsupervised) algorithm conclusion 15

16 signal model of the adaptive antenna; objective function Signal model of the adaptive antenna 1/3 ϕ m = 2π(m 1) M, m = 1,2,,6 - θ - angle of DOA azimuth angle s p (t) - waveform of the p-th user terminal; ν(t) is complex valued AGN 16

17 signal model of the adaptive antenna; objective function 2/3 ε(t) = y(t) - d(t) Objective Function MSE(y,d)= E[ε(t)ε(t)*] =E y(t) d(t) 2 NMSE(y,d) = MSE(gy,d) = 1 ρ yd 2 17

18 signal model of the adaptive antenna; objective function Objective Function Let s have y(n), d(n) - N-dimensional vectors that are discrete-time samples of y(t) and d(t).then the following objective function has to be minimized 3/3 n=1,2,,n ; x R M J(w) - quadratic (convex) in conventional adaptive array J(x) non-convex y(x)=f (I [YX] + [YX] 2 [YX] 3 ) 18

19 contents introduction background ESPAR antenna signal model of the adaptive antenna; objective function the stochastic approximation method Kiefer-Wolfowitz minimization procedure learning curves, simulation results and performance analysis further development. blind (unsupervised) algorithm conclusion 19

20 the stochastic approximation method J(w 1 ) deterministic optimization surface J(x 1 ) random w 1 x 1 local minima global minima 20

21 the stochastic approximation method Let J(x k ) denote the large sample average yield (N ) of Obj. Func. in the k th run (iteration) when the parameter is x k. The actual observed (not averaged or small sample averaged) yield J N (x k ) = J(x k ) + ξ k may fluctuate from run to run ξ k = J N (x k ) -J(x k ) ξ k observation noise don t confuse by AGN ν(n) SA : recursive Monte-Carlo algorithm for approximating the best value of x k 21

22 contents introduction background ESPAR antenna signal model of the adaptive antenna; objective function the stochastic approximation method Kiefer-Wolfowitz minimization procedure learning curves, simulation results and performance analysis further development. blind (unsupervised) algorithm conclusion 22

23 Kiefer-Wolfowitz minimization procedure 1/5 If J(x) were known and smooth the basic Newton procedure can be used x k+1 = x k H -1 (x k )g(x k ) g(x) = J(x) and H(x) = 2 J(x) The solution is searched as a noisy finite difference form of the above Eq. Let {Δx k } - sequence of positive finite difference intervals of reactances {x i,i=1,.., M}, Δx k 0 as k, e i denote the unit vector in the i th coordinate direction J (x ) = k th actual noise corrupted observation 23

24 Kiefer-Wolfowitz minimization procedure 2/5 Define the finite difference vector g dn (x k, Δx k ) by i th component and vector observation noise ξ k : ξ k = g dn (x k, Δx k ) g d (x k, Δx k ) 24

25 Kiefer-Wolfowitz minimization procedure 3/5 control algorithm x k+1 = x k -μ k g dn (x k, Δx k ) = x k -μ k [ g d (x k, Δx k ) +ξ k ] x k+1 = x k -μ k g dn (x k, Δx k ) / g dn (x k, Δx k ) μ k 0 {μ k } positive numbers, μ k = in order to help asymptotically cancel the noise effects, and for convergence to the right point or set. 25

26 Kiefer-Wolfowitz minimization procedure 4/5 convergence Define d k = x k x opt, g(x opt ) = 0, x k x opt C with P=1 C in Law (or in Probability (Distribution)) C in MQ sense In many types of applications it is quite restrictive 26

27 Kiefer-Wolfowitz minimization procedure 5/5 control step parameter SA μ k = μ (k + 1) -α Δx k = Δx(k+1) -γ 0 < γ < α 1 The influence of {μ, Δx,α,β,γ } on the stability, convergence, noise effect, bias term etc is subject of special study in the literature of SA STC μ k = μ[1+( k τ )] -1 Δx k = Δx(k+1) -γ 27

28 contents introduction background ESPAR antenna signal model of the adaptive antenna; objective function the stochastic approximation method Kiefer-Wolfowitz minimization procedure learning curves, simulation results and performance analysis further development. blind (unsupervised) algorithm conclusion 28

29 learning curves, simulation results and performance analysis The total number of symbols in the training sequence can be determined as N(2M+1)K or N(M+1)K 29

30 Adapted array pattern for SNR=20dB DOA: SOI:

31 SINR versus μ, SNR=30 db 31

32 Curves of NMSE for several runs (N=20) 32

33 contents introduction background ESPAR antenna signal model of the adaptive antenna; objective function the stochastic approximation method Kiefer-Wolfowitz minimization procedure learning curves, simulation results and performance analysis further development, blind (unsupervised) algorithm conclusion 33

34 further development, blind (unsupervised) algorithm 34

35 Adapted array pattern for SNR=20dB DOA: SOI:

36 contents introduction background ESPAR antenna signal model of the adaptive antenna; objective function the stochastic approximation method Kiefer-Wolfowitz minimization procedure learning curves, simulation results and performance analysis further development. blind (unsupervised) algorithm conclusion 36

37 conclusion 1/5 In this lecture, we propose a novel approach to create algorithms for the beamforming of one kind of unconventional antenna array- ESPAR antenna which is the core technology to implement Wireless Ad-hoc Community Network By this remarkable research study (Shishkov, Ohira, Cheng, 2001 Advanced Telecommunications Research Institute International, Kyoto, Japan) we have made a pioneering work of creating algorithm of ESPAR antenna. This was hard to do but it was made by inspiration. A novel approach based on SA theory is proposed to adaptive beamforming of ESPAR antenna as a nonlinear spatial filter. Theoretic study, simulation results and performance analysis 37 are presented for the adaptive control algorithm

38 conclusion 2/5 As shown, the algorithm can be easily transformed to a blind (unsupervised) algorithm in which there is no need of training signal. Direction-of-Arrival (DoA) estimation is another key function of adaptive antennas. The technique of conventional DoA estimation from (Shishkov, 2005) can be easily applied to the single-port configuration of ESPAR antenna. In the next figure one can see the block diagram and fabricated prototypes of the ESPAR antenna 38

39 conclusion 3/5 39

40 conclusion 4/5 40

41 conclusion 5/5 Another important issue was achieved - an application of our blind (unsupervised) algorithm to the control of beam in microwave power transmission (Shishkov, Matsumoto, Hashimoto ) which open the door to as a clean, inexhaustible large-scale base-load power supply. 41

42 42