Analog Electronics 2 ICS905

Transcription

1 Analog Electronics 2 ICS905 G. Rodriguez-Guisantes Dépt. COMELEC rodrigez/ens/cycle_master/ November 2016

2 2/ 67 Schedule Radio channel characteristics ; Analysis and conception of the couple Tx-Rx ; M-QAM Modulation - theoretical analysis ; Distortions in M-QAM ;

3 3/ 67 Schedule Radio channel characteristics ; Analysis and conception of the couple Tx-Rx ; M-QAM Modulation - theoretical analysis ; Distortions in M-QAM ;

4 4/ 67 Schedule Radio channel characteristics ; Analysis and conception of the couple Tx-Rx ; M-QAM Modulation - theoretical analysis ; Distortions in M-QAM ;

5 5/ 67 Schedule Radio channel characteristics ; Analysis and conception of the couple Tx-Rx ; M-QAM Modulation - theoretical analysis ; Distortions in M-QAM ;

6 6/ 67 Transmitted signal : Radio-channel characteristics Microscopic effects s(t) = Re{u(t).e j2πfct } = I(t) cos(2πf c t) Q(t) sin(2πf c t) f c carrier frequency - u(t) BB with B s Hz. Received Signal : N(t) r(t) = Re α n u(t τ n (t)).e j{2πfc(t τn(t))+φd n } n=0 φ n (t) = 2πf c τ n (t) φ D n, N(t) r(t) = Re ej2πfct. α n u(t τ n (t)).e jφn(t) n=0

7 7/ 67 Transmitted signal : Radio-channel characteristics Microscopic effects s(t) = Re{u(t).e j2πfct } = I(t) cos(2πf c t) Q(t) sin(2πf c t) f c carrier frequency - u(t) BB with B s Hz. Received Signal : N(t) r(t) = Re α n u(t τ n (t)).e j{2πfc(t τn(t))+φd n } n=0 φ n (t) = 2πf c τ n (t) φ D n, N(t) r(t) = Re ej2πfct. α n u(t τ n (t)).e jφn(t) n=0

8 8/ 67 Components of fading n corresponds to a path of length L n τ n = L n /c α n (t) = attenuation. φ D n = 2πf D n (t) dt = Doppler f c, f D n (t) = v cos θn(t) λ, θ n (t) angle relative to the mouvement direction. Paths are solvable if τ j τ i B 1 s

9 9/ 67 Impact of fading If the delay dispersion is small compared to Bs 1 narrowband fading ; If the delay dispersion is big compared to Bs 1 wideband fading ; T s T s Delay spread The delay dispersion is called Delay spread of the channel T m.

10 10/ 67 Impact of fading If the delay dispersion is small compared to Bs 1 narrowband fading ; If the delay dispersion is big compared to Bs 1 wideband fading ; T s T s Delay spread The delay dispersion is called Delay spread of the channel T m.

11 11/ 67 Impact of fading If the delay dispersion is small compared to Bs 1 narrowband fading ; If the delay dispersion is big compared to Bs 1 wideband fading ; T s T s Delay spread The delay dispersion is called Delay spread of the channel T m.

12 12/ 67 Model narrowband If T m T s. If τ i represents the ith delay, so τ i T m : u(t τ i ) u(t). { ( ) } r(t) = Re u(t) e j2πfct α n (t) e jφn(t). n }{{} A(t)

13 13/ 67 Model narrowband If T m T s. If τ i represents the ith delay, so τ i T m : u(t τ i ) u(t). { ( ) } r(t) = Re u(t) e j2πfct α n (t) e jφn(t). n }{{} A(t)

14 14/ 67 In this case T m T s. Model wideband Conclusion : if T m T s ISI

15 15/ 67 Doppler effect This phenomenon represents the variability of the channel in time : The mean dispersion of the frequency beside the carrier is called Doppler spread B D of the channel. We call Coherence time of the channel, the duration of a complete cycle of dynamics induced by the Doppler efect. T c 1/B D

16 16/ 67 Doppler effect This phenomenon represents the variability of the channel in time : The mean dispersion of the frequency beside the carrier is called Doppler spread B D of the channel. We call Coherence time of the channel, the duration of a complete cycle of dynamics induced by the Doppler efect. T c 1/B D

17 17/ 67 A "Resumé" Delay Spread - T m Delay spread give us a good idea of the dispersive characteristics of the channel in time. Doppler Spread - B D Doppler dispersion give us a good idea of the variability of the channel. Parameters Mean delay spread Coherence bandwidth T m B c Coherence time Doppler dispersion T c B D

18 18/ 67 A "Resumé" Delay Spread - T m Delay spread give us a good idea of the dispersive characteristics of the channel in time. Doppler Spread - B D Doppler dispersion give us a good idea of the variability of the channel. Parameters Mean delay spread Coherence bandwidth T m B c Coherence time Doppler dispersion T c B D

19 19/ 67 A "Resumé" Delay Spread - T m Delay spread give us a good idea of the dispersive characteristics of the channel in time. Doppler Spread - B D Doppler dispersion give us a good idea of the variability of the channel. Parameters Mean delay spread Coherence bandwidth T m B c Coherence time Doppler dispersion T c B D

20 20/ 67 Channel models

21 21/ 67 "Etat de l art"

22 22/ 67 Scheme of Tx-Rx

23 23/ 67 Scheme of Tx-Rx

24 24/ 67 Scheme of Tx-Rx

25 25/ 67 Scheme of Tx-Rx

26 26/ 67 Baseband Modulation Transmitted Signal : s(t) = Re{u(t).e j2πfct } = I(t) cos(2πf c t) + j.q(t) sin(2πf c t) f c carrier frequency - u(t) baseband signal. u(t) = I(t) + j.q(t) Complex representation I(t) In phase component Q(t) Quadrature phase component

27 27/ 67 Baseband modulation Digital modulation : build u(t) as a functions of source(discrete) states changes. Heuristic approach : {α n } state sequence of source u(t) impulse superposition! Example : S maxentropic binary source, {α n } = {a n } = A + A + A A A + A... u(t) = n a n.h(t nt )

28 28/ 67 Baseband modulation Digital modulation : build u(t) as a functions of source(discrete) states changes. Heuristic approach : {α n } state sequence of source u(t) impulse superposition! Example : S maxentropic binary source, {α n } = {a n } = A + A + A A A + A... u(t) = n a n.h(t nt )

29 29/ 67 Baseband modulation Digital modulation : build u(t) as a functions of source(discrete) states changes. Heuristic approach : {α n } state sequence of source u(t) impulse superposition! Example : S maxentropic binary source, {α n } = {a n } = A + A + A A A + A... u(t) = n a n.h(t nt )

30 Baseband modulation u(t) is built in two operations : bits amplitudes ; amplitudes waveforms (thanks h(t)!). In this example : I(t) = n a n.h(t nt ), Q(t) = 0. 30/ 67

31 31/ 67 Baseband modulation How to choose {a n }? Modulator architecture simplicity ; Spectral efficiency (η = D/BW ) ; Demodulator architecture simplicity ; Synchronization simplicity ; Probability of error (P b ) ; Robustness to RF imperfections.

32 32/ 67 Baseband modulation How to choose {h(t)}? simplicity of the BB filter ; Spectral efficiency (η = D/BW ) ; ISI (Nyquist) ; Power amplifier performance ; PAPR.

33 33/ 67 Vectorial description of {a n } Amplitudes {a n } are represented by real or complex numbers In the previous case : 0 A 1 +A Viewed in the complex plane I Q, this modulation can be represented by :

34 34/ 67 Vectorial description of {a n } Each «vector» carries 1 information bit Only one complex dimension is required!

35 35/ 67 Vectorial description of {u(t)} h(t) do the temporal link between the discrete vectors. Two ways to realize h(t) : h(t) limited in time h(t) 0 t [0, T ) ; h(t) Nyquist. h(nt ) = { 1 pour n = 0 ; 0 n 0.

36 36/ 67 Vectorial description of {u(t)}

37 37/ 67 Vectorial description of {u(t)}

38 38/ 67 u(t) C u(t) = n a n.h(t nt ) a n = {A + ja; A + ja; A ja; A ja}

39 39/ 67 u(t) C

40 40/ 67 Generalization to the M th order

41 41/ 67 Advantages of order M Each complex symbol represents : N = log 2 M bits T s = N.T b R = D N this means a great economy in bandwidth B w! Unfortunately, a significant increase in E b /N 0 to have the same performances!

42 42/ 67 Spectral efficiency

43 43/ 67 M-QAM Modulation - theoretical analysis Emitted signal s(t) = n a n h t (t nt ) Received signal r(t) = n a n h Rx (t nt ) + b(t) où h Rx (t) = h t (t) h c (t) h r (t) Sampled received signal r(kt + τ) = n a n h Rx (kt + τ nt ) + b(kt + τ)

44 44/ 67 M-QAM Modulation - theoretical analysis (2) r(k) = n a n h Rx (k n) + b(k) r(k) = h Rx (0).a k + a n h Rx (k n) + b(k) }{{}}{{} n k symbole k }{{} bruit IES H Rx (f + k T ) = T.h Rx(0) k H Rx (f) = { T f 1 2T 0 f > 1 2T.

45 45/ 67 M-QAM Modulation - theoretical analysis (3) T H Rx (f) = T 2 ( 1 sin[ πt α (f 1 2T )] ) Raised cosine filter 0 f 1 α 1 α 2T h Rx (t) = cos(απt/t ) 1 4α 2 t 2 sinc(t/t ). /T 2 2T < f < 1+α 2T.

46 46/ 67 M-QAM Modulation - Performance in AWGN

47 47/ 67 M-QAM Modulation - Structure of Tx/Rx

48 48/ 67 Distortions Distortion sources : channel linear distortion ; Tx distortions ; Rx distortions.

49 49/ 67 Channel distortions - M-QAM Possible sources : bandwidth limitation ; frequency selectivity (fading ) ; If B c 1 T ISI! ISI impact on Tx signal At sampling times, signal is not at RV!

50 50/ 67 Channel distortions - M-QAM Possible sources : bandwidth limitation ; frequency selectivity (fading ) ; If B c 1 T ISI! ISI impact on Tx signal At sampling times, signal is not at RV!

51 51/ 67 Channel distortions - M-QAM Possible sources : bandwidth limitation ; frequency selectivity (fading ) ; If B c 1 T ISI! ISI impact on Tx signal At sampling times, signal is not at RV!

52 52/ 67 Example - BPSK

53 53/ 67 Example - QPSK

54 54/ 67 Impact of ISI - Dispersion diagrams

55 55/ 67 Impact of ISI - Dispersion diagrams

56 56/ 67 Dispersion diagrams - 16-QAM

57 57/ 67 P symb - M-QAM in Rayleigh chanel

58 58/ 67 Equalisation The idea consists to suppress the distortion induced by channel. two ways to solve this problem : frequency domain filtering ; deconvolution in time (with the good IR!). Three techniques are possible : linear equalization ; decision feedback equalization ; sequence estimation equalization.

59 59/ 67 Equalisation The idea consists to suppress the distortion induced by channel. two ways to solve this problem : frequency domain filtering ; deconvolution in time (with the good IR!). Three techniques are possible : linear equalization ; decision feedback equalization ; sequence estimation equalization.

60 60/ 67 Equalisation The idea consists to suppress the distortion induced by channel. two ways to solve this problem : frequency domain filtering ; deconvolution in time (with the good IR!). Three techniques are possible : linear equalization ; decision feedback equalization ; sequence estimation equalization.

61 61/ 67 Linear equalization Model It s a linear filter with IR : c(kt ) = +N k= N c(k).z kt

62 62/ 67 Zero forcing and MSE criteria Model The filtre coefficients can be calculateur as : suppress the ISI in and sample interval ( N; +N) Zero Forcing ; minimise the mean error distortion EQM.

63 63/ 67 Zero forcing and MSE criteria If h(n) = y(n) c(n), we call Mean square error ; MSE = 1 h 2 (0) + k= ;k 0 To minimize the ISI, minimise the MSE MSE = ɛ = + k= ;k 0 h 2 (n) h 2 (n) h 2 (0) This is a quadratic fonction of the coefficients classic problem in spectral estimation (Levinson-Durbin).

64 64/ 67 Zero forcing and MSE criteria If h(n) = y(n) c(n), we call Mean square error ; MSE = 1 h 2 (0) + k= ;k 0 To minimize the ISI, minimise the MSE MSE = ɛ = + k= ;k 0 h 2 (n) h 2 (n) h 2 (0) This is a quadratic fonction of the coefficients classic problem in spectral estimation (Levinson-Durbin).

65 65/ 67 Zero forcing and MSE criteria If h(n) = y(n) c(n), we call Mean square error ; MSE = 1 h 2 (0) + k= ;k 0 To minimize the ISI, minimise the MSE MSE = ɛ = + k= ;k 0 h 2 (n) h 2 (n) h 2 (0) This is a quadratic fonction of the coefficients classic problem in spectral estimation (Levinson-Durbin).

66 66/ 67 Example MSE-16-QAM, 3 coeffs channel

67 67/ 67 The End