Transcript chapter4+5
Chapter 4 - Making It Work Multiple Access Radiowave Propagation Signal Processing The Network Making it work: Radiowave propagation 1 Radiowave Propagation • Multipath- radiowaves can reach mobile user by many paths Making it work: Radiowave propagation 2 Signal strength Signal varies in • Fast fading – due to multipath fading • Medium fading – due to geographical features or ground cover • Slow fading – due to power fall-off with distance Making it work: Radiowave propagation 3 Multipath fading • Signals from different paths may add or cancel • User in a 'multipath environment' or a fading environment Making it work: Radiowave propagation 4 Cell planning BT CellNet UK coverage Making it work: Radiowave propagation 5 Cell planning Problem 1 To establish edge of cell to enable placement of main base stations - do calculations using simple propagation models - do measurements and derive simple equations 2 To predict signal level within cell to discover if ‘fill-ins’ are needed - do difficult ray tracing models using reflection, diffraction, etc - do measurements Making it work: Radiowave propagation 6 Slow Signal Reduction -Propagation in Free Space Free space loss equation Pd = P.G1.G2.(/4..d)2 where Pd = power received P = power transmitted G1,2 = antenna gains = wavelength d = distance between antennas Making it work: Radiowave propagation 7 Putting the loss factor (4..d / )2 in dBs LdB = 32 + 20.log10fMHz + 20.log10dkm So that Pr = Pt + G1 + G2 - LdB Assuming a receiver noise, Nr, and that a signal to noise ratio of S is required. Then P > S + Nr + L – G1 – G2 Example, Find P for S = 20dB, Nr = -120dBm, G1 = G2 = -3dBi, f = 150MHz, d = 1km Answer L = 76dB and P = -18dBm Making it work: Radiowave propagation 8 Slow Signal Reduction - Propagation over ground Making it work: Radiowave propagation 9 • Direct wave: Ed = A.exp(-j.k.r0)/4..r0 (1) • Ground reflected wave: Er = A..exp(-j.k.r1)/4..r1 (2) where A is a constant that contains antenna gains and transmit power level and is the ground reflection coefficient. Making it work: Radiowave propagation 10 Total received wave: Etot = Ed + Er (3) Substituting from eqn (1) and (2) Etot = A. exp(-j.k.r0)/4..r0 . [1 + .exp(-j.k.(r1 - r0)).r0/r1] (4) or Etot = Ed.[1 + .exp(-j.k.(r1 - r0)).r0/r1] Making it work: Radiowave propagation (5) 11 If d >> hT, hR, as is usually the case, then R0/R1 1 and expression (5) simplifies to: Etot = Ed.[1 + .exp(-j.k.(R1 - R0))] (6) Now for low angle incidence on the ground .exp(j.) = -1 Making it work: Radiowave propagation 12 Furthermore, for d >> hT, hR, we have: (7) 2 and ( 1 Making it work: Radiowave propagation )2 (8) 13 Using = - 1 and eqn (8), we can see that the square bracket in eqn (6) becomes (9) Making it work: Radiowave propagation 14 Thus putting eqn (9) into eqn (5) Etot = 2.Ed.sin(k.ht.hr/d) (10) or in power terms Ptot = 4.Pd. sin2(k.ht.hr/d) (11) Now Pd = P.G1.G2.(/4..d)2 Thus Ptot = 4.P.G1.G2.(/4..d)2. sin2(2..ht.hr/ .d) Making it work: Radiowave propagation (12) 15 It can be seen that for grazing incidence d >> hT, hR and thus sin2(2..ht.hr/ .d) = (2..ht.hr/ .d)2 and Ptot = P.G1.G2.(ht.hr/d2)2 (13) Note that free space signal 1/d2 plane earth signal 1/d4 Making it work: Radiowave propagation 16 Loss factor is LdB = 40 log10d – 20 log10(ht.hr) So that Pr = Pt + G1 + G2 - LdB Example, Find P for S = 20dB, Nr = -120dBm, G1 = G2 = -3dBi, f = 150MHz, d =25km ht.hr = 100m2 (high base station and handheld receiver) Answer P = 16 watts Making it work: Radiowave propagation 17 To improve accuracy, include land usage factor 0 < L < 1 terrain height difference between tx and rx, H So LdB = 40 log10d – 20 log10(ht.hr) + 20 + fMHz/40 +1.08.L – 0.34.H Example, Example, Find P for S = 20dB, Nr = -120dBm, G1 = G2 = -3dBi, f = 150MHz, d =25km ht.hr = 100m2, L = 0.3, H = 50m Answer P = 125W Making it work: Radiowave propagation 18 Range of applicability of the two-ray model • Good for VHF band or above (>30MHz) • At high frequencies (when wavelength ~ roughness ) reflection coefficients not accurate reflection is diffuse • At long range (>25km) earth not flat but spherical Making it work: Radiowave propagation 19 Fast and medium fading -ray tracing methods Find ray paths including • Reflections • Diffractions • Combinations of the two Pictures taken from http://www.awe-communications.com/main.html Making it work: Radiowave propagation 20 Diffraction • Ray is scattered by any edge Illuminated region Shadow region Making it work: Radiowave propagation 21 Result from commercial modelling tool Direct ray only Making it work: Radiowave propagation 22 Direct + 2 reflections + 1 diffraction Direct + 1 reflection Making it work: Radiowave propagation 23 Direct + 6 reflections + diffraction + double diffraction + diffraction/reflection + diffraction/2 reflections Making it work: Radiowave propagation 24 Making it work: Radiowave propagation 25 Making it work: Radiowave propagation 26 How to model propagation losses? • expressions based on analytical results • parameters determined by lots of measurements Making it work: Radiowave propagation 27 How to model propagation losses? Simple model. Free space loss Pr = Pt.Gt.Gr. (/4d)2 or putting loss factor (4d / )2 in dBs LdB = 32 + 20.log10fMHz + 10.v.log10dkm (so that Pr = Pt + Gt + Gr – LdB ) where v = 2 Making it work: Radiowave propagation 28 How to model propagation losses? Simple model. Plane earth loss Pr = Pt.Gt.Gr. (/4d)2 .sin2(2ht.hr/d) = Pt.Gt.Gr. (ht.hr /d2)2 or putting loss factor in dBs LdB = 10.v.log10d – 20.log10(ht.hr) (so that Pr = Pt + Gt + Gr – LdB ) where v = 4 Making it work: Radiowave propagation 29 How to model propagation losses? Simple model. In many cases of communications 2<v<4 Lower values of v correspond to rural or sub-urban areas Higher values of v correspond to urban areas Making it work: Radiowave propagation 30 How to model propagation losses? Simple model. Fig 2.7 shankar Making it work: Radiowave propagation 31 How to model propagation losses? Hata’s model. For urban areas LdB = 69.55 + 26.16.log10fMHz + (44.9 – 6.55.log10hb).log10d - 13.82.log10hb – a(hm) where d = separation in km, (must be > 1km) hb, hm = base and mobile antenna heights in m a(hm) = mobile antenna height correction factor Making it work: Radiowave propagation 32 How to model propagation losses? Hata’s model. For large cities a(hm) = 3.2[log10(11.75.hm)]2 – 4.97 f > 400MHz For small and medium cities a(hm) = [1.1.log10f – 0.7].hm – [1.56.log10f-0.8] Making it work: Radiowave propagation 33 How to model propagation losses? Hata’s model. For suburban areas LdB = Lp – 2[log10(fMHz/28)]2 where Lp = loss for small to medium cities (from previous expression) Making it work: Radiowave propagation 34 How to model propagation losses? Hata’s model. For rural areas LdB = Lp – 4.78.[log10fMHz]2 + 18.33.log10fMHz – 40.94 where Lp = loss for small to medium cities (from previous expression) Making it work: Radiowave propagation 35 Results - Note that large and small to medium loss different by only 1dB Making it work: Radiowave propagation 36 How to model propagation losses? Hata’s model. Received power given by Pr(d) (dBm) = Pt – Ploss(d) where Ploss(d) = LdB(dB) for a given d from above expressions Making it work: Radiowave propagation 37 How to model propagation losses? Hata’s model. We know that from simple model Pr(d) (1/d)v At a distance dref Ploss(dref) 10.v.log10(dref) and Ploss(d) 10.v.log10(d) so that v = [Ploss(d) - Ploss(dref)] / 10.[log10(d) - log10(dref)] Making it work: Radiowave propagation 38 How to model propagation losses? Hata’s model. Examples of value of v For d > 5km large city small to medium city suburbs rural Making it work: Radiowave propagation v = 4.05 v = 4.04 v = 3.3 v = 2.11 39 Cell Planning BT CellNet UK coverage Making it work: Radiowave propagation 40 Network Planning Microwave links to mobile switching centres Making it work: Radiowave propagation 41 The Multipath Environment Propagation mechanisms •Diffraction •Multiple diffraction •Reflection •Vertex diffraction •Scattered paths with long delays Making it work: Radiowave propagation 42 The Multipath Environment Signal varies in • Fast fading – due to multipath fading • Medium fading – due to geographical features or ground cover • Slow fading – due to power fall-off with distance Making it work: Radiowave propagation 43 Movement creates fading important to know statistics of fading to optimally design system threshold Making it work: Radiowave propagation 44 The Multipath Environment-Fading Urban Channels Rayleigh probability density function describes short term fading if mobile moves characteristic of deep urban environments Making it work: Radiowave propagation 45 To create a suitable statistical model, assume No direct ray Many (>10) approximately equal amplitude reflected/diffracted rays Rays have random phase and angle of arrival, with • uniform arrival angle distribution 0 < < 360 • uniform arrival phase distribution 0 < < 360 Making it work: Radiowave propagation 46 Then probability of received signal envelope, a, is a f (a ) . exp 2 2 2 a 2 where a = received signal envelope 2 = variance, ( = standard deviation) and 22 = mean square value This is a Rayleigh statistical model Making it work: Radiowave propagation 47 Characteristics • Zero probability of zero signal • Zero probability of infinite signal 0.7 f(a) • Peak value at • Non symmetrical shape 0 5 a Making it work: Radiowave propagation 48 Movement creates fading system will have threshold above which signal will be detectable; below it will be lost Key parameters • outage probability • level crossing rate threshold Making it work: Radiowave propagation • average duration of fades All needed to choose best bit rates, word lengths and coding schemes 49 Outage Probability The outage probability is the probability that the signal level will be below the threshold level, athresh. Pout prob [a a thresh ] pthresh f (a ).da 0 a2 .da . exp 2 2 2 0 a 2 thresh 1 exp 2 2 a thresh a Making it work: Radiowave propagation 50 Outage Probability Example If average signal is 100W, what is probability of outage, if athesh = 50 W. Now remember that 22 = = and also a2thresh = = So mean square envelope value c x average power square threshold envelope value c x threshold power Pout = [1 – exp(-50/100)] = 0.3935 Making it work: Radiowave propagation 51 Level crossing rate and average duration of fades Rate of positive (or negative) going crossings and average time spent below threshold in fades must be quantified Making it work: Radiowave propagation 52 Level crossing rate To find rate, need to know joint probability of signal being at given level, a, and at a given slope (or rate of change of signal), da/dt. Assuming that these are uncorreleated, then da p a , dt then Na where da p(a ). p dt 2 . f m . .exp( 2 ) a 2 . a a RMS Making it work: Radiowave propagation Not able to prove in scope of course 53 Level crossing rate NR 2 . f m . .exp( 2 ) Note NR is dependent on velocity (by fm) and envelope level. Result:NR/fm is number of crossings per wavelength, Peaks when a is on aRMS value and low elsewhere Making it work: Radiowave propagation 54 Average duration of fades Average duration of fades is average period of fade below threshold, that is ave. of τ1, τ2, τ3, etc. It is given by the outage probability / level crossing rate. Making it work: Radiowave propagation 55 Average duration of fades E a Pout Na a2 1 exp 2 2 2 . f m . . exp 2 1 2 . f m . where a 2 . .exp 1 2 a a RMS Making it work: Radiowave propagation 56 Calculation Assume, fm = 100Hz, (fast car) ρ = 1 (signal envelope at RMS value), so exp(1) = 2.72 E 2.72 1 2 .100.1 6.9 m sec Making it work: Radiowave propagation 57 Statistics for Non-Urban Cases Other fading models - Rician Rician probability density function describes short term fading if mobile moves characteristic of suburban and rural environments Same assumptions as Rayleigh, with some direct ray f(a) = (a/2).exp[-(a2 + A02)/22].I[aA0/ 2 ] where A0 is amplitude of direct ray Making it work: Radiowave propagation 58 Rician characterised by K K(dB) = 10log10[A02/22] For K = - Rician becomes Rayleigh, with increasing direct ray K increases and for very large K Rician tends to Gaussian K = 0.8dB 0.7 K = 6dB f(a) K = 14dB 0 a 10 Making it work: Radiowave propagation 59 Lognormal probability distribution describes case when multiple scattering of single ray occurs f(P) = (1/(22P2)).exp[-ln2(P/P0)/22] 0.7 f(P) P 0 Making it work: Radiowave propagation 5 60 The Multipath Environment - Dispersion Rays arriving at different times result in pulse broadening or time dispersion Transmitted pulse Effect is to produce Inter symbol interference Received pulses and envelope Making it work: Radiowave propagation 61 The Multipath Environment - Dispersion Rms delay spread, d, is a measure of the broadening. Thus channel bandwidth is given by Bc = 1/(5d) If Bc > Bm channel is flat fading ( no ISI ) and if Bc < Bm channel is frequency selective ( ISI occurs) where Bm is the message bandwidth Making it work: Radiowave propagation 62 The Multipath Environment - Dispersion If mobile is moving then repetitive fading will take place Assume two rays coming from 0 and 180. Interference will produce a standing wave with /2 wavelength Fading rate, R = 2v/ where v = velocity of mobile Example, freq = 100MHz, v = 34mph = 15m/s, R = 10Hz Making it work: Radiowave propagation 63 The Multipath Environment - Dispersion If mobile is moving then frequency dispersion will take place Rays will be received from all directions and each will experience a Doppler shift of f = (v/).cos where = angle of arrival (0 < < 360) and when = 0, f = fm, the maximum shift, = v/ Assume that the frequency seen by the mobile is f = fc + fm cos where fc = the carrier frequency Making it work: Radiowave propagation 64 The Multipath Environment - Dispersion Now to preserve power the power spectral density must equal the power arrival density so S(f).df = P().d Assuming equal arrival probability from all angles, then S(f) = d/df Now d/df = -1/(fm.sin ) = -(1/fm) / (1 – cos2 ) So S(f) = -(1/fm) / [1 – (f - fc)2/fm2] Making it work: Radiowave propagation 65 The Multipath Environment - Dispersion S(f) Received frequencies will be smeared over range from –fm to fm Channel coherence time given by f Tc = 9/16fm -fm fm Pulse duration is Tp then if Tp < Tc no pulse distortion, channel has slow fading if Tp > Tc distortion occurs, channel has fast fading Making it work: Radiowave propagation 66 Diversity Basic Principle : if two or more independent samples of a random process are taken then these samples will fade in an uncorrelated manner. Diversity Methods Frequency - unacceptable as it would increase spectrum congestion. Polarisation - possible but depends on degree of depolarisation in scattering process. Field - E and H field may be uncorrelated but antenna design may be hard. Space - best method, but needs > antenna spacing. - OK at VHF on vehicles and at > 900 MHz on handsets Making it work: Radiowave propagation 67 Diversity Can be done at base station or mobile but normally at base station to keep cost of handsets down Making it work: Radiowave propagation 68 Key concept is sampling of multipath waveform at two points or creation of two uncorrelated waveforms in multipath environment Making it work: Radiowave propagation 69 Multipath scattering Base station diversity (mainly down-link) area two antennas create two uncorrelated multipath field environments at mobile Handset diversity (mainly down-link) two antennas sample multipath field environments at two uncorrelated points Making it work: Radiowave propagation 70 Typical diversity base station antennas (a) USA, (b) UK, (c) Japan Making it work: Radiowave propagation 71 How to combine signals from multiple antennas in a diversity system (a) Switching • • • Simple Cheap Least effective Improvement in SNR M 1 D( M ) k 1 k So for M = 2 D(M) = 1.5 Making it work: Radiowave propagation 72 (b) Cophasing and summing Better performance But requires phase shifters Improvement in SNR D( M ) 1 4 ( M 1) So for M = 2 D(M) = 1.8 Making it work: Radiowave propagation 73 (c) Maximal ratio combining Best performance But requires phase shifters and variable gain amps Improvement in SNR D( M ) M So for M = 2 D(M) = 2.0 Making it work: Radiowave propagation 74 Switching strategies for diversity systems • switch and stay (until threshold is dropped below). • switch and examine (and keep switching if other SNR is below threshold). • selection diversity (selected best SNR) Making it work: Radiowave propagation 75 Making it work: Radiowave propagation 76