making it work: radiowave propagation 1 chapter 4 - making it work multiple access radiowave...
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Chapter 4 - Making It WorkMultiple AccessRadiowave PropagationSignal ProcessingThe Network
Making it work: Radiowave propagation
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Radiowave PropagationMultipath- radiowaves can reach mobile user by many paths
Making it work: Radiowave propagation
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Signal strength Signal varies inFast fading due to multipath fadingMedium fading due to geographical features or ground coverSlow fading due to power fall-off with distance Signal varies inFast fading due to multipath fadingMedium fading due to geographical features or ground coverSlow fading due to power fall-off with distance Signal varies inFast fading due to multipath fadingMedium fading due to geographical features or ground coverSlow fading due to power fall-off with distance
Making it work: Radiowave propagation
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Multipath fadingSignals from different paths may add or cancel User in a 'multipath environment' or a fading environment
Making it work: Radiowave propagation
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Cell planningBT CellNetUK coverage
Making it work: Radiowave propagation
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Cell planningProblem
1To establish edge of cellto enable placement of main base stations- do calculations using simple propagation models- do measurements and derive simple equations
2To 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
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Slow Signal Reduction-Propagation in Free SpaceFree space loss equation
Pd = P.G1.G2.(/4..d)2
where Pd = power receivedP = power transmittedG1,2 = antenna gains = wavelengthd = distance between antennas
Making it work: Radiowave propagation
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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 = 1kmAnswer L = 76dB and P = -18dBm
Making it work: Radiowave propagation
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Slow Signal Reduction - Propagation over ground
Making it work: Radiowave propagation
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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 r is the ground reflection coefficient.
Making it work: Radiowave propagation
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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] (5)
Making it work: Radiowave propagation
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If d >> hT, hR, as is usually the case, then R0/R1 1and 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
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Furthermore, for d >> hT, hR, we have:
and (8)
Making it work: Radiowave propagation
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Using r= - 1 and eqn (8), we can see that the square bracket in eqn (6) becomes (9)
Making it work: Radiowave propagation
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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)(12)
Making it work: Radiowave propagation
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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/d2plane earth signal 1/d4
Making it work: Radiowave propagation
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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 =25kmht.hr = 100m2 (high base station and handheld receiver)Answer P = 16 watts
Making it work: Radiowave propagation
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To improve accuracy, includeland usage factor 0 < L < 1terrain 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 =25kmht.hr = 100m2, L = 0.3, H = 50m
Answer P = 125W
Making it work: Radiowave propagation
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Range of applicability of the two-ray model
Good for VHF band or above (>30MHz)At high frequencies (when wavelength ~ roughness )reflection coefficients not accuratereflection is diffuseAt long range (>25km)earth not flat but spherical
Making it work: Radiowave propagation
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Fast and medium fading-ray tracing methodsFind ray paths includingReflectionsDiffractionsCombinations of the two
Pictures taken fromhttp://www.awe-communications.com/main.html
Making it work: Radiowave propagation
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Diffraction Ray is scattered by any edgeShadow regionIlluminated region
Making it work: Radiowave propagation
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Result from commercial modelling toolDirect ray only
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Direct + 2 reflections + 1 diffractionDirect + 1 reflection
Making it work: Radiowave propagation
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Direct + 6 reflections + diffraction + double diffraction + diffraction/reflection + diffraction/2 reflections
Making it work: Radiowave propagation
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Making it work: Radiowave propagation
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Making it work: Radiowave propagation
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How to model propagation losses? expressions based on analytical results parameters determined by lots of measurements
Making it work: Radiowave propagation
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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
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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
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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
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How to model propagation losses?Simple model.Fig 2.7 shankar
Making it work: Radiowave propagation
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How to model propagation losses?Hatas model.For urban areas
LdB = 69.55 + 26.16.log10fMHz + (44.9 6.55.log10hb).log10d
- 13.82.log10hb a(hm)
whered = 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
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How to model propagation losses?Hatas model.For large cities
a(hm) = 3.2[log10(11.75.hm)]2 4.97f > 400MHz
For small and medium cities
a(hm) = [1.1.log10f 0.7].hm [1.56.log10f-0.8]
Making it work: Radiowave propagation
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How to model propagation losses?Hatas model.For suburban areas
LdB = Lp 2[log10(fMHz/28)]2
whereLp = loss for small to medium cities(from previous expression)
Making it work: Radiowave propagation
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How to model propagation losses?Hatas model.For rural areas
LdB = Lp 4.78.[log10fMHz]2 + 18.33.log10fMHz 40.94
whereLp = loss for small to medium cities(from previous expression)
Making it work: Radiowave propagation
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Results - Note that large and small to medium loss different by only 1dB
Making it work: Radiowave propagation
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How to model propagation losses?Hatas 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
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How to model propagation losses?Hatas model.We know that from simple model
Pr(d) (1/d)v
At a distance dref
Ploss(dref) 10.v.log10(dref)andPloss(d) 10.v.log10(d)so thatv = [Ploss(d) - Ploss(dref)] / 10.[log10(d) - log10(dref)]
Making it work: Radiowave propagation
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How to model propagation losses?Hatas model.Examples of value of v
For d > 5km
large cityv = 4.05small to medium city v = 4.04suburbsv = 3.3ruralv = 2.11
Making it work: Radiowave propagation
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Cell PlanningBT CellNetUK coverage
Making it work: Radiowave propagation
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Network PlanningMicrowave links to mobile switching centres
Making it work: Radiowave propagation
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The Multipath EnvironmentPropagation mechanismsDiffractionMultiple diffractionReflectionVertex diffractionScattered paths with long delays
Making it work: Radiowave propagation
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The Multipath EnvironmentSignal varies inFast fading due to multipath fadingMedium fading due to geographical features or ground coverSlow fading due to power fall-off with distance
Making it work: Radiowave propagation
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Movement creates fadingimportant to know statistics of fading to optimally design system
Making it work: Radiowave propagation
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The Multipath Environment-FadingUrban ChannelsRayleigh probability density function describes short term fading if mobile moves characteristic of deep urban environments
Making it work: Radiowave propagation
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To create a suitable statistical model, assume
No direct rayMany (>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
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wherea = received signal envelope 2 = variance,( = standard deviation)and22 = mean square value
This is a Rayleigh statistical modelThen probability of received signal envelope, a, is
Making it work: Radiowave propagation
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Characteristics Zero probability of zero signal Zero probability of infinite signal Peak value at Non symmetrical shape
Making it work: Radiowave propagation
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Movement creates fadingsystem will have threshold above which signal will be detectable; below it will be lostKey parameters outage probability level crossing rate average duration of fadesAll needed to choose best bit rates, word lengths and coding schemes
Making it work: Radiowave propagation
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The outage probability is the probability that the signal level will be below the threshold level, athresh.Outage Probability
Making it work: Radiowave propagation
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ExampleIf average signal is 100W, what is probability of outage, if athesh = 50 W.
Now remember that 22 = mean square envelope value= c x average powerand also a2thresh = square threshold envelope value= c x threshold powerSo
Pout = [1 exp(-50/100)] = 0.3935
Outage Probability
Making it work: Radiowave propagation
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Level crossing rate and average duration of fadesRate of positive (or negative) going crossings and average time spent below threshold in fades must be quantified
Making it work: Radiowave propagation
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Level crossing rateTo 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, thenthenwhereNot able to prove in scope of course
Making it work: Radiowave propagation
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Level crossing rateNote 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
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Average duration of fadesAverage duration of fades is average period of fade below threshold, that is ave. of 1, 2, 3, etc. It is given by the outage probability / level crossing rate.
Making it work: Radiowave propagation
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Average duration of fadeswhere
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CalculationAssume, fm = 100Hz, (fast car) = 1 (signal envelope at RMS value), so exp(1) = 2.72
Making it work: Radiowave propagation
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Statistics for Non-Urban CasesOther 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
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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
Making it work: Radiowave propagation
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Lognormal probability distributiondescribes case when multiple scattering of single ray occurs
f(P) = (1/(22P2)).exp[-ln2(P/P0)/22]
Making it work: Radiowave propagation
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The Multipath Environment - DispersionRays arriving at different timesresult in pulse broadening or timedispersionTransmitted pulseReceived pulses and envelopeEffect is to produce Inter symbol interference
Making it work: Radiowave propagation
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The Multipath Environment - DispersionRms 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
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The Multipath Environment - DispersionIf 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 wavelengthFading rate, R = 2v/ wherev = velocity of mobileExample, freq = 100MHz, v = 34mph = 15m/s, R = 10Hz
Making it work: Radiowave propagation
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The Multipath Environment - DispersionIf mobile is moving then frequency dispersion will take placeRays 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 wherefc = the carrier frequency
Making it work: Radiowave propagation
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The Multipath Environment - DispersionNow to preserve powerthe power spectral density must equal the power arrival densitysoS(f).df = P().d
Assuming equal arrival probability from all angles, then
S(f) = d/dfNowd/df = -1/(fm.sin ) = -(1/fm) / (1 cos2 )SoS(f) = -(1/fm) / [1 (f - fc)2/fm2]
Making it work: Radiowave propagation
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The Multipath Environment - DispersionReceived frequencies will besmeared over range from fm to fm
Channel coherence time given by
Tc = 9/16fm
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
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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
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DiversityCan be done at base station or mobilebut normally at base station to keep cost of handsets down
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Key concept is sampling of multipath waveform at two pointsor creation of two uncorrelated waveforms in multipath environment
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Base station diversity (mainly down-link)two antennas create two uncorrelatedmultipath field environments at mobileHandset diversity (mainly down-link)two antennas sample multipath field environments at two uncorrelated points
Making it work: Radiowave propagation
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Typical diversity base station antennas(a) USA, (b) UK, (c) Japan
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How to combine signals from multiple antennas in a diversity systemSwitching
SimpleCheapLeast effective
Improvement in SNRSo for M = 2D(M) = 1.5
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(b) Cophasing and summing
Better performanceBut requires phase shifters
Improvement in SNRSo for M = 2D(M) = 1.8
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(c) Maximal ratio combining
Best performanceBut requiresphase shifters and variable gain amps
Improvement in SNRSo for M = 2D(M) = 2.0
Making it work: Radiowave propagation
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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
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Making it work: Radiowave propagation
signals from different paths may add or cancel giving large variations in signal strength as user moves user is said to be in a 'multipath environment' of a fading environment "Radiowaves, at the frequencies used in mobile communications systems, can be considered to travel in straight lines. However when they meet an obstacle, such as building, the wave may be reflected or it may be diffracted around the bent building edge. Other obstacles such as trees may attenuate the signal. This is an urban area where there are many buildings the radiowave energy may reach the receiver by many simultaneous paths. The signals incident from these paths may add or cancel, depending on the path length. Such reinforcement or cancellation gives rise to large variations of signal strength, within the region surrounding the receiver. This region is thus said to be a 'multipath' of 'fading' environment. More material on the multipath effect can be found at .
We assume that proximity of the ground does not influence the individual radiation patterns of the two antennas, f1(q) and f2(q), and that the two antennas are in the two antennas are in the far-field of each other.
The predictions of the two-ray model are generally good for frequencies in the VHF band or above (> 30 MHz). At lower frequencies the model breaks down because it does not take into account the surface wave supported by the air-ground interface, and the non-specular nature of the ground reflection. At high frequencies when the wavelength becomes comparable to the roughness of the ground (i.e. the size of the irregularities on the ground), the Fresnel reflection coefficients (equations (8) and (9)) can no longer be used, as the reflection becomes diffuse. At ranges beyond approximately 10-30 km, the spherical nature of the earth needs to be taken into account explicitly (the maximum range depends on the antenna heights).