making it work: radiowave propagation 1 chapter 4 - making it work multiple access radiowave...

Chapter 4 - Making It WorkMultiple AccessRadiowave PropagationSignal ProcessingThe Network

Making it work: Radiowave propagation

Radiowave PropagationMultipath- radiowaves can reach mobile user by many paths


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


Multipath fadingSignals from different paths may add or cancel User in a 'multipath environment' or a fading environment


Cell planningBT CellNetUK coverage


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


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


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


Slow Signal Reduction - Propagation over ground


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.


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)


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


Furthermore, for d >> hT, hR, we have:

and (8)


Using r= - 1 and eqn (8), we can see that the square bracket in eqn (6) becomes (9)


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)


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


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


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


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


Fast and medium fading-ray tracing methodsFind ray paths includingReflectionsDiffractionsCombinations of the two

Pictures taken fromhttp://www.awe-communications.com/main.html


Diffraction Ray is scattered by any edgeShadow regionIlluminated region


Result from commercial modelling toolDirect ray only


Direct + 2 reflections + 1 diffractionDirect + 1 reflection


Direct + 6 reflections + diffraction + double diffraction + diffraction/reflection + diffraction/2 reflections


How to model propagation losses? expressions based on analytical results parameters determined by lots of measurements


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


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


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


How to model propagation losses?Simple model.Fig 2.7 shankar


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


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]


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)


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)


Results - Note that large and small to medium loss different by only 1dB


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


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)]


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


Cell PlanningBT CellNetUK coverage


Network PlanningMicrowave links to mobile switching centres


The Multipath EnvironmentPropagation mechanismsDiffractionMultiple diffractionReflectionVertex diffractionScattered paths with long delays


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


Movement creates fadingimportant to know statistics of fading to optimally design system


The Multipath Environment-FadingUrban ChannelsRayleigh probability density function describes short term fading if mobile moves characteristic of deep urban environments


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


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


Characteristics Zero probability of zero signal Zero probability of infinite signal Peak value at Non symmetrical shape


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


The outage probability is the probability that the signal level will be below the threshold level, athresh.Outage Probability


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


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


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


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


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.


Average duration of fadeswhere


CalculationAssume, fm = 100Hz, (fast car) = 1 (signal envelope at RMS value), so exp(1) = 2.72


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


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


Lognormal probability distributiondescribes case when multiple scattering of single ray occurs

f(P) = (1/(22P2)).exp[-ln2(P/P0)/22]


The Multipath Environment - DispersionRays arriving at different timesresult in pulse broadening or timedispersionTransmitted pulseReceived pulses and envelopeEffect is to produce Inter symbol interference


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


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


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


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]


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


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


DiversityCan be done at base station or mobilebut normally at base station to keep cost of handsets down


Key concept is sampling of multipath waveform at two pointsor creation of two uncorrelated waveforms in multipath environment


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


Typical diversity base station antennas(a) USA, (b) UK, (c) Japan


How to combine signals from multiple antennas in a diversity systemSwitching

SimpleCheapLeast effective

Improvement in SNRSo for M = 2D(M) = 1.5


(b) Cophasing and summing

Better performanceBut requires phase shifters



(c) Maximal ratio combining

Best performanceBut requiresphase shifters and variable gain amps



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)



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).

making it work: radiowave propagation 1 chapter 4 - making it work multiple access radiowave...

Documents