Presentation on theme: "Link Budgets and Outage Calculations"— Presentation transcript:
1 Link Budgets and Outage Calculations Dr Costas ConstantinouSchool of Electronic, Electrical & Computer EngineeringUniversity of BirminghamW:E:
2 DecibelsLogarithmic units of measurement suitable for describing both very large and very small numbers convenientlyNamed by telephone engineers in honour of Alexander Graham Bell
3 Why work with DecibelsDecibels can be used to express a set of values having a very large dynamic range without losing the fine detailThey allow gain and signal strengths to be added and subtracted in a link budget calculationThe American mathematician Edward Kasner once asked his nine-year-old nephew Milton Sirotta to invent a name for a very large number, ten to the power of one hundred; and the boy called it a googol. He thought this was a number to overflow people's minds, being bigger than anything that can ever be put into words …
4 Why work with Decibels1 googol =1 googol = log = 10 x 100= 1000 dBdBs are easier to write down!
5 Why work with DecibelsThe figure shows a large carrier and also something else higher up the frequency band which is hardly visibleIf we plot the result in dBm (decibels relative to 1mW – see later) we can see all of the information clearly
6 Decibels A power P can be expressed in decibels by where Pref is the power (unit) to which P is compared
7 DecibelsIf for example P = 20 Watts Pref = 1 Watt then P dB = 13 dBW where the W after the dB denotes a reference value of 1 W. If Pref = 1 milliWatt P dB = 43 dBm where the m after the dB refers to a mW.
8 DecibelsThe decibel can also be used to refer to the power gain or power loss of a componentPinPout
9 DecibelsThus for an amplifier with Pin = 0.1 W Pout = 1 W G dB = 10 dB Similarly if the component is a long cable with Pin = 1 W Pout = 0.1 W then G = –10 dB which represents a loss of 10dB.
10 DecibelsIf the input and output signals are known in voltage or current terms, thenassuming that the impedances at the input and output are the same (Zout = Zin).
12 Decibels Previous chart is useful for converting from numbers to dBs ExamplesPout/Pin = 30 dB= 8 x 102 29 dB= 6 dB= –10 dBMemorising the chart will help you perform most conversions in your head to an accuracy necessary for estimation purposes.
13 Cascaded amplifiers What happens if we have two amplifiers in series? Conclusion – we add gains in dB.PinPoutPintG1G2
14 Cascaded amplifiersExample Pin = 10 mW, Pint = 1 W, Pout = 100 W So G1 = 1/10x10-3 = 100 = 20 dB G2 = 100/1 = 100 = 20 dB And G = 100/10x10-3 = 10,000 = 40 dB G = G1 + G2PinPoutPintG1G2
15 Cascaded attenuatorsWhat happens if we have two attenuators in series?Conclusion – losses are negative gains in dBConclusion – can add losses in dBs.PinPoutPintG1G2
16 Cascaded attenuatorsExample Pin = 10 W, Pint = 1 W, Pout = 1 mW So G1 = 1/10 = 0.1 = –10 dB G2 = 10–3/1 = 10–3 = – 30 dB And G = 10–3/10 = 10–4 = – 40 dB G = G1 + G2
17 Cascaded amplifier & attenuator What happens if we have an amplifier followed by a loss, such as a long cable?Conclusion – now we can proceed to do real systemsPinPoutPintG1G2
18 Cascaded amplifier & attenuator PinPoutPintG1G2Example Pin = 1 mW, Pint = 1 W, Pout = 1 mW So G1 = 1/10–3 = 1000 = 30 dB G2 = 10–3/1 = 10–3 = –30 dB And G = 10–3/10–3 = 1 = 0 dB G = G1 + G2
19 Link budgets G = G1 + G2 is a rudimentary system link budget Link budgets are used in all RF systemsto get rough feel for viabilityto fine tune actual designPinPoutPintG1G2
20 Example – submarine cable communications Birmingham to BeijingDistance = 8171 kmCable attenuation = 0.3 dB/kmVelocity of electromagnetic wave in cable = c/1.46Delay = 1.46 x 8191 x 103 / (3 x 108) sAttenuation = 0.3 x 8171 dB = 2451 dBAttenuation is bigger than a googol – it will never work!
21 Simple link budget example PinPoutP1G1L2L1P2P3P4amplaser diodedetector diodefibreWant a zero gain system, so they can be cascaded to cover long distanceAmp to get input signal power big enough to drive diodegain = 20 dBLaser converts digital signal to lightconversion gain = –20 dB, (or loss = 20 dB) –20Fibre 100 km long gives 100 x 0.3 = 30 dBso gain = –30 dB –30Diode converts light back to digital signalAmp to bring signal back to input levelgain = 50 dBOverall gain dB
22 Example – geosynchronous satellite link 35,855 kmBirmingham to Beijing(assuming single satellite trip, up and down)Delay = 2 x 35,855 x 103 / 3 x 108 s= 0.23 sBut what is link budget?
23 Link budgets – satellite downlink model TransponderEarth station RxΣFree space + other lossesantennanoise
24 Link budgets – downlink model Satellite transponder output power = PtAntenna gain = GtEffective isotropic radiated power = EIRP = PtGtFree space path loss = (λ/4πd)2 = LpAtmospheric loss = LaAntenna loss (feeder loss, pointing error, etc) = Lat, LarClear air margin = MpCoverage contour margin = Mc
26 Link budgets – downlink model Power at receiverS = EIRP + Gr – Lp – La – Lat – Lar (dBW)(all terms in dBs)Noise at receiverN = kTsB = k(Ta + Te)B (dBW)Note that Ts = Noise temperature of system in KelvinTa = Noise temperature of antenna in KTe = Noise temperature of receiver in K
27 Typical link budgets12/14 GHz link; satellite antenna = earth antenna = 1.8m, low cost earth stationup linkdown linkPt tx power2520dBWGt tx ant gain4644dBLat tx ant loss-1Lp free space loss-208-206La atmos loss-0.5-0.6Gr rx ant gainLar rx ant lossPr rx power-93.5-100.6Note – up/down link values different due to different frequencies
31 NoiseElectromagnetic noise is produced by all bodies above absolute zero temperature (0 K)ExamplesEarthSkyAtmosphereSunGalaxyUniverseMan-made noiseInterference
32 Antenna temperatureThe summation is taken over all bodies in the field of view of the antennagi = fraction of total antenna sensitivity (gain) in direction of body i.xi = greyness of body i (xi = 1 for a black body)Ti = temperature of body i (K)Li = transmission factor from body i to antenna
33 Sample noise calculation for typical satellite earth station at 20 GHz SourcegixiLiTi (K)gxTLsky0.70.991.05034.6earth0.330027.0sun0.0050.0170000.4sky-earth0.99.(1.0 – 0.3)10.4sun-earth14.5Tant86.9
34 Receiver noise temperature Assuming no loss in the connection between antenna and receiver, the total noise temperature (at input to receiver)where Te, F = effective noise temp and noise figure of receiverT0 = reference temp for noise figure (normally 290 K)Noise power (at input to receiver)where k = Boltzmann’s constant = 1.38 x JK–1B = receiver bandwidth
35 Typical link budgetsup linkdown linkPr rx power-93.5-100.6dBWT noise temp8001000KB bandwidth36MHzN noise power-124-123S/N at rx30.522.4dBS/N required10.0Mp clear air margin20.512.4La atmospheric loss in bad storm10dBS/N at rx20.512.4S/N required10.0Mp margin10.52.4Note – down link margin only just acceptable in storm
36 Outage calculationsIn the case of mobile radio the path loss is not known fully; it is described bya deterministic component anda stochastic (randomly varying) componentThe overall link budget is then computed from a desirable BER as
37 Area mean path loss model example The Hata-Okumura model, derives from extensive measurements made by Okumura in 1968 in and around Tokyo between 200 MHz and 2 GHzThe measurements were approximated in a set of simple median path loss formulae by HataThe model has been standardised by the ITU as recommendation ITU-R P.529-2
38 Area mean path loss model example The model applies to three clutter and terrain categoriesUrban area: built-up city or large town with large buildings and houses with two or more storeys, or larger villages with closely built houses and tall, thickly grown treesSuburban area: village or highway scattered with trees and houses, some obstacles being near the mobile, but not very congestedOpen area: open space, no tall trees or buildings in path, plot of land cleared for 300 – 400 m ahead, e.g. farmland, rice fields, open fields
40 Area mean path loss model example The Hata-Okumura model is only valid for:Carrier frequencies: 150 MHz fc 1500 MHzBase station/transmitter heights: 30 m hb 200 mMobile station/receiver heights: 1 m hm 10 mCommunication range: R > 1 kmA large city is defined as having an average building height in excess of 15 m
41 Local mean modelThe departure of the local mean received power from the area mean prediction is given by a multiplicative factor which is found empirically to be described by a log-normal distributionThis is the same as an additive deviation in dB from the area mean model being described by a normal distribution
42 Local mean modelWorking in logarithmic units (decibels, dB), the total path loss is given bywhere Xs is a random variable obeying a lognormal distribution with standard deviation s (again measured in dB)If x is measured in linear units (e.g. Volts)where mx is the mean value of the signal given by the area mean model
43 Outage calculations Cumulative probability density function Xmax plays the role of the link margin that you can afford to lose and still maintain an acceptable BER - This is called an outage calculation
44 What next?Attempt tutorial questions on link budgets