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Link Budgets and Outage Calculations Dr Costas Constantinou School of Electronic, Electrical & Computer Engineering University of Birmingham W: www.eee.bham.ac.uk/ConstantinouCC/ E: c.constantinou@bham.ac.uk

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Decibels Logarithmic units of measurement suitable for describing both very large and very small numbers conveniently Named by telephone engineers in honour of Alexander Graham Bell 2

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Why work with Decibels 1.Decibels can be used to express a set of values having a very large dynamic range without losing the fine detail 2.They allow gain and signal strengths to be added and subtracted in a link budget calculation The 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 … 3

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1 googol = 10 000 000 000 000 000 000 000 000 000 000 000 000 000 000 000 000 000 000 000 000 000 000 000 000 000 000 000 000 000 000 000 000 000 1 googol = 10 100 10 log 10 10 100 = 10 x 100 = 1000 dB dBs are easier to write down! 4 Why work with Decibels

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The figure shows a large carrier and also something else higher up the frequency band which is hardly visible If we plot the result in dBm (decibels relative to 1mW – see later) we can see all of the information clearly 5 Why work with Decibels

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Decibels A power P can be expressed in decibels by where P ref is the power (unit) to which P is compared 6

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Decibels If for example P = 20 Watts P ref = 1 Watt then P dB = 13 dBW where the W after the dB denotes a reference value of 1 W. If P ref = 1 milliWatt then P dB = 43 dBm where the m after the dB refers to a mW. 7

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The decibel can also be used to refer to the power gain or power loss of a component 8 P in P out Decibels

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Thus for an amplifier with P in = 0.1 W P out = 1 W G dB = 10 dB Similarly if the component is a long cable with P in = 1 W P out = 0.1 W then G = –10 dB which represents a loss of 10dB. 9

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Decibels If the input and output signals are known in voltage or current terms, then assuming that the impedances at the input and output are the same ( Z out = Z in ). 10

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Decibels 11

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Decibels Previous chart is useful for converting from numbers to dBs Examples P out /P in =10 3 30 dB = 8 x 10 2 29 dB = 4 6 dB = 10 -1 –10 dB Memorising the chart will help you perform most conversions in your head to an accuracy necessary for estimation purposes. 12

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Cascaded amplifiers What happens if we have two amplifiers in series? Conclusion – we add gains in dB. 13 P in P out P int G1G1 G2G2

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Cascaded amplifiers Example P in = 10 mW, P int = 1 W, P out = 100 W So G 1 = 1/10x10 -3 = 100 = 20 dB G 2 = 100/1 = 100 = 20 dB And G = 100/10x10 -3 = 10,000 = 40 dB G = G 1 + G 2 14 P in P out P int G1G1 G2G2

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Cascaded attenuators 15 P in P out P int G1G1 G2G2 What happens if we have two attenuators in series? Conclusion – losses are negative gains in dB Conclusion – can add losses in dBs.

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Cascaded attenuators Example P in = 10 W, P int = 1 W, P out = 1 mW So G 1 = 1/10 = 0.1 = –10 dB G 2 = 10 –3 /1 = 10 –3 = – 30 dB And G = 10 –3 /10 = 10 –4 = – 40 dB G = G 1 + G 2 16

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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 systems 17 P in P out P int G1G1 G2G2

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Cascaded amplifier & attenuator Example P in = 1 mW, P int = 1 W, P out = 1 mW So G 1 = 1/10 –3 = 1000 = 30 dB G 2 = 10 –3 /1 = 10 –3 = –30 dB And G = 10 –3 /10 –3 = 1 = 0 dB G = G 1 + G 2 18 P in P out P int G1G1 G2G2

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Link budgets G = G 1 + G 2 is a rudimentary system link budget Link budgets are used in all RF systems – to get rough feel for viability – to fine tune actual design 19 P in P out P int G1G1 G2G2

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Example – submarine cable communications Birmingham to Beijing – Distance = 8171 km – Cable attenuation = 0.3 dB/km – Velocity of electromagnetic wave in cable = c/1.46 Delay = 1.46 x 8191 x 10 3 / (3 x 10 8 ) s Attenuation = 0.3 x 8171 dB = 2451 dB Attenuation is bigger than a googol – it will never work! 20

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Want a zero gain system, so they can be cascaded to cover long distance Ampto get input signal power big enough to drive diode gain = 20 dB 20 Laserconverts digital signal to light conversion gain = –20 dB, (or loss = 20 dB)–20 Fibre100 km long gives 100 x 0.3 = 30 dB so gain = –30 dB–30 Diodeconverts light back to digital signal conversion gain = –20 dB, (or loss = 20 dB)–20 Ampto bring signal back to input level gain = 50 dB 50 Overall gain 0 dB P in P out P1P1 G1G1 L2L2 L1L1 P2P2 P3P3 P4P4 amp laser diode detector diode fibre Simple link budget example 21

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Birmingham to Beijing (assuming single satellite trip, up and down) Delay = 2 x 35,855 x 10 3 / 3 x 10 8 s = 0.23 s But what is link budget? 35,855 km Example – geosynchronous satellite link 22

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Link budgets – satellite downlink model 23 Transponder Earth station Rx Σ Free space + other losses antenna noise

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Link budgets – downlink model Satellite transponder output power = P t Antenna gain = G t Effective isotropic radiated power = EIRP = P t G t Free space path loss = (λ/4πd) 2 = L p Atmospheric loss = L a Antenna loss (feeder loss, pointing error, etc) = L at, L ar Clear air margin = M p Coverage contour margin = M c 24

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Link budgets – downlink model Power at receiver S = EIRP + G r – L p – L a – L at – L ar (dBW) (all terms in dBs) Noise at receiver N = kT s B = k(T a + T e )B(dBW) Note that T s = Noise temperature of system in Kelvin T a = Noise temperature of antenna in K T e = Noise temperature of receiver in K 26

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up linkdown link P t tx power2520 dBW G t tx ant gain4644 dB L at tx ant loss dB L p free space loss-208-206 dB L a atmos loss-0.5-0.6 dB G r rx ant gain4644 dB L ar rx ant loss dB P r rx power-93.5-100.6 dBW Note – up/down link values different due to different frequencies 27 12/14 GHz link; satellite antenna = earth antenna = 1.8m, low cost earth station Typical link budgets

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28 Typical link budgets

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mm/hr 29 Typical link budgets Rain loss

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30 Rain distribution Typical link budgets

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Noise Electromagnetic noise is produced by all bodies above absolute zero temperature (0 K) Examples – Earth – Sky – Atmosphere – Sun – Galaxy – Universe – Man-made noise – Interference 31

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Antenna temperature The summation is taken over all bodies in the field of view of the antenna – g i = fraction of total antenna sensitivity (gain) in direction of body i. – x i = greyness of body i ( x i = 1 for a black body) – T i = temperature of body i ( K ) – L i = transmission factor from body i to antenna 32

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Sourcegigi xixi LiLi T i (K)gxTL sky0.70.991.05034.6 earth0.3 1.030027.0 sun0.0050.990.0170000.4 sky- earth 0.30.99.(1.0 – 0.3)1.05010.4 sun- earth 0.30.99.(1.0 – 0.3)0.01700014.5 T ant 86.9 Sample noise calculation for typical satellite earth station at 20 GHz 33

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Assuming no loss in the connection between antenna and receiver, the total noise temperature (at input to receiver) where T e, F = effective noise temp and noise figure of receiver T 0 = reference temp for noise figure (normally 290 K ) Noise power (at input to receiver) where k = Boltzmann’s constant = 1.38 x 10 -23 JK –1 B = receiver bandwidth Receiver noise temperature 34

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L a atmospheric loss in bad storm 10 dB S/N at rx 20.512.4 dB S/N required 10.0 dB M p margin 10.52.4 dB up linkdown link P r rx power -93.5-100.6 dBW T noise temp 8001000 K B bandwidth 36 MHz N noise power -124-123 dBW S/N at rx 30.522.4 dB S/N required 10.0 dB M p clear air margin 20.512.4 dB Note – down link margin only just acceptable in storm 35 Typical link budgets

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Outage calculations In the case of mobile radio the path loss is not known fully; it is described by – a deterministic component and – a stochastic (randomly varying) component The overall link budget is then computed from a desirable BER as 36

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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 GHz The measurements were approximated in a set of simple median path loss formulae by Hata The model has been standardised by the ITU as recommendation ITU-R P.529-2

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Area mean path loss model example The model applies to three clutter and terrain categories – Urban 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 trees – Suburban area: village or highway scattered with trees and houses, some obstacles being near the mobile, but not very congested – Open 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

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Area mean path loss model example where

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Area mean path loss model example The Hata-Okumura model is only valid for: – Carrier frequencies: 150 MHz f c 1500 MHz – Base station/transmitter heights: 30 m h b 200 m – Mobile station/receiver heights: 1 m h m 10 m – Communication range: R > 1 km – A large city is defined as having an average building height in excess of 15 m

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Local mean model The 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 distribution This is the same as an additive deviation in dB from the area mean model being described by a normal distribution

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Local mean model Working in logarithmic units (decibels, dB), the total path loss is given by where X is a random variable obeying a lognormal distribution with standard deviation (again measured in dB ) If x is measured in linear units (e.g. Volts) where m x is the mean value of the signal given by the area mean model

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Outage calculations Cumulative probability density function X max 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

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What next? Attempt tutorial questions on link budgets 44

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