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Link Budgets and Outage Calculations Dr Costas Constantinou School of Electronic, Electrical & Computer Engineering University of Birmingham W: E:

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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 = googol = log = 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 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 dB L a atmos loss dB G r rx ant gain4644 dB L ar rx ant loss dB P r rx power 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 sky earth sun sky- earth (1.0 – 0.3) sun- earth (1.0 – 0.3) 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 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 dB S/N required 10.0 dB M p margin dB up linkdown link P r rx power dBW T noise temp K B bandwidth 36 MHz N noise power dBW S/N at rx dB S/N required 10.0 dB M p clear air margin 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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