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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: [email protected] 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 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 Why work with Decibels 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 = 10100 10 log1010100 = 10 x 100 = 1000 dB dBs are easier to write down! 4 Why work with Decibels 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 Decibels • A power P can be expressed in decibels by PdB P 10 log10 Pref where Pref is the power (unit) to which P is compared 6 Decibels If for example then P = 20 Watts Pref = 1 Watt P dB = 13 dBW where the W after the dB denotes a reference value of 1 W. If then Pref = 1 milliWatt P dB = 43 dBm where the m after the dB refers to a mW. 7 Decibels • The decibel can also be used to refer to the power gain or power loss of a component Pout Pin GdB Pout 10 log10 Pin 8 Decibels Thus 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. 9 Decibels • If the input and output signals are known in voltage or current terms, then 2 Pout Vout 2 Zout GdB 10log10 10log10 2 Pin Vin 2Z in Vout 20 log10 Vin assuming that the impedances at the input and output are the same (Zout = Zin). 10 Decibels Decibels 1000 30 number 10 dB number 10 dB 0.1 number -10 dB 100 20 8 9 0.125 -9 10 10 4 6 0.25 -6 1 0 2 3 0.5 -3 -10 1 0 1 0 0.1 11 Decibels • Previous chart is useful for converting from numbers to dBs • Examples Pout/Pin = = = = 103 8 x 102 4 10-1 30 dB 29 dB 6 dB –10 dB • Memorising the chart will help you perform most conversions in your head to an accuracy necessary for estimation purposes. 12 Cascaded amplifiers • What happens if we have two amplifiers in series? Pint Pin Pout G1 GdB P 10 log10 out Pin G2 Pint Pout 10 log10 P P in int 10 log10 G1 G2 10 log10 G1 10 log10 G2 G1dB G2 dB Conclusion – we add gains in dB. 13 Cascaded amplifiers Example Pin = 10 mW, Pint = 1 W, Pout = 100 W Pint Pin So G1 Pout G2 G1 = 1/10x10-3 = 100 = 20 dB G2 = 100/1 = 100 = 20 dB And G = 100/10x10-3 = 10,000 = 40 dB G = G1 + G2 14 Cascaded attenuators • What happens if we have two attenuators in series? Pint Pin G1 GdB P 10 log10 out Pin Pout G2 Pint Pout 10 log10 P P in int 10 log10 G1 G2 10 log10 G1 10 log10 G2 G1dB G2 dB • Conclusion – losses are negative gains in dB • Conclusion – can add losses in dBs. 15 Cascaded attenuators Example 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 16 Cascaded amplifier & attenuator • What happens if we have an amplifier followed by a loss, such as a long cable? Pin Pint Pout G1 GdB Pout 10 log10 Pin Pint Pout 10 log10 P P in int G2 10 log10 G1 G2 10 log10 G1 10 log10 G2 G1dB G2 dB • Conclusion – now we can proceed to do real systems 17 Cascaded amplifier & attenuator Pin G1 Example Pin = 1 mW, Pint = 1 W, Pout = 1 mW Pint Pout G2 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 18 Link budgets • G = G1 + G2 is a rudimentary system link budget Pint Pin G1 Pout G2 • Link budgets are used in all RF systems – to get rough feel for viability – to fine tune actual design 19 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 103 / (3 x 108) s • Attenuation = 0.3 x 8171 dB = 2451 dB • Attenuation is bigger than a googol – it will never work! 20 Simple link budget example Pin amp laser P1 diode G1 fibre P2 L1 P3 detector diode amp P4 Pout L2 Want a zero gain system, so they can be cascaded to cover long distance Amp Laser Fibre Diode Amp to get input signal power big enough to drive diode gain = 20 dB converts digital signal to light conversion gain = –20 dB, (or loss = 20 dB) 100 km long gives 100 x 0.3 = 30 dB so gain = –30 dB converts light back to digital signal conversion gain = –20 dB, (or loss = 20 dB) to bring signal back to input level gain = 50 dB Overall gain 20 –20 –30 –20 50 0 dB 21 Example – geosynchronous satellite link • Birmingham to Beijing (assuming single satellite trip, up and down) g d d c 3108 m / s 35,855 km • Delay = 2 x 35,855 x 103 / 3 x 108 s = 0.23 s • But what is link budget? 22 Link budgets – satellite downlink model Transponder Free space + other losses noise antenna Σ Earth station Rx 23 Link budgets – downlink model • • • • • • Satellite transponder output power = Pt Antenna gain = Gt Effective isotropic radiated power = EIRP = PtGt Free space path loss = (λ/4πd)2 = Lp Atmospheric loss = La Antenna loss (feeder loss, pointing error, etc) = Lat, Lar • Clear air margin = Mp • Coverage contour margin = Mc 24 25 Link budgets – downlink model • Power at receiver S = EIRP + Gr – Lp – La – Lat – Lar (all terms in dBs) • Noise at receiver N = kTsB = k(Ta + Te)B (dBW) (dBW) • Note that Ts = Noise temperature of system in Kelvin Ta = Noise temperature of antenna in K Te = Noise temperature of receiver in K 26 Typical link budgets 12/14 GHz link; satellite antenna = earth antenna = 1.8m, low cost earth station up link down link Pt tx power 25 20 dBW Gt tx ant gain 46 44 dB Lat tx ant loss -1 -1 dB Lp free space loss -208 -206 dB La atmos loss -0.5 -0.6 dB Gr rx ant gain 46 44 dB Lar rx ant loss -1 -1 dB -93.5 -100.6 dBW Pr rx power Note – up/down link values different due to different frequencies 27 Typical link budgets 28 Typical link budgets Rain loss mm/hr 29 Typical link budgets Rain distribution 30 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 Antenna temperature Tant g x T L i i i i i • The summation is taken over all bodies in the field of view of the antenna – gi = 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 32 Sample noise calculation for typical satellite earth station at 20 GHz Source gi xi Li Ti (K) gxTL sky 0.7 0.99 1.0 50 34.6 earth 0.3 0.3 1.0 300 27.0 sun 0.005 0.99 0.01 7000 0.4 skyearth 0.3 0.99.(1.0 – 0.3) 1.0 50 10.4 sunearth 0.3 0.99.(1.0 – 0.3) 0.01 7000 14.5 Tant 86.9 33 Receiver noise temperature • Assuming no loss in the connection between antenna and receiver, the total noise temperature (at input to receiver) T Tant Te Tant ( F 1) T0 where Te, F = effective noise temp and noise figure of receiver T0 = reference temp for noise figure (normally 290 K) • Noise power (at input to receiver) N kTB where k = Boltzmann’s constant = 1.38 x 10-23 JK–1 B = receiver bandwidth 34 Typical link budgets up link down link Pr rx power -93.5 -100.6 dBW T noise temp 800 1000 K B bandwidth 36 36 MHz N noise power -124 -123 dBW S/N at rx 30.5 22.4 dB S/N required 10.0 10.0 dB Mp clear air margin 20.5 12.4 dB 10 10 dB S/N at rx 20.5 12.4 dB S/N required 10.0 10.0 dB Mp margin 10.5 2.4 dB La atmospheric loss in bad storm Note – down link margin only just acceptable in storm 35 Outage calculations • In the case of mobile radio the path loss is not known fully; it is described by L d L d X – a deterministic component L d and – a stochastic (randomly varying) component X • The overall link budget is then computed from a desirable BER as S BER f N S S N N min S EIRP Gr L (d ) X 10log10 k (Tant ( F 1)T0 ) B N min 36 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 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 Area mean path loss model example urban areas: L dB A B log R E suburban areas: L dB A B log R C open areas: L dB A B log R D where A 69.55 26.16 log f c 13.82 log hb B 44.9 6.55log hb C 2log f c 28 5.4 2 D 4.78log f c 18.33log f c 40.94 2 E 3.2log11.75hm 4.97 for large cities, f c 300MHz 2 E 8.29log1.54hm 1.1 2 for large cities, f c 300MHz E 1.1 log f c 0.7 hm 1.56 log f c 0.8 for medium to small cities Area mean path loss model example • The Hata-Okumura model is only valid for: – – – – – Carrier frequencies: 150 MHz fc 1500 MHz Base station/transmitter heights: 30 m hb 200 m Mobile station/receiver heights: 1 m hm 10 m Communication range: R > 1 km A large city is defined as having an average building height in excess of 15 m 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 Local mean model • Working in logarithmic units (decibels, dB), the total path loss is given by L d L d Xs where Xs is a random variable obeying a lognormal distribution with standard deviation s (again measured in dB) 1 2 pX exp X 2 2s dB s dB 2 • If x is measured in linear units (e.g. Volts) ln x ln mx 1 px exp 2 2s dB s dB x 2 where mx is the mean value of the signal given by the area mean model Outage calculations • Cumulative probability density function S X EIRP Gr L (d ) 10log10 k (Tant ( F 1)T0 ) B N min X X max P BER Threshold X max 1 s dB 2 2 exp X 2 2s dB dX 1 X max 1 erfc 2 2 • 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 What next? • Attempt tutorial questions on link budgets 44