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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

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Why work with Decibels Decibels can be used to express a set of values having a very large dynamic range without losing the fine detail 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 …

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

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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

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**Decibels A power P can be expressed in decibels by**

where Pref is the power (unit) to which P is compared

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Decibels If 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.

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Decibels The decibel can also be used to refer to the power gain or power loss of a component Pin Pout

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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.

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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 (Zout = Zin).

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Decibels

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**Decibels Previous chart is useful for converting from numbers to dBs**

Examples Pout/Pin = 30 dB = 8 x 102 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.

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**Cascaded amplifiers What happens if we have two amplifiers in series?**

Conclusion – we add gains in dB. Pin Pout Pint G1 G2

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Cascaded amplifiers Example 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 + G2 Pin Pout Pint G1 G2

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Cascaded attenuators What happens if we have two attenuators in series? Conclusion – losses are negative gains in dB Conclusion – can add losses in dBs. Pin Pout Pint G1 G2

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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

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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 Pin Pout Pint G1 G2

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**Cascaded amplifier & attenuator**

Pin Pout Pint G1 G2 Example 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

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**Link budgets G = G1 + G2 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 Pin Pout Pint G1 G2

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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 103 / (3 x 108) s Attenuation = 0.3 x 8171 dB = 2451 dB Attenuation is bigger than a googol – it will never work!

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**Simple link budget example**

Pin Pout P1 G1 L2 L1 P2 P3 P4 amp laser diode detector diode fibre Want a zero gain system, so they can be cascaded to cover long distance Amp to get input signal power big enough to drive diode gain = 20 dB Laser converts digital signal to light conversion gain = –20 dB, (or loss = 20 dB) –20 Fibre 100 km long gives 100 x 0.3 = 30 dB so gain = –30 dB –30 Diode converts light back to digital signal Amp to bring signal back to input level gain = 50 dB Overall gain dB

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**Example – geosynchronous satellite link**

35,855 km Birmingham to Beijing (assuming single satellite trip, up and down) Delay = 2 x 35,855 x 103 / 3 x 108 s = 0.23 s But what is link budget?

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**Link budgets – satellite downlink model**

Transponder Earth station Rx Σ Free space + other losses antenna noise

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**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

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**Link budgets – downlink model**

Power at receiver S = EIRP + Gr – Lp – La – Lat – Lar (dBW) (all terms in dBs) Noise at receiver N = kTsB = k(Ta + Te)B (dBW) Note that Ts = Noise temperature of system in Kelvin Ta = Noise temperature of antenna in K Te = Noise temperature of receiver in K

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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 Lp free space loss -208 -206 La atmos loss -0.5 -0.6 Gr rx ant gain Lar rx ant loss Pr rx power -93.5 -100.6 Note – up/down link values different due to different frequencies

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Typical link budgets

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Typical link budgets Rain loss mm/hr

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Typical link budgets Rain distribution

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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

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Antenna temperature 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

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**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 0.3 300 27.0 sun 0.005 0.01 7000 0.4 sky-earth 0.99.(1.0 – 0.3) 10.4 sun-earth 14.5 Tant 86.9

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**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 receiver T0 = 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

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Typical link budgets up link down link Pr rx power -93.5 -100.6 dBW T noise temp 800 1000 K B bandwidth 36 MHz N noise power -124 -123 S/N at rx 30.5 22.4 dB S/N required 10.0 Mp clear air margin 20.5 12.4 La atmospheric loss in bad storm 10 dB S/N at rx 20.5 12.4 S/N required 10.0 Mp margin 10.5 2.4 Note – down link margin only just acceptable in storm

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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

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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 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

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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 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

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**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

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What next? Attempt tutorial questions on link budgets

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