Link Budgets and Outage Calculations

1. 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

2. 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

3. 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 Sirottato 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 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!

5. 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

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

7. 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 then P dB = 43 dBm where the m after the dB refers to a mW.

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

9. 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.

10. 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).

11. Decibels

12. Decibels • Previous chart is useful for converting from numbers to dBs • Examples Pout/Pin = 103 30 dB = 8 x 102 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.

13. Cascaded amplifiers • What happens if we have two amplifiers in series? Conclusion – we add gains in dB. Pint Pout Pin G1 G2

14. 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 Pint Pout Pin G1 G2

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

16. 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

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 systems Pint Pout Pin G1 G2

18. Cascaded amplifier & attenuator 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 Pint Pout Pin G1 G2

19. 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 Pint Pout Pin G1 G2

20. 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!

21. detector diode laser diode amp amp fibre Simple link budget example Pout Pin P1 P4 P3 P2 L1 G1 L2 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 20 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 conversion gain = –20 dB, (or loss = 20 dB) –20 Amp to bring signal back to input level gain = 50 dB 50 Overall gain 0 dB

22. Example – geosynchronous satellite link • 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? 35,855 km

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

24. 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

26. 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

27. Typical link budgets 12/14 GHz link; satellite antenna = earth antenna = 1.8m, low cost earth station Note – up/down link values different due to different frequencies

28. Typical link budgets

29. Typical link budgets Rain loss mm/hr

30. Typical link budgets Rain distribution

31. 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

32. 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

33. Sample noise calculation for typical satellite earth station at 20 GHz

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 receiver • T0 = 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

35. Typical link budgets Note – down link margin only just acceptable in storm

36. 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

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 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

38. 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

39. Area mean path loss model example where

40. 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

41. 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

42. 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

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