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

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 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 …

4. Why work with Decibels
1 googol =
1 googol = log = 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 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
Pin
Pout

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 =  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.

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

18. 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

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
Pin
Pout
Pint 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. 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

22. 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?

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

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
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

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
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

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 JK–1
B = receiver bandwidth

35. 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

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