Link Budgets and Outage CalculationsDr Costas Constantinou

School of Electronic, Electrical & Computer EngineeringUniversity 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

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 …

4

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!

Why work with Decibels

5

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

Why work with Decibels

6

Decibels

• A power P can be expressed in decibels by

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

10ref

10 logdB

PP

P

7

DecibelsIf for example

P = 20 WattsPref = 1 Watt

thenP dB = 13 dBW

where the W after the dB denotes a reference value of 1 W.

IfPref = 1 milliWatt

thenP dB = 43 dBm

where the m after the dB refers to a mW.

8

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

1010 log outdB

in

PG

P

Pin Pout

Decibels

9

DecibelsThus for an amplifier with

Pin = 0.1 WPout = 1 W

G dB = 10 dB

Similarly if the component is a long cable with

Pin = 1 WPout = 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).

2

10 10 2

10

210log 10log

2

20 log

out out outdB

in in in

out

in

P V ZG

P V Z

V

V

11

Decibels

Decibels 1000

number

100

10

1

0.1

30

dB

20

10

0

-10

10

number

8

4

2

1

10

dB

9

6

3

0

0.1

number

0.125

0.25

0.5

1

-10

dB

-9

-6

-3

0

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.

int10 10

int

10 1 2

10 1 10 2

1 2

10 log 10 log

10 log

10 log 10 log

out outdB

in in

dB dB

P P PG

P P P

G G

G G

G G

PinPoutPint

G1 G2

14

Cascaded amplifiers

ExamplePin = 10 mW, Pint = 1 W, Pout = 100 W

So G1 = 1/10x10-3 = 100 = 20 dB

G2 = 100/1 = 100 = 20 dB

AndG = 100/10x10-3 = 10,000 = 40 dB

G = G1 + G2

PinPoutPint

G1 G2

15

Cascaded attenuators

int10 10

int

10 1 2

10 1 10 2

1 2

10 log 10 log

10 log

10 log 10 log

out outdB

in in

dB dB

P P PG

P P P

G G

G G

G G

PinPoutPint

G1 G2

• What happens if we have two attenuators in series?

• Conclusion – losses are negative gains in dB• Conclusion – can add losses in dBs.

16

Cascaded attenuators

ExamplePin = 10 W, Pint = 1 W, Pout = 1 mW

So G1 = 1/10 = 0.1 = –10 dB

G2 = 10–3/1 = 10–3 = – 30 dB

AndG = 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

int10 10

int

10 1 2

10 1 10 2

1 2

10 log 10 log

10 log

10 log 10 log

out outdB

in in

dB dB

P P PG

P P P

G G

G G

G G

PinPoutPint

G1 G2

18

Cascaded amplifier & attenuatorExample

Pin = 1 mW, Pint = 1 W, Pout = 1 mW

So G1 = 1/10–3 = 1000 = 30 dBG2 = 10–3/1 = 10–3 = –30 dB

AndG = 10–3/10–3 = 1 = 0 dBG = G1 + G2

PinPoutPint

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

PinPoutPint

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

Want a zero gain system, so they can be cascaded to cover long distance

Amp to get input signal power big enough to drive diodegain = 20 dB 20

Laser converts digital signal to lightconversion gain = –20 dB, (or loss = 20 dB) –20

Fibre 100 km long gives 100 x 0.3 = 30 dBso 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 levelgain = 50 dB 50

Overall gain 0 dB

Pin PoutP1

G1 L2L1

P2 P3 P4

amp amplaser diode

detector diodefibre

Simple link budget example

22

• 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?

83 10 /g

dc m s

d

35,855 km

Example – geosynchronous satellite link

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

25

26

Link budgets – downlink model

• Power at receiverS = EIRP + Gr – Lp – La – Lat – Lar (dBW)

(all terms in dBs)

• Noise at receiverN = 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

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

Pr rx power -93.5 -100.6 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

28

Typical link budgets

29

mm/hr

Typical link budgetsRain loss

30

Rain distribution

Typical link budgets

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

ant i i i ii

T g x T L

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

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

sky-earth

0.3 0.99.(1.0 – 0.3) 1.0 50 10.4

sun-earth

0.3 0.99.(1.0 – 0.3) 0.01 7000 14.5

Tant 86.9

Sample noise calculation for typical satellite earth station at 20 GHz

• 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

Receiver noise temperature

34

0( 1)ant e

ant

T T T

T F T

N kTB

La atmospheric loss in bad storm

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

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

Note – down link margin only just acceptable in storm

35

Typical link budgets

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

10 0min

( ) 10log ( ( 1) )r ant

SEIRP G L d X k T F T B

N

min

S S SBER f

N N N

L d L d X

L d

X

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

where

cities small tomediumfor 8.0log56.17.0log1.1

MHz300 cities, largefor 1.154.1log29.8

MHz300 cities, largefor 97.475.11log2.3

94.40log33.18log78.4

4.528log2

log55.69.44

log82.13log16.2655.69

2

2

2

2

cmc

cm

cm

cc

c

b

bc

fhfE

fhE

fhE

ffD

fC

hB

hfA

urban areas: dB log

suburban areas: dB log

open areas: dB log

L A B R E

L A B R C

L A B R D

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

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

L d L d X

2 2dB

dB

1exp 2

2p X X

2dBdB 2

lnlnexp

2

1

xmx

xxp

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

max

2 2dB

dB

max

1exp 2

2

11 erfc

2 2

X

P BER Threshold X dX

X

10 0min

max

( ) 10log ( ( 1) )r ant

SX EIRP G L d k T F T B

N

X X

44

What next?

• Attempt tutorial questions on link budgets