Link Budget Analysisfor RF Engineers and Managers

Wireless Facilities Incorporated

Introduction

ÄÄDefinitions and ObjectivesDefinitions and Objectives

ÄÄReview of Decibel (Optional)Review of Decibel (Optional)

ÄÄInputsInputs

ÄÄOutputsOutputs

ÄÄProcessProcess

ÄÄExamplesExamples

RF Path

BSSensitivity

MSSensitivity

Path Loss Down Link

Path Loss Up Link

PBS

PMS

End to End Channel•Noise•Fading, •Interference,•Hardware Losses• .......

End to End Channel•Noise•Fading, •Interference,•Hardware Losses• .......

Objectives and Definitions

Inputs

n Base and Mobile Receiver Sensitivity Parameters– Minimum Acceptable Signal to Noise Ratio

– Environmental/Thermal Noise Assumption

– Receiver Noise Figure

n Antenna Gain at Base and Mobile Station

n Hardware Losses (Cable, Connectors, Combiner,....)

n Target Coverage Reliability

n Propagation Characteristics of the Channel

n Receiving Environment

L B AL B A

Outputs

n Coverage Threshold– In-Building

– In-Car

– On-Street

n Base Station ERP

n Maximum Allowable Path Loss

n Cell Size Estimate

n Cell Count Estimate

L B AL B A

Path Balancing

Uplink Limited:BS Can Reach MS butMS Cannot Reach BS

Uplink Limited:BS Can Reach MS butMS Cannot Reach BS

Downlink Limited:MS Can Reach BS butBS Cannot Reach MS

Downlink Limited:MS Can Reach BS butBS Cannot Reach MS

Communication is possible only when bothboth links are available.

UNDESIREDUNDESIRED

Need dB Review?

How About ReviewingHow About ReviewingDecibel Units, e.g. Decibel Units, e.g. dB,dB, dBm dBm,, dBw dBw,, dBu dBu

dBidBi,, dBd dBd

Go to Appendix

A1Continue

List of Gains and Losses

Gainsn Base Station Antenna

Gain

n Mobile Antenna Gain

n Diversity Gains

Lossesn Hardware

– Combiner

– Cables

– Connectors

– Duplexer

n Air Interface– Fade Margin

– Penetration Losses» In-car

» In-Building

» Body Loss

+ _

Antenna Gains

Portable antennastypically have nogain

OmniDirectional

DirectionalAntenna

0-9 dBd 9-14 dBd

Base Station AntennasMobile Station Antennas

Portable Phones

Vehicle MountedPhones

-1 to 0 dBd 1-3dBd

Antenna Gain Units: dBi and dBd

n dBi– is a unit to measure antenna gain in reference to an isotropic

antenna.– So: an isotropic antenna has a power gain of unity; i.e., 0 dBi.

n dBd– is a unit to measure antenna gain in reference to a lossless Half-

Wave Dipole antenna.

– So, a lossless half-wave dipole antenna has a power gain of 0 dBdor 2.15 dBi.

G dBi = GdBd + 2.15 dB

2 wire Balanced feed

λ/4λ/4

λ/4λ/4

Half-Wave DipoleHalf-Wave Dipole

Converting dBd to dBi

Diversity Gain

n If we use multiple receiving antennas withcertain spatial separation at the BS along withadaptive combining techniques we will have adiversity gain.

n Diversity gain should be considered in LBAwhenever it is used.

n It is usually used at the base station.

n Sometimes it is used only for the receivingantennas.

Effective Radiated Power (ERP)

Power Amplifier

HardWare Losses

PALCCC

Gantenna

ERP

ERP=PA - Lccc + GAntenna

ERP vs. EIRP

n ERP (Effective Radiated Power):– is the transmitted power with respect to a dipole antenna within a

given geographic area.

n EIRP (Effective Isotropic Radiated Power):– is the transmitted power with respect to a dipole antenna within a

given geographic area.

Converting ERP to EIRPEIRP(dBw) = ERP (dBw) + 2.15 (dB)

RF Components in a Typical Base Station

LNA

TX/RX2RX1

LightningArrestor

PA RX1 RX2

Duplexer

Combiner

Top Jumper Cables

Main Cable

ConnectorReceiver Multicoupler

High Power Amplifier

Receiver

Bottom Jumper Cables

Cable Loss Jumper Cable

Main Cable

Cable Size Recommended Use Loss (per 100 ft.at 900 MHz)

Loss (per 100ft at 1800MHz)

LDF4-50 1/2 inch Heliax Foam Jumper Cables 2.160 dB

LDF5-50 7/8 inch Heliax Foam Main Cable < 55 m 1.210 dB 1.97 dB

LDF6-50 1 1/4 inch Heliax Foam Main Cable < 75 m 0.907 dB 1.45 dB

LDF7-50 1 5/8 inch Heliax Foam Main Cable < 90 m 0.750 dB 1.25 dB

HJ12-50 2 1/4 inch Air Dielectric Main Cable > 90 m 0.535 dB

HJ8-50B 3 inch Air Dielectric Main Cable > 90 m 0.510 dB

HJ9-50 5 inch Air Dielectric Main Cable > 90 m 0.750 dB

Connector Losses

oConnectors, used to connect RF components, typicallyeach have a loss of 0.1 dB.oIn US, a typical 50W connector is the “N-type”coaxial connector. whereas in Europe, it is the “7/16DIN” connector.

Combiner

Characteristic Cavity Hybrid

Frequency Range (MHz) 806-960 806-1000

Continuous Input Power (W) 150 150

Insertion Loss (dB) 2 to 4.8 3.8 to 7.4

Maximum VSWR 1.5:1 1.5:1

Freq.1

Freq.2

Freq.3

A combiner is a devicethat enables severaltransmitters of differentfrequencies to transmitfrom the same antenna.

Duplexer

Duplexer Characteristic ValueIsolation (accross all 3 ports, with unused ports terminatedat 50 Ω)

> 60 dB

Insertion Loss (across all ports) 0.5 dBPower handling 500 W

Input VSWR 1.5:1 (max)

n A Duplexter enables us to simultaneously transmit and receivesignals on the same antenna.

n It provides an isolation between the transmitted and receivedsignals.

Coverage Environments

In-CarIn-Building

On-Street

Table of Penetration Losses

In Building Penetration (dB) 15-25

In Car Penetration (dB) 3-10Body Loss (dB) 2-5

n For all receiving environmentsa loss associated with the effectof users body on propagationhas to be included.

n This effect is in the form of afew dB loss in both uplink anddownlink directions

Contour Coverage Reliability

n Due to various shadowing and terrain effects the signal level measuredon a circle around the base station shows some random fluctuationsaround the estimated value given by the propagation model.

n This random signal level along the cell boundary has lognormalvariations.

Normal Distribution

LogNormal Distribution

0 0.001031 1.50.2 0.001594 20.4 0.002420.6 0.003610.8 0.005291

1 0.0076171.2 0.0107741.4 0.0149691.6 0.0204321.8 0.027397

2 0.0360892.2 0.0467022.4 0.0593692.6 0.0741432.8 0.090962

3 0.109633.2 0.1298013.4 0.1509743.6 0.1725083.8 0.19364

4 0.213534.2 0.2313144.4 0.246164

0

0.05

0.1

0.15

0.2

0.25

0.3

0

0.6

1.2

1.8

2.4 3

3.6

4.2

4.8

5.4 6

6.6

7.2

7.8

8.4 9

9.6

n A lognormal random process when expressed in dB’s has a normali.e. Gaussian distribution.

n According to this distribution 50% of time the signal level is below itsmean value.

n Therefore by setting the coverage threshold at any level L we can onlyensure about 50% of coverage reliability.

-(x - x)2_p(x) = exp[ ]

σ(2π)σ(2π)1/21/2 2σ2σ2211

%50%50

Lognormal Fade Margin

0 0.001031 1.50.2 0.001594 20.4 0.002420.6 0.003610.8 0.005291

1 0.0076171.2 0.0107741.4 0.0149691.6 0.0204321.8 0.027397

2 0.0360892.2 0.0467022.4 0.0593692.6 0.0741432.8 0.090962

3 0.109633.2 0.1298013.4 0.1509743.6 0.1725083.8 0.19364

4 0.213534.2 0.2313144.4 0.246164

0

0.05

0.1

0.15

0.2

0.25

0.3

0

0.6

1.2

1.8

2.4 3

3.6

4.2

4.8

5.4 6

6.6

7.2

7.8

8.4 9

9.6

n Therefore by setting the coverage threshold at any level L we can onlyensure about 50% of coverage reliability.

n Usually contour coverage reliability of 70-80% is needed..

n Therefore to assure e.g. %80 contour coverage reliability one has toshift the distribution toward higher signal levels so that the dashedarea reduces to %20.

n This requires providing additional signal power called fade margin orlognormal margin.

%20 %80

Fade Margin

Area Coverage Reliability

n Coverage design objectives are usually defined in terms ofArea Reliability.

n Area Reliability is the percentage of area where thereceived signal is above the threshold.

n It can be thought of as the average of contour reliability'sfor all circles of radii r, 0 < r < R.

99%

97%

94%

90%95%

From Area to Contour Reliability

0.5

0.55

0.6

0.65

0.7

0.75

0.8

0.85

0.9

0.95

1

σσ/n

Are

a R

elia

bili

ty

0 1 2 3 4 5 6 7 8

PX0(R) = 0.95

0.9

0.850.80.75

0.7

0.65

0.6

0.550.5

Area Reliability

σσ/nContour Reliability

Fade Margin vs Contour Reliability

0

2

4

6

8

10

12

14

16

18

20

0.5 0.55 0.6 0.65 0.7 0.75 0.8 0.85 0.9 0.95

Location Probability at Cell Edge

Fad

e M

arg

in in

dB

σσ =12 dB

1110

98

7

6

StandardDeviation

Contour Reliability

Contour Reliability

Standard Deviation of FadeFade Margin

Summary of Fade margin Calculation

n For a given– standard deviation for the local mean σ, – the propagation loss factor, n:

Compute σ/n.

n For the required area reliability and computed σ/n– Estimate coverage contour reliability from plot_I

n Use the contour reliability and the standard deviation σ andplot-II to estimate the fade margin Mfade.

n Enter the Mfade (fade margin) into the LBA work sheet toestimate the maximum path loss & coverage threshold.

Case Study I

n Example: Check with Plots (I,II)– Let signal attenuation law be 40 dB per decade, i.e. n=2.5

– Standard deviation of lognormal fading is estimated as 10dB.

– Clients ask for 90% area reliability

– From Plot _I and σ/n=4 and 90% area reliability, contourreliability is 80%.

– From Plot_II with σ=10 and 80% contour reliability thefade margin is about 8.5 dB.

Case Study II

n Example: Check with Plots (I,II)– Let signal attenuation law be 40 dB per decade, i.e. n=2.5

– Standard deviation of lognormal fading is estimated as 10dB.

– Clients ask for 90% area reliability

– From Plot _I and σ/n=4 and 90% area reliability, contourreliability is 80%.

– From Plot_II with σ=10 and 80% contour reliability thefade margin is about 8.5 dB.

Sample Fade/Log-normal Margin

Terrain Standarddeviation σ(dB)

Propoga-tion Law

CellBoundaryP(n) for 90%Coverage

FadeMargin(dB)

Urban 6 3.5-3.75 70 % 4 to 6Suburban 8 3.0-3.5 76 % 6

Rural 12 2.5-3.0 82 % 10Fade Margin and Cell Coverage

Receiver Sensitivity

n Receiver sensitivity– is the minimum acceptable input signal level in

dBm, at the input of the receiver’s low noiseamplifer, required by the system for reliablecommunication.

n Carrier to Noise Ratio (CNR)– For a given FER, e.g. of about 1%, the each type

of modulation and coding requires a minimumsignal to noise ratio which at the bit level isstated as Eb/ N0.

n Thermal/Environmental Noise:– is a combination of

» Antenna Noise (dBm)

» Receiver Noise Figure(NF) in dB

» Temprature and System Bandwidth

RX

Receiver Sensitivity Calculation

ReceiverNF

k T B (S/N)out

(S/N)in

Thermal Noise Noise Figure

Absolute SensitivityRX Sensitivity

( ) ( )

( )

( )

log( ) ( )

S N S N NF

S N S N NF

S N S N NF

S k T B NF S N

in out

in in out

in in out

in out

== ++−− == ++== ++ ++

== ⋅⋅ ⋅⋅ ++ ++10

All values areAll values are in dB’s in dB’s

or Eb/No

Overview of Up-Link Budget Analysis

Starting with the reverse link

n Find the Maximum Allowable Path Loss (MAPL)– Start from MS maximum power

– Subtract all the losses in due to, RF components

– Subtract all the margins due to fading and interference for a giventarget loading

– Add all the gains in the path e.g. antenna and diversity gains

– Subtract the receiver sensitivity of the base station for a given FER

– The result is MAPL.

MAPL=PLUp = PAm - All Losses + All Gains - RXBaseMAPL=PLUp = PAm - All Losses + All Gains - RXBase

Overview of LBA Forward Link

In the forward link:

n For each channel– Compute the MS sensitivity for a given Eb/No requirement

– Add the reverse link path loss and add a path imbalance if needed

– Add/subtract all losses/gains not considered in the reverse linkcalculations

– The result is ERP of base station

Gains and Losses in UpLink

LCCC

RX

Combiner,Cable &ConnectorLosses

GA

Path Loss

Fade Margin

ERP

In-Building/CarPenetration Loss

Body Loss

MS AntennaGain/Loss

PA

RXBase = PAm + GM - LBody - LBldg - MFade- PLUp + GB - LCCC

PLUp = PAm + GM - LBody - LBldg - MFade- RXBase + GB - LCCC

Gains and Losses in Down Link

Power Amplifier

Combiner,Cable &ConnectorLosses

PA

LCCC

GBPath Loss

Fade Margin

ERP

In-Building/CarPenetration Loss

Body Loss

MS AntennaGain/Loss

RX

RXMobile = PAB - LCCC + GB - MFade- PLDown - LBldg - LBody + GM

PAB = RXMobile + LCCC - GB + MFade+ PLDown + LBldg + LBody - GM

Cell Size/Count Estimation

n Objective:– To determine the number of cells required to provide coverage for

a given area.

n Required Input:– Maximum Allowable Path Loss (MAPL)

– Propagation Loss Model

n Using Hata’s Empirical Formula

Cell Size Estimatation

o Solve it backward to Cell radius estimate based on Hata’sformula:

PL f h

h R a hc b

b m

= + − +− −

69 55 26 16 13 82

44 9 6 5510 10

10 10

. . log . log

( . . log ) log ( )

log. . log . log ( )

. . log1010 10

10

69 55 2616 13 8244 9 6 55

RMAPL f h a h

hc b m

b

== −− −− ++ ++−−

Cell Count Estimation

1

2

3

4

5

7

6

98

10

12

11

Link Budget Analysis

Max Allowable Path Loss)

Estimate Cell Radius

Estimate Cell Count

Market Boundary

Outline

dB Unit for Gains and Losses

n Decibell (dB) is a logarithmic unit forrepresenting power gains and losses.

n Gain Glinear=Pout/Pin is equivalent to GdB

where

Examples:– A gain of 100 is equivalent to 20dB gain

– A 10 times attenuation in power = -10 dB loss

SubsystemPin

PoutPout

Pin

GdB= 10 Log ( GLinear) =10 Log ( )

dB Units for Signal Power

n By fixing P0 as a reference power,e.g.... to 1 Watt or 1Miliwatt, one candefine similar units for power.

n Examples:– (P) dBw = 10 log P/(1Watt)

– (P) dBm = 10 log P/(1mW)

P0 Name of unit Example InterpretationW dBw 10dBw 10:1 over 1W

or 10WmW dBm 20dBm 100:1 over 1mW

or 100 mWDecibel in reference to a power unit

dB Units for Signal Level (Voltage)

n dB is also a logarithmic unit for voltage gains and losses.

n Gain G=V/V0 = g dB where g=20 log (P/P0)

n Since power is proportional to voltage squared the twodefinitions are consistent.

n Similarly by fixing V0 as a reference voltage, e.g.... to 1volt or 1microvolt, one can define similar units forvoltage.

n Examples:– (V) dBV = 10 log V/(1Volt)

– (V) dBu = 10 log V/(1µW)V0 Name of the unit Example InterpretationV dBv 20dBv 10:1 over 1V

or 10VµV dBu 20dBu 10:1 over 1µµV

or 10 µ µVDecibel in reference to a voltage unit

Relation between dBv and dBw

n Converting a voltage in dBµV to its received powerin dBm with 50Ω terminal impedance is given by:0dBu =20log(V/V0) where V0 = 1 µV

0dBu = 10 log[(10-6)2 (1000)/50]dBm

= -107 dBm

where P(mW) = V2/R * 1000 mW for R = 50Ω

n Converting a field strength in dBµV/m to itsreceived power in dBm with a 50Ω optimum terminalimpedance and effective length of a half dipole: λ/π.0dBu = 10 log[(10-6)2 (1000)(λ/π)2/(4∗50)] dBm

At 850MHz: 0dBu (=) -132 dBm

39dBu (=) -93 dBm

32dBu (=) -100dBm

50ΩΩ

Common Mistakes Regarding dB Units

n Remember the difference between dB as a unitless measureof gain or loss and dBm as a unit of power or voltage.

n Also note that addition in the logarithmic scale e.g.... in dBdomain is like multiplication in the linear scale.

n Therefore the following are meaningless and not correct:– Adding two signal levels in dBm domain.

– Multiplication of gains or losses expressed in dB’s

– Looking at the ratio between two signal in dB domain.

dBm+dBmdB*dBdBm/dBm

dBm+dB=dBmdBm-dB=dBmdB+dB=dB

Incorrect

Correct

n Let’s consider two signals– S1 with power P1 Watts or Q1 dBm

– S2 with power P2 Watts or Q2 dBm

n From Watts to dBm– (Q1)dBm =10 log (P1 W/1mW)=10 log(103 P1)=30 + 10 log P1

n From dBm to Watts– (P1)mW= 10(Q1/10) and (P1)W=10-3 x 10(Q1/10)

n Adding two signals has to be in the linear domain:

– S1+S2 = P1 + P2 = 10 Q1/10+ 10 Q2/10 Q1 +Q2

n The ratio between two signals or signal to noise ratio has to becalculated in the linear domain– S1/S2= P1 / P2 = (Q1-Q2) dBm Q1/Q2

dB to linear conversion & vice versa