System NOise and Link Budget

8/18/2019 System NOise and Link Budget

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SYSTEM NOISE AND

LINK BUDGETUpdates: 9/24/13; 10/6/14


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Introduction

• Any system (wired or wireless) receives and generatesunwanted signals

• Natural phenomena or man-made (Noise)

• Unwanted signals from other systems (Interferences)

•

Man-made Noise: due to other subsystems (e.g.; powersupply)

• Natural Noise: due to random movements and agitation of

electrons in resistive components (e.g., due totemperature)

We focus on system thermal noise!


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Thermal Noise Characteristics

• Thermal noise due to agitation of electrons• Except at absolute zero temperature, the electrons in

every conductor (resistor) are always in thermal motion

• Function of temperature

•

Present in all electronic devices and transmissionmedia

• Cannot be eliminated

• Particularly significant for satellite communication•

The Sun contributes to the thermal noise at the receiver

http://homes.esat.kuleuven.be/~cuypers/satellite_noise.pdf


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Spectral Power Density of (white)

Noise• Amount of thermal noise to be found in abandwidth of 1Hz in any device or conductoris:

• N 0 = noise power density (in watts) per 1 Hz ofbandwidth

• k = Boltzmann's constant = 1.3803 ! 10-23 J/K (or W/

(K.Hz))

•

T = temperature, in kelvin (absolute temperature)

• Note Watt = J/sec = J.Hz

N 0

= kT W/Hz

( )


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Thermal Noise Noise Power

• Noise is assumed to be independent of frequency

• Thermal noise present in a bandwidth of B Hertz (in

watts):

or, in decibel-watts( )W/Hzk 0 T N = TB N k =

BT N log10log10klog10 ++=

!


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Thermal or White Noise

• From the plot of the spectral density of thermal noise overfrequency, can see that the noise is flat frequency

spectrum till around 100GHz or so and starts to fall off at

around 1TeraHz


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Thermal Noise Model

• At any temperature, thermal motion of electrons result inthermal noise

• This is due to difference between the resistor’s terminals

• The thermal noise source in the resistor delivers a

power to the load (watt)

• Or in Watt/Hz: We call this noise power density :

TB N k = Noise randomprocess has

Gaussian

Distribution withzero mean and

some SD( )W/Hzk

0 T N =


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Modeling the Thermal

Noise (Open Circuit – No Load) • The noise generated due to temperature T by a resistivecomponent has normalized power spectrum (also called

mean-square voltage spectrum): 2RkT(V^2/Hz)

• k = Boltzmann's constant = 1.3803 ! 10-23 J/K

•

T = temperature, in kelvin (absolute temperature)• Therefore the average power that a voltage or current

source can deliver (available) is: 2RkT.2B=4RkTB (V^2)

• The RMS voltage equivalent of the thermal noise will be

V rms = AveragenoisePower = 4kTRB V ( )Example A: Calculate the open-circuit Vrms reading when we connect a true RMSvoltmeter to a 100Kohm resistor at room temperature (20 deg. C) with BW=1MHz to

measure the generated thermal noise. Draw the equivalent circuit.

True RMSMultimeter

R

Vrms

Equivalent Thermal Noise Model


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Noise Power Delivered to the Load

• The voltage delivered to the load is maximum whenRs=RL=R

• Thus, VL(t) = Vs(t)/2!

•

Spectral Noise Density at the load will be:kT/2=No/2 (W/Hz)

Sub

system

Rs

Vs(t) RL

VL(t)


P Load

=

V L

(t )2

2=

[V s(t ) / 2]

2

R=

V s(t )

2

4 R=

V rms

2

4 R


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Thermal Noise Power

%MATLAB CODE:T= 10:1:1000;

k= 1.3803*10^-23;B=10^6;No=k*T;N=k*T*B;N_in_dB=10*log10(N);

semilogy(T,N_in_dB)title(‘Impact of temperature in

generating thermal noise in dB’)

xlabel(‘Temperature in Kelvin’)ylabel(‘Thermal Noise in dB’)

0 100 200 300 400 500 600 700 800 900 1000

-102.15

-102.16

-102.17

-102.18

-102.19

-102.2

Impact of temperature in generating thermal noise in dB

Temperature in Kelvin

T h e r m a l N o i s e i n d B


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Two-Ports Sub-System Noise Characterization

• A subsystem’s noise behavior can be characterized byseveral parameters:

• Available Gain (G)

• Noise Bandwidth (B)

•

Noise Figure or Factor (F)

G, B,F

Input signal &

noise

output signal &

noise

Subsystem

Rs

Vs(t)RL

VL(t)



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Two-Ports Sub-System Noise Characterization




•

Noise Figure or Factor (F)• Available Gain:

• The available output noise spectral density due to input white noise

will be:

• The available output noise power due to input white noise will be:

S ao

=G ! N 0

/ 2 W/Hz( )

Pao

=G ! 2 B ! N 0

/ 2 W( )

G, B,F

Input signal &noise

output signal &noise

Sao & PaoNo /2


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System Noise Bandwidth (B)

Two-Ports System•

Assuming the system isdriven by white noise!

• So is the available

output power spectraldensity (W/Hz)

•

Pao is the available

output power (W)

• G=Go is the mid-band

available gain (DC gain)

S o( f ) =G( f )S i( f ) =G( f ) N o

2

Pao = S o( f )df =!"

"

# N o

2G( f )df

!"

"

#

Pao =G $2 B $ N 0 / 2 W( )

% B =1

2GG( f )df

!"

"

#

G(f)

Output PowerSpectrum Density

So(f)

Input PowerSpectrum Density

Si(f)

The availableoutput noise

power due to

input white noise


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Example A

• (1) Find the BW for a first-order low-pass Butterworth filterwhose gain is given as follow (assume DC gain Go=1):

•

(2) Assuming the input of the system above is driven bywhite noise, find the output available power.

G( f )=1

1+ ( f / f 3dB )2

G(f)

Output PowerSpectrum Density

So(f)

Input PowerSpectrum Density

Si(f)

f 3dB


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Remember:Two-Ports Sub-System Noise Characterization




•

Noise Figure or Factor (F)

G, B,F

Input signal &

noise

output signal &

noise

Subsystem

Rs

Vs(t)RL

VL(t)


Let’s talk aboutthis!


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System Noise Figure (F)

F = SNRi / SNRo

=1+Te

To

• The most basic definition of noise figure came intopopular use in the 1940’s when Harold Friis defined the

noise figure F of a network to be the ratio of the signal-to-

noise power ratio at the input to the signal-to-noise power

ratio at the output.

http://cp.literature.agilent.com/litweb/pdf/5952-8255E.pdf


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G, B,

F, Te

SubSystem

Input Signal Power=Psi

Input Noise Power

Spectrum DensitySni=kT

Psi.G

Available Noise PowerDue to input thermal noise:

kTGB

Available Noise PowerDue to internal noise:kToGB(F-1) = Nr

System Noise Figure (F)• We define the Noise Figure (Noise Factor) as:!

• We often express F in dB

• Note that F>1

• Nr is the available output noise power due to the two-portsub-system

• Te is effective (internal) temperature of the subsystem

•

To is output equivalent temperature into the subsystem

F = SNRi / SNR

o

=1+Te

To

Pao(noise) =

kTGB+ kToGB(F !1)=

kGB(T +To(F !1))) =

k (T +Te) "G " B

Find the expression forSNRi? SNRi = Psi/kToB

Note: T=To


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Example B

• Assume the antenna contributes to the input thermal noise of the system by

T=10K

• Find the available input noise spectral density (Sai)

• Find the available output noise spectral density (Sao)

• Find the available output noise power (Pao)

•

Find the noise figure for the system (F)• Draw the thermal noise circuit model for the antenna

Gain = 100dBB=150 KHzTe = 140 K

output signal &

noise

Antenna


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Cascaded System

•

!"#$"%&% #()*#+#,&-# $". )& #/-01/2 )+ $3-)/./.4 "5"/1")1&

4"/.# ".% .3/#& 0630&67 89:9;:9?@

• AB,3,"1 : A3 : A;?A


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Example CCascaded System

• FB".,:


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]V"-01& ̂

_/6&1# F6".#-/`&6

•

N##(-& MN:aR%9-O b36 ,K& ".,&.." A, : ;R%9%O

C&&%1/.& 13## : =%9O T3## ,K63(4K ,K& -",$K&%.&,Z36c /# R?Y%9?

• C/.% ]\PM ".% ]PM b36 " %/031& ".,&.."?

• \# ,K/# PC ,6".#-/`&6 -36& 1/c&1+ ,3 )& " K".%#&, 36 "

)"#& #,"73.d

Power Amplifier(PA)

C&&%1/.&

M,

RFTransmitter^/4/,"1

^","

Freq. ConverterMatchedNetwork

Do it on yourown!


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Expression E b /N 0• Ratio of signal energy per bit (J/b) to noise power densityper Hertz (W/Hz)

• R = 1/Tb; R = bit rate; Tb = time required to send one

bit; S = Signal Power

TR

S

N

RS

N

E b

k

/

00

==

Eb = S . Tb = W x Sec / bit = Energy (J) / bit

• Given a value for E b /N 0 to achieve a desired error rate,

parameters of this formula can be selected

• As bit rate R increases, transmitted signal power must

increase to maintain required E b /N 0


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Probability of Bit Error Rate

(PBER)

Question: Assume we requireEb/No = 8.4 dB for bit error of

10^-4. Assume temperature is290 Kelvin and data rate is set

to 2.4 Kbps. Calculate therequired level of the received

signal.

8.4 dB

10^-4


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T/.c 9(%4&, N."1+#/#

• Link characteristics (in terms of power, capacity, and frequency of

operation)• Noise Analysis is generally significant to characterize the received signalby the receiver

• System is generally balanced in term of dynamic range (in TX and RXdirections)

• Design Objective: – Offer good quality of service (QoS)

– Provide high signal level (SNR and SNIR)

–

Guarantee intelligibility and fidelity (PBER) – High accuracy (BER)

• Conflicting Parameters (next slide)

C36Z"6% 1/.c

8%3Z.13"%@

P&5&6#& 1/.c

8(013"%@


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Link Budget

Detailed View

RF UnitReceiver

(F, Go, B)C&&%1/.&

M6

DecoderM. ^/4/,"1

^","

Power AmplifierC&&%1/.&

M,

RF Transmitter^/4/,"1

^","

Freq. Converter


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Budget Link Analysis -

Conflicting Parameters

• 9_ e f3[ e FK&6-"1 J3/#&

• [JP e f3[EC/%&1/,+ e M, e !3#,

• 9]P e f3[ e [JP e M, e !3#,

•

C6&g? e C/%&1/,+ e ^+."-/$ P".4&

• [+#,&- T3## e ^+."-/$ P".4& e f3[ e U",&6/"1 e !3#,

• f(/$&., M3Z&6 ^/##/0"73. e T/b& F/-& e !3#, e !3-01&V/,+

• 9/, 6",& e J3/#&

•

F&-0&6",(6& e [JP

•

Let us see how through an example!!


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]V"-01& ]

• Assume the frequency of

operation is 1900 MHz. The

following parameters are given

• Antenna gain is 0dBd

•

Feedline loss is 0.5 dB• Noise figure of the RF unit is 8 dB

• RF Unit gain is 40 dB

• Antenna noise temp is 60 Kelvin

• Detector BW is 100 kHz

• Detector’s SNR is 12dB

•

Use a design margin of 3 dB(above the required sensitivity)

• Transmit power is 43 dBm

• Part I: Find the following

– Total system noise figure

– Total system gain

– Noise power at the detector (Pn)

• Part II: Find the signal power

required into the detector indBm

•

Part III: Find the RX power into

the receiver (Pr) such that the

detector operates properly

(Psen of the receiver)

•

Part IV: The maximum dynamicrange

RF UnitReceiver

(F2, G2, B2)C&&%1/.&8C;O A;@

M6

DecoderM.% ^/4/,"1

^","

N.,&.."

8A3O F3OP@M#%


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]V"-01& ] GM"6, \ [31(73.

• J3 : SF

• C;: C&&%1/.& T3##

• A; : ;EC; : b36 F6".#-/##/3. T/.&

• CB,3,"1 : C; D 8C


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Budget Link Analysis - Review

Conflicting Parameters

• 9_ e f3[ e FK&6-"1 J3/#&

• [JP e f3[EC/%&1/,+ e M, e !3#,

• 9]P e f3[ e [JP e M, e !3#,

•

C6&g? e C/%&1/,+ e ^+."-/$ P".4&

• [+#,&- T3## e ^+."-/$ P".4& e f3[ e U",&6/"1 e !3#,

• f(/$&., M3Z&6 ^/##/0"73. e T/b& F/-& e !3#, e !3-01&V/,+

• 9/, 6",& e J3/#&

•

F&-0&6",(6& e [JP•


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Other Types of Noise

• Intermodulation noise – occurs if signals with differentfrequencies share the same medium

• Interference caused by a signal produced at a frequency thatis the sum or difference of original frequencies

• Crosstalk – unwanted coupling between signal paths

• Impulse noise – irregular pulses or noise spikes• Short duration and of relatively high amplitude

• Caused by external electromagnetic disturbances, or faultsand flaws in the communications system

Question: Assume the impulse noise is 10 msec. How manybits of DATA are corrupted if we are using a Modem operating

at 64 Kbps with 1 Stop bit?

64000 x 7/8 = 56000 bit / sec56000 x .01 = 560 data bits effected


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Other Types of Noise - Example

Intermodulation noise(Diff. signals sharing the

Same medium)

Crosstalk(coupling)

Impulse noise


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What Next?

• Other types of impairments!..

• Channel characteristics


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Other Impairments

• Atmospheric absorption – water vapor and oxygencontribute to attenuation

• Multipath – obstacles reflect signals so that

multiple copies with varying delays are received

•

Refraction – bending of radio waves as theypropagate through the atmosphere


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ImpairmentsWhy are they important?


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References

• Black, Bruce A., et al. Introduction to wireless systems.Prentice Hall PTR, 2008, Chapter 2

• Stallings, William. Wireless Communications & Networks, 2/E .Pearson Education India, 2009; Section 5.3

•

M F Mesiya, Contemporary Communication Systems, First edition

Chapter 6.

Documents

System NOise and Link Budget