SYSTEM NOISE AND LINK BUDGET Updates: 9/24/13; 10/6/14

Introduction • Any system (wired or wireless) receives and generates

unwanted signals •  Natural phenomena or man-made (Noise) •  Unwanted signals from other systems (Interferences)

• Man-made Noise: due to other subsystems (e.g.; power supply)

• Natural Noise: due to random movements and agitation of electrons in resistive components (e.g., due to temperature)

We focus on system thermal noise!

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 transmission media

• 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

Spectral Power Density of (white) Noise • Amount of thermal noise to be found in a bandwidth of 1Hz in any device or conductor is:

•  N0 = noise power density (in watts) per 1 Hz of bandwidth

•  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

N0 = kT W/Hz( )

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/Hz k0 TN = TBN k=

BTN log10 log 10k log10 ++=

à

Thermal or White Noise •  From the plot of the spectral density of thermal noise over

frequency, can see that the noise is flat frequency spectrum till around 100GHz or so and starts to fall off at around 1TeraHz

Thermal Noise Model

• At any temperature, thermal motion of electrons result in thermal 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 :

TBN k= Noise random process has

Gaussian Distribution with zero mean and

some SD ( )W/Hz k0 TN =

Modeling the Thermal Noise (Open Circuit – No Load) •  The noise generated due to temperature T by a resistive

component 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

Vrms = AveragenoisePower = 4kTRB V( )

Example A: Calculate the open-circuit Vrms reading when we connect a true RMS voltmeter to a 100Kohm resistor at room temperature (20 deg. C) with BW=1MHz to measure the generated thermal noise. Draw the equivalent circuit.

True RMS Multimeter

R

Vrms

Equivalent Thermal Noise Model

Noise Power Delivered to the Load •  The voltage delivered to the load is maximum when

Rs=RL=R •  Thus, VL(t) = Vs(t)/2 à

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

Subsystem

Rs

Vs(t) RL

VL(t)

Equivalent Thermal Noise Model

PLoad =VL (t)

2

2=[Vs (t) / 2]

2

R=Vs (t)

2

4R=Vrms2

4R

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

Ther

mal

Noi

se in

dB

Two-Ports Sub-System Noise Characterization

• A subsystem’s noise behavior can be characterized by several 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)

Equivalent Thermal Noise Model

Two-Ports Sub-System Noise Characterization

• A subsystem’s noise behavior can be characterized by several parameters: •  Available Gain (G) •  Noise Bandwidth (B) •  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:

Sao =G ⋅N0 / 2 W/Hz( )

Pao =G ⋅2B ⋅N0 / 2 W( )

G, B,F

Input signal & noise

output signal & noise

Sao & Pao No /2

System Noise Bandwidth (B) Two-Ports System

• Assuming the system is driven by white noise!

• So is the available output power spectral density (W/Hz)

• Pao is the available output power (W)

• G=Go is the mid-band available gain (DC gain)

So( f ) =G( f )Si ( f ) =G( f )No

2

Pao = So( f )df =−∞

∞

∫ No

2G( f )df

−∞

∞

∫

Pao =G ⋅2B ⋅N0 / 2 W( )

→ B = 12G

G( f )df−∞

∞

∫

G(f)

Output Power Spectrum Density

So(f)

Input Power Spectrum Density

Si(f)

The available output noise power due to input white noise

Example A •  (1) Find the BW for a first-order low-pass Butterworth filter

whose gain is given as follow (assume DC gain Go=1):

•  (2) Assuming the input of the system above is driven by

white noise, find the output available power.

G( f ) = 11+ ( f / f3dB )

2

G(f)

Output Power Spectrum Density

So(f)

Input Power Spectrum Density

Si(f)

f3dB

Remember: Two-Ports Sub-System Noise Characterization • A subsystem’s noise behavior can be characterized by

several 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)

Equivalent Thermal Noise Model

Let’s talk about this!

System Noise Figure (F)

F = SNRi / SNRo

=1+ TeTo

•  The most basic definition of noise figure came into popular 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

G, B,F, Te

SubSystem

Input Signal Power =Psi

Input Noise PowerSpectrum Density Sni=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: à •  We often express F in dB •  Note that F>1 •  Nr is the available output noise power due to the two-port

sub-system •  Te is effective (internal) temperature of the subsystem •  To is output equivalent temperature into the subsystem

F = SNRi / SNRo

=1+ TeTo

Pao(noise) =kTGB+ kToGB(F −1) =kGB(T +To(F −1))) =k(T +Te) ⋅G ⋅B

Find the expression for SNRi? SNRi = Psi/kToB

Note: T=To

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 = 100dB B=150 KHz Te = 140 K

output signal & noise

Antenna

Cascaded System

•  Cascaded  sub-­‐systems  can  be  simplifies  by  combining  available  gains  and  noise  proper7es  (B=B1=B2=B3….)  •  G_total  =  Go  =  G1.G2.G3…..  •  F_total  =  F1  +  (F2-­‐1)/G1  +  (F3-­‐1)/(G1.G2)  +  …….    •  Te_total  =  (F_total  –  1).Toà  F_total  =  1+[Te_total  /To]    

• Note  that:  

Unit 2 (F2, G2, B2) Pao  

Antenna  (G,  To,  R)  Or    à(G,  T)  

Unit 1 (F1, G1, B1)

Unit 3 (F3, G3, B3)

Total Gain

R is the equivalent antenna resistance T is effective temperature resulting in noise

Example C Cascaded System

• T_ant=20K  • For  LNA:  G1=10  dB,  F1  =  3  dB    • For  Mixer:  G2  =  9  dB,  F2  =  6.5  dB  • Find  G_total,  F_total,  Te,  Noise  Power,  Pnd  • Simplified  Model:  

• G_total  =  G1.G2  •  F_total  =  F1  +  (F2-­‐1)/G1  •  Te  =  (F_total  –  1).To  

 

Mixer (F2, G2, B2) Pnd  

Antenna  (G,  T)  

To  IF  Amp  Low Noise Amp (F1, G1, B1)

RX Model (F_total, G_total, Te, B) Pnd=Pao  

Psd  Antenna    Noise  

Received    Power  

See notes!

Example  D    Wireless  Transmi`er  

• Assume  PA=40dBm,  for  the  antenna  Gt  =  10dBd,  Feedline  loss  =  3dB,  Loss  through  the  matched  network  is  0.5dB.    

• Find  EIRP  and  ERP  for  a  dipole  antenna.    •  Is  this  RF  transmi`er  more  likely  to  be  a  handset  or  a  base  sta7on?    

Power Amplifier (PA) Feedline  

Pt  

RF Transmitter Digital    

Data  

Freq. Converter Matched Network

Do it on your own!

Expression Eb/N0 •  Ratio of signal energy per bit (J/b) to noise power density per Hertz (W/Hz)

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

TRS

NRS

NEb

k/

00

==

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

•  Given a value for Eb/N0 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 Eb/N0

Probability of Bit Error Rate (PBER)

Question: Assume we require Eb/No = 8.4 dB for bit error of 10^-4. Assume temperature is 290 Kelvin and data rate is set

to 2.4 Kbps. Calculate the required level of the received

signal.

8.4 dB

10^-4

Link  Budget  Analysis    

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

•  Noise Analysis is generally significant to characterize the received signal by the receiver

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

•  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)

Forward  link  (download)  

Reverse  link  (upload)  

Link Budget Detailed View

RF Unit Receiver (F, Go, B) Feedline  

Pr  

Decoder Pn   Digital    

Data  

Power Amplifier Feedline  

Pt  

RF Transmitter Digital    Data  

Freq. Converter

Budget Link Analysis - Conflicting Parameters

•  BW  &  QoS  &  Thermal  Noise    •  SNR  &  QoS/Fidelity  &  Pt  &  Cost    •  BER  &  QoS  &  SNR    &  Pt  &  Cost    •  Freq.  &  Fidelity  &  Dynamic  Range    •  System  Loss  &  Dynamic  Range  &  QoS  &  Material  &  Cost    • Quiescent  Power  Dissipa7on  &  Life  Time  &  Cost  &  Complexity  •  Bit  rate  &  Noise    •  Temperature  &  SNR  •     

Let us see how through an example! à

Example  E  •  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 in dBm

•  Part III: Find the RX power into the receiver (Pr) such that the detector operates properly (Psen of the receiver)

•  Part IV: The maximum dynamic range

RF Unit Receiver

(F2, G2, B2) Feedline  (F1,  G1)  

Pr  

Decoder Pnd   Digital    

Data  

Antenna  (Go,  To,R)  

Psd  

Example  E  –  Part  I  Solu7on  • No  =  KT  •  F1=  Feedline  Loss  • G1  =  1/F1  =  for  Transmission  Line  •  F_total  =  F1  +  (F2-­‐1)/G1  • Go=0  dB;  G_total=Go.G1.G2  •  Pnd  =  k.To.G_total.B.F_total  •  Te  =  (F_total  –  1).To  

RF Unit Receiver

(F2, G2, B2) Feedline  (F1,  G1)  

Pr  

Decoder Pnd   Digital    

Data  

Antenna  (Go,  T)  

Psd  

RX Model (F_total, G_total, Te, B) Pnd  

Psd  Antenna    Noise  

Received    Power  

Part  II  Solu+on:  •  Signal  Power  Required  for  the  Detector  –  Noise  Power  =  Psd  –  Pnd  =  SNR  dB  

             Part  III  Solu+on:  •  Pr  (min)  +  G_total  =  Psdà  Psens  =  Psd  –  G_total  

Part  IV  Solu+on:  

• L_path  +  Pt  –  P_marg  =  Psens  (dB)  

Budget Link Analysis - Review Conflicting Parameters

•  BW  &  QoS  &  Thermal  Noise    •  SNR  &  QoS/Fidelity  &  Pt  &  Cost    •  BER  &  QoS  &  SNR    &  Pt  &  Cost    •  Freq.  &  Fidelity  &  Dynamic  Range    •  System  Loss  &  Dynamic  Range  &  QoS  &  Material  &  Cost    • Quiescent  Power  Dissipa7on  &  Life  Time  &  Cost  &  Complexity  •  Bit  rate  &  Noise    •  Temperature  &  SNR  •     

Other Types of Noise

•  Intermodulation noise – occurs if signals with different frequencies share the same medium •  Interference caused by a signal produced at a frequency that

is 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 faults

and flaws in the communications system

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

at 64 Kbps with 1 Stop bit?

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

Other Types of Noise - Example

Intermodulation noise (Diff. signals sharing the Same medium)

Crosstalk (coupling)

Impulse noise

What Next? • Other types of impairments….. • Channel characteristics

Other Impairments • Atmospheric absorption – water vapor and oxygen contribute to attenuation

• Multipath – obstacles reflect signals so that multiple copies with varying delays are received

• Refraction – bending of radio waves as they propagate through the atmosphere

Impairments Why are they important?

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.