integration of nonlinear, radiation and propagation analysis techniques · pdf...

Scuola di Dottorato in Scienze ed Ingegneria dell’Informazione 1

INTEGRATION OF NONLINEAR, INTEGRATION OF NONLINEAR, RADIATION AND PROPAGATION RADIATION AND PROPAGATION ANALYSIS TECHNIQUES FOR ANALYSIS TECHNIQUES FOR CIRCUITCIRCUIT--LEVEL DESIGN OF LEVEL DESIGN OF

ENTIRE RF LINKSENTIRE RF LINKS

SpeakersSpeakers::Masotti Diego

Costanzo Alessandra


Standard Standard approachapproach toto link link analysisanalysis

• Frequency dispersion

• Linear and non linearreflections at I/O ports

NOT ACCOUNTED NOT ACCOUNTED FOR!FOR!

LimitationsLimitations::

• ideal I/O terminations

• radio channel toosimple

• antennas as isotropicradiators

behavioral models ofinterconnectedsubsystems

schematicschematic descriptiondescriptionofof channelchannel and and circuitcircuit--antennaantenna interactionsinteractions

Available approaches for link computation:


Combination of Nonlinear, EM and Combination of Nonlinear, EM and Propagation Analysis TechniquesPropagation Analysis Techniques

forfor link link analysisanalysis

Antenna elements are EM analysed- as single radiators (SISO)- as antenna arrays (MIMO)

Transmitters and receivers are analysed at circuit-level by HB method

NONLINEARBEHAVIOR

near- and far-fieldELECTROMAGNETIC

BEHAVIOR

PROPAGATIONSCENARIO

Ray-tracing computation of the channel transfer matrix

• An in-depth circuit-level characterization of compact SISO/MIMO links can be carried out by means of a general and exhaustive CAD procedure, which combines:

EM theory


SchematicSchematic ofof a a RxRx//TxTx FRONTFRONT--ENDEND

filteringDown-

converter

Local oscillatorVCO

Low Noise Amplifier

LNA

Antenna

RF signal

filteringUp-

converter

PowerAmplifier

PA

Duplexer/T/R switch


NonlinearNonlinear simulationsimulation ofof frontfront--endsends (1)(1)

• The project of entire RF links is verydemanding in terms of CPU time and memory occupation, since it basicallyrelies upon the characterization ofmicrowave front-ends with realistic(complex) topology.

• Hence, designers need to disregard the nonlinear project of front-ends and usesimplified models for the transceivers; this may lead to an inaccurate prediction of the end-to-end RF link.


NonlinearNonlinear simulationsimulation ofof frontfront--endsends (2)(2)• We propose a solution approach based

on a state-of-the-art version of HBHB(=HHarmonic BBalance) technique, in orderto systematically handle each subsystemas well as the interactions amongsubsystems in a most general and accurate way.

• Thus we can avoid to tackle computer-aided simulation of entire RF links by a handful of simplifying assumptions, whose combined impact on the overallanalysis accuracy may be difficult toestablish.


StateState--ofof--thethe--artart versionversion ofof HB HB

• Our home-made software allows to design and simulate the behavior of (complex) nonlinearcircuits by means of an implementation of the InexactInexact Newton Newton iterationiteration.

( ) ( )

ii1i

iii

nXX

0nXJXE

+=

=+

+

( ) ( )

ii1i

iiiiii )(f

sXX

XEsXJXEr

+=

≤+=

+

E(X) = 0 dim = NHB solving system

Exact Newton iteration

Inexact Newton iteration

Jacobianmatrix


InexactInexact Newton Newton iterationiteration• We have proposed new approaches to further reduce

the problem dimension in order to tackle the analysis/design of realistic front-ends

• [2001] Domain Domain partitioningpartitioning HB HB (DHBDHB): the (complex) nonlinear circuit is automatically split into the interconnection of a number of nonlinear blocks. We introduce a set of auxiliary state variables, namely the voltages at the block connections ports. This leads to strong increase of the jacobian sparsityat the expense of a small overhead due to the slightly increased number of state variables

• [2006] DHB method with ReducedReduced spectraspectra (DHBRDHBR): each block of the DHB method is described by itsown spectrum, which is a subset of the overallspectrum.


Standard HBStandard HB

Huge memory and CPU time resources required!

Dense Jacobian matrix

OUT

IN

BLOCK 1

BLOCK 2

BLOCK 3

DEVICEPORTS

Nonlinearsubnetwork

Linearsubnetwork

JacobianJacobian matrixmatrix



DHB [2001]DHB [2001]

0 ; 1; -1

0 ; 1; -1

Sparse and a-priori knownJacobian matrix

VVC3C3

(3)(2)

BLOCK 1IN

CONNECTION PORTS

OUTBLOCK 2

V

VV

VC1

C2C2

C1

(2)

(2)(1)

(1)

BLOCK 3

Reduction of both memory and CPU time requirements!


DHBR [2006]DHBR [2006]

Further important reduction of both memory and CPU time requirements!

Highly sparse and a priori known Jacobian matrix

BLOCK 1 BLOCK 2IN OUTBLOCK 3

0 ; 1; -1

0 ; 1; -1



MIMO MIMO TxTx frontfront--endend BLOCK 1 BLOCK 2 BLOCK 3 BLOCK 4

IF IN

IF IN

EIN

IN

TX1

TX6

ANTENNA

LO IN

LO IN

RF OUT

RF OUT

MIXER

MIXER

The overall number of unknowns is reduced to almost one tenth!

Full spectrum = 184 lines

IF

TXn

LO RF

OUTININ

No. device ports = 152


Normalized farNormalized far--field spectra (at 10 m)field spectra (at 10 m)

-80.0

-70.0

-60.0

-50.0

-40.0

-30.0

-20.0

-10.0

0.0

897 898 899 900 901 902 903 904 905

Frequency (MHz)

No

rma

lize

d r

ad

iate

d f

ield

(d

B) Pout = + 6 dBm Pout = -11 dBm • Two IF carriers at 45 MHz

and 47 MHz, corresponding to RF output frequencies of 900 and 902 MHz.

• Each carrier is phase and amplitude modulated according to the 16-QAM format at a bit rate of 5.12 Mb/s.

• 512 symbols: each symbol is sampled at a rate of 8 points per symbol, for a total of 4,096 envelope sampling instants.


Waveforms of farWaveforms of far--field envelopesfield envelopes

-1.0

-0.5

0.0

0.5

1.0

0 1 2 3 4

time (µµµµs)

I(t)

-1.0

-0.5

0.0

0.5

1.0

0 1 2 3 4

time (µµµµs)

Q(t

)

Standard HBDHB with reduced spectra

Time slot corresponding to 5 symbols


CPU time and memory savingsCPU time and memory savings

100days

1.5days


CircuitCircuit--levellevel descriptiondescription ofof the the entireentire linklink

• Besides the circuit-level description of the Tx/Rx front ends we also need:– EM characterization of Tx/Rx antennas:

this provides• The actual load to the Tx front-end• The actual source to the Rx front-end

– Description of the channel:• Friis formula• Ray tracing (RT) technique• Statistical channel model• …

– Accurate evaluation of the actual receivedpower (on the Rx side)• Reciprocity theorem


FarFar--fieldfield evaluationevaluation• Since the radiating linear subnetwork is LINEAR the far-field

can be expressed as a linear combination of the voltages at the subnetwork input ports (device or connection ports): VT(ω)

excitationports

connection ports

Nonlinearsubnetwork

TX/RXEM

based

NRAD

deviceports

NNORAD

TX/RX

TX/RX

TX/RX

1

2

NT

( ) ( ) ( )[ ])(;,)(;,;,, 2211 ωωφθ+ωωφθ=ωφθβ−

TT

rj

VAVAr

erE

Far-field (at distance r, in direction θ,φ)(Es. 2-port subnetwork)

radiating linear subnetwork (at

millimeter-wave and/or compact solutions)

radiating linear subnetwork (at microwave

and/or not compact solutions)

VT1 = voltage at port 1

VT2 = voltage at port 2


ReciprocityReciprocity TheoremTheorem (1/5)(1/5)

1

1

2

2

O

O

O

O

Antenna

in Rx mode

RF source

Antennain Tx mode

situation “a”

situation “b”

0 A eq

a

b

R Y J

I

I

AZU

0R

RECEIVER

TRANSMITTER

RECEIVER

TRANSMITTER

Norton

equivalent circuit

referenceantenna in receiving

mode

Theveninequivalent circuit

Tx antenna(Ea,Ha)

(Eb,Hb)

Ja(P2)

referenceantenna in

transmitting mode



Situation “a”

• Say “Jeq” the Norton current source equivalent to the field incident onto the reference antenna. By the application ofthe Kirchhoff’s Current Law (KCLKCL), itresults that

)1(YR1

JI

IRYIJ

A0

eqa

a0A

aeq

+−=

⇒

+=−



Situation “b”

• The circuit equivalent to the transmitter is a voltage source U with a series resistance R0, so that we can apply the Kirchhoff’s Voltage Law (KVLKVL) to the circuit:

)2(YR1

YUI

ZR

UIIZVbutVIRU

A0

Ab

A0

bbA

bbb0

+−=

⇒

+−=⇒−==+



Application of the Reciprocity Theorem

• By combining (1), (2) and (3) we obtainthe rigorous expression for the Norton equivalent current source Jeq:

( ) ( ) ( )

∈

•=+ ∫

22

V

22b

2aba

A0

VP

)3(dVPPIIZR2

EJ

( ) ( ) )4(dVPP

YR1U1

J2V

22b

2a

A0

eq ∫ •

+

= EJ



Application of the Reciprocity Theorem• Formula (4) is the rigorous way to

calculate the Norton current source equivalent to an EM field incident ontoan antenna in receiving mode

1) the impressed current source of the incident EM field Ja(P2)2) the EM field radiated by the Rxantenna in transmitting mode Eb(P2), after the suppression of the source Ja(P2)

by means of:


( ) ( ) (5)φθ,φθ,e2λ

YR1

U

1jJ bajβ

A0

eq EE •η

+

= rr

JJeqeq evaluationevaluation in ORDINARY linkin ORDINARY linkTypical situation:

• each antenna is in the Fraunhofer region ofthe other one

• the EM field incident onto the receivingantenna is a plane wave

Hence, previous formula changes as follows:

Far-field radiated by theTx antenna/RF source

Far-field radiated by theRx antenna


JJeqeq evaluationevaluation in NON CONVENTIONAL linkin NON CONVENTIONAL link

• In RF energy harvestingsystems, or in wireless sensor networks:– Locations of Tx and Rx

antennas are absolutely random

– Rx antenna can be located in the Tx near-field region

n

nEM

HnJ

Ssurf

Ssurf

ˆ)()(

)(ˆ)(

xPP

PxP

ΣΣ

ΣΣ

=

=

[ ] Σ×−×

•ω+

=

ΣΣΣΣ

Σ

•

∫ dPPPP

U

YR R

)()()()(

ˆ)(1

J 0eq

SRRS HEHE

n

Equivalencetheorem

(6)


ExampleExample ofof applicationapplication

0

10

20

30

40

50

0 5 10 15 20 25 30

d/λλλλ

|Jeq

| (m

A)

Plane-wave approximation

still valid

This work:

Plane-wave approximation:

ψ = 0°

ψ = 0°

ψ = 90°

ψ = 90°

Near-fieldregion

Fraunhoferregion

• Tx antenna: patch @ 1800MHz, gain=7dB

• Rx antenna: harvester @ 1800MHz, gain=1dB


ExampleExample ofof applicationapplication

• Tx antenna: base station

• Rx antenna: harvester @ 1800MHz, gain=1dB

Maximum link direction

0.00

0.04

0.08

0.12

0.16

0.20

0 100 200 300 400 500 600

d (m)

|Jeq

| (m

A)

This work Plane-wave approximation

case A

case Bcase C

Far-field Max direction

Far-field Almost max direction

Far-field No max direction

Plane-wave approx. still valid


11stst applicationapplication: RF SISO link: RF SISO link


RigorousRigorous SISO link SISO link simulationsimulation

TxTx RxRx

• EM simulation of antennas

• Application of Reciprocity Theorem

• Realistic channel description

Nonlinear simulation of transmitterand receiver front-ends

channelchannel


TX TX FrontFront--endend

IF 45 MHzLO 855 MHzRF 900 MHzIF power -26 dBm

Single sideband configuration

LO power 0 dBmRF power 20.4 dBmSmall signal gain 53 dBDevice ports number (nD) 98


RxRx FrontFront--endend

RF 900 MHzLO 810 MHzIF 90 MHzRF power -80 dBm

LO power 0 dBmIF power -28 dBmSmall signal gain 55 dBDevice ports number (nD) 208

Image-rejection configuration


AntennasAntennas

TxTx RxRx

Base stationantenna

(collinear4-dipoles)

Dual-bandPIFA

antenna

@ 900 MHz


ReciprocityReciprocity TheoremTheorem ((freefree--spacespace conditionsconditions))• The transmitted field can be computed as a linear function of

the Tx antenna excitation VT(ωRF):

• The Norton equivalent generator of the received field is evaluated by rigorous application of the Reciprocity Theorem:

( ) ( ) ( ) ( )( ) ( )RFTRFφRFθRFT ωVωφ;θ,Aφωφ;θ,Aθjβexp

ωφ;θ,, +−

=r

rrE

( )RFTTT ω;φ,θ,rE

Tx Rx

( )RFRRR ω;φ,θr,E

• Tx ant. excited• Far-field evaluated in the

phase center of Rx ant.

11stst stepstep• Rx ant. in tx mode• Far-field evaluated in the phase

center of Tx ant.

22ndnd stepstep


( ) ( )RFRF

rRFRF

rω•ω

η

ω+=ω ;φ,θr,;φ,θr,e

2λ

U

)(YR1j)(J TTRR

jβA0R TR EE

ReciprocityReciprocity TheoremTheorem ((freefree--spacespace conditionsconditions))

Norton equivalent

circuit of the receiver

Tx Rx

Norton equivalent current source accounting for the field received by the Rx antenna

22ndnd stepstep

11stst stepstep

( )RFR ωJ ( )RFA ωY

Rx


I/O I/O relationshiprelationship• The whole procedure determines a relationshipbetween the radiating subnetwork input VT(ω) and the excitation source of the receiver (equivalent tothe received field) JR(ωRF)

• In this case, H(ωRF) takes into account the propagation of the signal in free-space (FriisFriisformulaformula), only. As will be demonstrated later on, a realistic description of the channel can be included in a straightforward way.

• After the Norton equivalent excitation of the receiver JR(ωRF) has been evaluated, an HB analysisof the receiver can be performed in order toobtain the actual output of the entire link.

( ) ( ) ( )RFTRFRFR ωωω VHJ =


ππ/4/4--DQPSK DQPSK modulationmodulation formatformat

-1.00

-0.50

0.00

0.50

1.00

7.0 7.5 8.0

time (ms)

I(t)

-1.00

-0.50

0.00

0.50

1.00

7.0 7.5 8.0

time (ms)

Q(t

)

normalized Rx output voltagenormalized Tx input voltage

-0.01

0.00

0.01

-0.01 0.00 0.01

I(t) (V)

Q(t

) (V

)

output

-0.05

0.00

0.05

-0.05 0.00 0.05

I(t) (V)

Q(t

) (V

)

input


Radio Radio channelchannel descriptiondescription

•• Ray Ray TracingTracing (RTRT) models are recognizedamong the most appropriate fieldprediction tools for the study and planning of radio systems in complexpropagation environments.

• The ability of RT models consist of the predictionprediction ofof the the multipathmultipath pattern and pattern and thusthus the the timetime-- and and angleangle--dispersiondispersion ofofthe radio the radio transmittedtransmitted signalsignal.

• The need for a detailed 3D database ofthe environment has become lesscritical thanks to the availability ofdigitized maps.


Radio Radio channelchannel descriptiondescription

• The RT approach allows to give a scenario-dependent expression to the channel transfer function H(ω):

( ) ( )i

Ν

1ιι jω-expρωH

P

τ∑=

=

i-th path complex amplitude i-th path time delay

number of multipath components

EM EM fieldfield asas the the actualactual physicalphysical link link betweenbetween the the transmittertransmitter and and receiverreceiver side!side!


Radio Radio channelchannel descriptiondescription•• Ray Ray TracingTracing phasesphases

1) Tracking of rays: computation of

2) Application of the ReciprocityReciprocity TheoremTheoremfor each ray to evaluate the amplitude ρi

3) Superposition of all contributions

p

ii v

r=τ

i-th path length

free-space phase velocity

( )∑=

=pN

1i

iJJ eqeq


Different situationsconsidered

Tx: 30 m high over a building

Rx: 700 m away

Free-space

TxTxLOSLOS

NLOSNLOSNon line of sight (NLOS)

Line of sight (LOS)

Link analysis in realistic channel conditions

MODULATION FORMAT

CHANNEL

16-QAM, low bit rate: 72 kb/s16-QAM, high bit rate: 1.28 Mb/s


Transfer Transfer functionfunction amplitudeamplitude: NLOS and LOS: NLOS and LOS

0.E+0

1.E-6

2.E-6

3.E-6

4.E-6

5.E-6

6.E-6

899 899.5 900 900.5 901

Frequency (MHz)

|H(f

)|

1.9E-4

2.0E-4

2.1E-4

2.2E-4

899 899.5 900 900.5 901

Frequency (MHz)

|H(f

)|

“Selective fading” more evident forNLOS than LOS case

(LOS) (NLOS)(NLOS)


Linear Linear phasephase behaviourbehaviourvs. vs. frequencyfrequency (LOS)(LOS)

NonlinearNonlinear phasephasebehaviourbehaviour vs. vs. frequencyfrequency

(NLOS)(NLOS)

-180

-120

-60

0

60

120

180

899 899.5 900 900.5 901

Frequency (MHz)

arg

(H(f

)) (

°)

-180

-120

-60

0

60

120

180

899 899.5 900 900.5 901

Frequency (MHz)

arg

(H(f

)) (

°)

Transfer Transfer functionfunction phasephase: NLOS and LOS: NLOS and LOS


NLOS NLOS channelchannel introducesintroducesdistortiondistortion

RX output (NLOS)RX output (NLOS)

RX output (LOS)TX inputTX input

RX output (free-space)

LOS case LOS case similarsimilar totofreefree--spacespace casecase

NormalizedNormalized TxTx input and input and RxRx output output (B(Brr=72 =72 kbkb/s)/s)

0

0.2

0.4

0.6

0.8

1

2 2.2 2.4 2.6 2.8 3

time(ms)

0

0.2

0.4

0.6

0.8

1

2 2.2 2.4 2.6 2.8 3

time(ms)

0

0.2

0.4

0.6

0.8

1

2 2.2 2.4 2.6 2.8 3

time(ms)

0

0.2

0.4

0.6

0.8

1

2 2.2 2.4 2.6 2.8 3

time(ms)

(V)


-1.5

-1

-0.5

0

0.5

1

1.5

-1.5 -1 -0.5 0 0.5 1 1.5

I(t)

Q(t

)-1.5

-1

-0.5

0

0.5

1

1.5

-1.5 -1 -0.5 0 0.5 1 1.5

I(t)

Q(t

)-1.5

-1

-0.5

0

0.5

1

1.5

-1.5 -1 -0.5 0 0.5 1 1.5

I(t)

Q(t

)

TxTx inputinputRxRx output output

(NLOS)(NLOS)

RxRx output output

(LOS)(LOS)

PhasePhase trajectoriestrajectories -- BBrr=72 =72 kbkb/s/s


0

0.2

0.4

0.6

0.8

1

85 90 95 100 105 110

time(µµµµs)

0

0.2

0.4

0.6

0.8

1

85 90 95 100 105 110

time(µµµµs)

0

0.2

0.4

0.6

0.8

1

85 90 95 100 105 110

time(µµµµs)

0

0.2

0.4

0.6

0.8

1

85 90 95 100 105 110time(µµµµs)

High High distortiondistortion bothboth in in LOS and NLOS LOS and NLOS casescases

ChannelChannel behaviourbehaviourdependentdependent on biton bit--raterate

NormalizedNormalized TxTx input and input and RxRx output output (B(Brr=1.28 Mb/s)=1.28 Mb/s)

RX output (NLOS)RX output (NLOS)

RX output (LOS)TX inputTX input

RX output (free-space)

(V)

22ndnd applicationapplication: RF MIMO link: RF MIMO link

45Scuola di Dottorato in Scienze ed Ingegneria dell’Informazione

46

OutlineOutline

•The performances of a wireless mobile system can be strongly influenced by :

1) thermal noise (noisenoise--limitedlimited system)system)2) co-channel interference caused by spatial

frequency reuse (interferenceinterference--limitedlimitedsystem)system)

3) anomalous propagation effects due toradio-channel variability

Scuola di Dottorato in Scienze ed Ingegneria dell’Informazione

47

FadingFading

••FadingFading: physical phenomenon that can beexpressed as the time- and space-variationof the power Pr received by a terminal.

•We can determine three causes for the variation of Pr:

1) multipath fast fadingfast fading2) shadowing slow fadingslow fading3) pathlosspathloss


48

FadingFading

•The multipathmultipath phenomenon can bedescribed in many ways. A very common method is the so-called Ray TracingAlgorithm: the overall received signal is the superposition of all echoes (of the transmitted signal) generated by the reflections/refractions/diffractions of the EM field on objects placed along the propagation link. Such phenomena can makethe received power vary very fast fast fast fadingfading.


49

FadingFading

•The shadowingshadowing effect originates fromchangings in the lay of the land and, aboveall, from big obstacles that can bepositioned along the path from the transmitter to the receiver. Thus we can observe variations of the received powerslower than the ones of the fast fading-case: this is why we call this phenomenonslow fadingslow fading.

•The pathlosspathloss is the attenuation constantterm due to free-space-propagation.


50

Fading Fading -- OverviewOverview

•The fast fading fast fading is the fast variation of the received power around a local mean value, at a reference distance of about 20λ∻40λfrom the terminal, due to obstacles withlittle size near the receiver.

•The slow fading slow fading is the slow variation of the received power over distances not biggerthan 100∻200 m; in this case, the attentions is focused on obstacles with big size (i.e. groups of buildings, hills, mountains…).


51


•For the statistical characterization of the fast fadingfast fading, the Rayleigh-model is typicallyused, so the fast fading can be defined asRayleighRayleigh--fadingfading.

•For the slow fadingslow fading, the so-called “log-normal statistical model” is usually used.

•For the pathlosspathloss, there are severalaccurate models. One of these is the “Hata-model”, which is nowadays the mostused propagation model in urbanenvironments.


52


fast fading slow fading

pathloss


53

DiversityDiversity techniquestechniques

•The effects of the fading phenomenon can generate a huge amount of transmissionerrors and, in the case of “selective fading”, we could encounter a dangerous lineardistorsion of the transmitted signal: thiswould lead to InterSymbol Interference(ISI) at the receiver side.

•The diversitydiversity techniquestechniques are one of the possible countermeasures to fading effects.


54


•A diversity technique consists of the transmission of several replica of the samesignal over different incorrelated channels. Thus, say “p” the “outage probability” forthe generic channel; if we consider N replica (hence, N channels) of the originalsignal, we can calculate the outageprobability for N channels:

Poutage|N channels=pN<<p ADVANTAGE!ADVANTAGE!

•Types of diversity techniques: time, frequency and spacespace.


55


•For our purpose, we consider now a particular space diversity technique, i.e. MIMOMIMO (=MMultiple IInput MMultiple OOutput): in its original meaning, a MIMO system consists of multiple antennas both at the transmitter- and receiver-side. The distance between two antennas is largeenough to provide incorrelatedincorrelated transmissiontransmissionchannelschannels.

•The received replies have to beconveniently combined in order to minimizethe Bit Error Rate (BERBER).


56

OutlineOutline

•Frewuently MIMO systems have been studiedwith respect to the situation of incorrelatedchannels: that means, antennas spacing is greateror equal to 10λ in order to obtain independentreplies of the transmitted signal.

•In many cases, due to space limitations, MIMO systems require compact antenna arrays with reduced spacing between radiators. In order to accurately predict MIMO performance in such cases it is of primary importance that both near-field coupling effects between antenna elements and far-field radiating behavior of the antenna array for specific channel scenarios be simultaneously accounted for


57

ApplicationsApplications ofof MIMO MIMO techniquetechnique (1)(1)

Router ADSL Router ADSL forfor WLANWLAN

Smart Smart AntennasAntennas


58

ApplicationsApplications ofof MIMO MIMO techniquetechnique (2)(2)

Access Point Access Point forfor WiWi--FiFi networksnetworks


59

MIMO MIMO futurefuture……

PerformancesPerformances enhancementenhancement!!


60

Near-field couplings determine front-end nonlinear behavior

The embedded far-field influences the channel transfer matrix H(ω)

In-depth exploitation of spatial diversity:

spectral regrowth reduction

improvement of the MIMO link BER

Antenna spacing is a crucial feature

for MIMO system design

In multipath and “selective fading”channel scenario…

MotivationMotivation


61

MIMO link MIMO link analysisanalysis

•Our approach allows to consider MIMO systems in a rigorous way through a non-linear/electromagnetic co-simulation.

•All non-linear effects of front-ends at bothtransmitter and receiver side are taken intoaccount.

•Every front-end is connected to an antenna array that can be characterized with an EM simulator.

•The overall results are combined with the characteristics of the channel through the ReciprocityReciprocity TheoremTheorem.


62

I

I

I

1

r

NR

NLOS orLOS

channel

A schematic view

Multiple Transmitter

TX

TX

TX

TX

TX

1

2

3

5

4

Multiple Receiver

RX

RX

RX

RX

RX

1

3

2

4

5

NDT

device ports

NRADT

connectionports

NET

excitation ports

NDR

deviceports

NER

excitationports

NRADR

connectionports


63

MultiMulti--domain simulation of the MIMO linkdomain simulation of the MIMO link

TX

RADN

hhembedded radiated

field for the actual

nonlinear regime

hhembedded radiated

field at the r-th receiver

( )RF

tq,r, ω,θ,r, φRE

( )RF

tq,

T ω,θ,r, φE

RX

RADN

embedded

radiated field for

a unit-source

eTX (r,θ,φ,ωRF)

transmitting antennas

EM modelled as

ONE -port antenna TX

Cn

TX

RADN TX

RADN

admittance matrix

( )

[ ]TX

C

TX

C

RF

nn

ω

×

TX

AY

receiving antennas

EM modelled as

ONE -port antenna RX

Cn

embedded

radiated field for

a unit-source

eRX (r,θ,φ,ωRF)

admittance matrix

( )

[ ]RX

C

RX

C

RF

RX

nn

ω

×

AY

RX

RADN

RECIPROCITY RELATIONRECIPROCITY RELATION


64

NDT

device ports

NET

excitation ports

Nonlinearsubnetwork

TX NNORADT

TX

TX

TX

1

t

NT

TRADN

[ ]

s

k

sk

k

T,RF

tr

21LOT2IFT1T,

Ωω

kk;ωkωkΩ

=⇒=

=+=Harmonic balance analysis under multitone excitation

NRADT

connection ports

Broadband EM analysis of the antenna array

Nonlinear circuit techniques +

CircuitCircuit--level computation of the level computation of the multiple transmittermultiple transmitter


65

ComputationComputation ofof the antenna the antenna excitationsexcitations

From the linear subnetwork equations…

… at the spectral line corresponding to the RF frequency ωRF

Where the admittance submatrices:• YDT relates the device ports to the connection ports (dim: NRAD

TxNDT)

• YTT is seen from the connection ports (dim: NRADTxNRAD

T) • YAT results from EM analysis of the antenna array (dim: NRAD

TxNRADT)

At the antenna-array ports… ( ) ss VYI T,RFATT, ω=

NRADT-vector of complex

phasors of the voltage excitations at the antenna array ports are:

( ) ( )[ ] ( ) s

-1

s XYYYV- T,RFDTRFTTRFATT, ωωω +=

… the complex phasors of the currents flowing out of the NRAD

T connection ports are computed:

( ) ( ) sss VYXYI T,RFTTT,RFDTT, ωω +=−


66

The The ““embeddedembedded”” radiationradiation pattern pattern ofof the the tt--thth arrayarray elementelement

• With the assumption of free-space propagation, the total radiated field associated with the t-th array element in the presence of the other ones at ωRF is:

The radiated field is a linear functional of the complex phasors of the voltage excitations

( )tT,V s

Due to linearity

where:

are the scalar components of the normalized field in a sphericalcoordinate system with origin in the phase center OT of the transmitting array. Such components are generated by EM simulation with a unit-voltage sinusoidal source of angular frequency ωRF connected to the t-th port and the remaining ports short-circuited.

( ) ( )( ) ( )

RFtφT

RFt

Tθ

ω;φθ,A

ω;φθ,A

( ) ( ) ( ) ( )( ) (t)T,RF

(t)TφRF

(t)TθRF

(t)T Vωφ;θ,Aφωφ;θ,Aθ

jβexpωφ;θ,, sE +

−=

rr

r


67

NARROWBAND ARRAY: unique multipath pattern for a given environment and TX-RX phase center positions

( ) ( ) ( )( ) tq,r,

qdβj

RFDDDtq,

Tq

N

ql

q1

t)(q,RFAA

tq,r,R eω;φ,θ,As,...,s,...,sΓ)ω;φ,θ,( ±⋅= rrA EE

φD

θD

( )( )RFDDDtq,

T ω;φ,θ,rE

φA

θA

( )( )RFAAAtq,r,

R ω;φ,θ,rE

RXTX

q-th ray

Nq scattering points

Phase shift at the r-th receiving element

Effects of ray interactionsScalar spreading factor: s

lq is the

length of the l-th segment of the q-th path

Channel description by a Channel description by a Ray Tracing approachRay Tracing approach


68

( ) ( ) ( )RRFAAAtq,r,

RRF'

A'

ArRNrr

tq,r, Nr1)ω;φ,θ,()ω;φ,(θYλη

2jJ ≤≤⋅= rEEs

By the Reciprocity Theorem:

I. Antenna in receiving mode

r-th element excitation

φA’

θA’

II. Antenna in transmitting mode

(normalized) radiation pattern of the r-th receiving element

( )RFAArRN ω;'φ,'θE

φA

θA

Scattering point

q-th ray incident from the t-th transmitter

( ) )ω;φ,θ,( RFAAAtq,r,

R rE

Excitation of the receiving arrayExcitation of the receiving arrayassociated with the qassociated with the q--th rayth ray


69

( ) ss VHJ T,RFR, ω=

( ) sss JVYI R,R,RFARR, ω +=

RXr

RX1

RXNR

Nonlinearsubnetwork

RXI

I

I

1

r

NR

NRADR

Y ( )AR ω

NRNORAD

( )∑∑= =

=T

tRAYN

1t

N

1q

tq,r,r JJ ss

Superposition of the ray contributions

• r-th connection port• NT: n° of transmitters • Nt

RAY: n° of rays

computation of the (NRxNT)

channel transfer matrix

Computation of the Computation of the channel transfer matrixchannel transfer matrix

computation of the channel outputs


70

2x2 MIMO link: near2x2 MIMO link: near--field couplingsfield couplings……

single dipole

and d 4= λ

d /8= λ

d = λ/2

d = λ

φ 2

4

6

8 [V/m]

30

210

60

240

90

270

120

300

150

330

180 0

Remarkable pattern deformation due to mutual couplings

d 2x2 MIMO link fRF = 2.437 GHz (WLAN band) Half-wave dipoles Variable d for transmitting

antennas

-20

-15

-10

-5

0

2.2 2.3 2.4 2.5

Frequency [GHz]

|S1

1| [d

B]

-70

-60

-50

-40

-30

-20

-10

0

|S2

1| [d

B]

SISO λ/8 λ/2 λ


71

…… and influence on transmitter performancesand influence on transmitter performances

Interactions between transmitting antenna array and nonlinear front-end

Strong influence on the gain compression curve

0.0

0.4

0.8

1.2

1.6

-30 -25 -20 -15 -10

IF power (dBm)

Far-

fiel

d p

ow

er d

ensi

ty

(mW

/m2)

single dipole and d=4λ d=λ/8 d=λ/2 d=λ

η2

*

TT EE ⋅

MIMO front-ends must always

be analysed under the

assumption of realistic

EM behavior!


72

Channel transfer matrixChannel transfer matrix

Variable dipoles spacing Distance between TRANSMITTING

antennas = λ /2 (fixed) Scenario: NLOS (more than 3,000 rays)

d=3λ/8 d=λ/8Quasi-optimal

0.0E+00

3.0E-07

6.0E-07

9.0E-07

1.2E-06

-1.28 -0.64 0.00 0.64 1.28

Frequency offset (MHz)

|H | |H | |H | |H |11 21 12 22

0.0E+00

3.0E-07

6.0E-07

9.0E-07

1.2E-06

-1.28 -0.64 0.00 0.64 1.28


|H | |H | |H | |H |11 21 12 22


73

NLOS scenario in SISO case – starting point

Modulation format: 16-QAM Signal bit rate = 1.28 Mb/s Modulation-oriented Harmonic

Balance technique Equal Gain Combining Technique

Input vs. output power spectrumInput vs. output power spectrum

-100

-90

-80

-70

-60

-50

-40

-30

-20

-10

0

-2.5 -1.5 -0.5 0.5 1.5 2.5


No

rma

lize

d p

ow

er s

pec

tru

m (

dB

)Input Output


74

d=λ/8ACPR ≈ -49.2 dBc

By varying the antennas spacing d: MIMO

worst case…

… and MIMOoptimal case

ACPR ≈ -46.2 dBc

MIMO vs. SISO spectral regrowthMIMO vs. SISO spectral regrowth

-100

-90

-80

-70

-60

-50

-40

-30

-20

-10

0

-2.5 -1.5 -0.5 0.5 1.5 2.5


No

rm

ali

zed

po

wer s

pectr

um

(d

B)

Input Output

d=λ/4ACPR ≈ -50.1 dBc

-100

-80

-60

-40

-20

0

-2.5 -1.5 -0.5 0.5 1.5 2.5


No

rma

lize

d p

ow

er s

pec

tru

m (

dB

)

Input

Output

SISO

-100

-80

-60

-40

-20

0

-2.5 -1.5 -0.5 0.5 1.5 2.5


Norm

ali

zed

pow

er s

pec

tru

m (

dB

)

Input

Output


75

MIMO BER computationMIMO BER computation

• BER computation in a AWGN (Additive White Gaussian Noise) link by means of AWR AWR –– VSS Design EnvironmentVSS Design Environment. A two-port block connected in cascode to Js

r at each receiving antenna port models noise.

• Results computation: for a fixed signal-to-noise ratio (SNR) of 10dB at the receiver input.

TPID=TP1

SRC_CID=A2VAL="output_canale_fort_49"COL=1TCOL= CTRFRQ=2.437 GHzSMPFRQ=_DRATE*8 Hz

SRC_CID=A1VAL="output_canale_fort_48"COL=1TCOL= CTRFRQ=2.437 GHzSMPFRQ=_DRATE*8 Hz

TPID=TP2

AWGNID=A3PWR=10PWRTYP=Es/N0 (dB)LOSS=0 dB

AWGNID=A4PWR=10PWRTYP=Es/N0 (dB)LOSS=0 dB

Channel

output 1

AWGN = 10 dB

Channel

output 2

Ch. out. 1

noise

Ch. out. 2

noise

Representation of LINK NOISERepresentation of LINK NOISE

( )( ) s12

s11s

VH

VHJ

T2,RF

T1,RFR1,

ω

ω +=

( )( ) s22

s21s

VH

VHJ

T2,RF

T1,RFR2,

ω

ω +=


76

Artificial Neural NetworkArtificial Neural Network• The previous results have been used to create two sequences of

1,500,000 samples by means of an artificial-neural-network (ANN) link model trained by a sequence of 512 simulated samples.

Ch. out. 1

noise

Ch. out. 2

noise

RECEIVER 1

RECEIVER 2

A

N

N

1,500,000

samples

1,500,000

samples


77

BER computationBER computation• BER has been estimated by using the 1,500,000-samples signals in a

VSS ad-hoc block diagram, which implements the Equal Gain Combining technique. The BER block calculates BER by direct I/O comparison.

1

2

3

ADD_OLDID=A5PRIMINP=0NIN=2

TPID=TPDEMOD1

SRC_CID=A3VAL="16QAM_750000_meno27dBm"COL=1TCOL= CTRFRQ=0.4 GHzSMPFRQ=_DRATE*8 Hz

SRC_CID=A2VAL="output_VR1_750000"COL=1TCOL= CTRFRQ=0.09 GHzSMPFRQ=_DRATE*8 Hz

SRC_CID=A1VAL="output_VR2_750000"COL=1TCOL= CTRFRQ=0.09 GHzSMPFRQ=_DRATE*8 Hz

QAM_DETID=A9

QAM_DETID=A8

1 2

3 4

IQ_DMODID=A6

BER

BER_EXTID=BER1VARNAME=""VALUES= OUTFL=""

1

2

3

4

5 6

ALIGNID=A4N= REEVAL= CORRDLY= DLYCOMP=YesINTRPSPN=0GAINCOMP=PowerPHSCOMP=Rotation & reversalSMPLPTS=

1 2

3 4

IQ_DMODID=A7

TPID=TPDEC2

TPID=TPDEC1

TPID=TPTX

TPID=TPRX2

TPID=TPRX1

TPID=TPDEMOD2

TPID=TP3

1,500,000

samples

1,500,000

samples

Equal Gain Combining Demodulation/Decoding

BERBER

computationcomputation

Input signalScuola di Dottorato in Scienze ed Ingegneria dell’Informazione

78

Noticeable improvement

Variable dipoles spacing: optimal and worst case

d=λ/4 d=λ/8

Output signal constellationsOutput signal constellations

-1

-0.5

0

0.5

1

-1 -0.5 0 0.5 1

I

Q

-1

-0.5

0

0.5

1

-1 -0.5 0 0.5 1

I

Q


79

BER BER -- ResultsResults

1.E-4

1.E-3

1.E-2

1.E-1

1.E+0

0 0.5 1 1.5 2

Distance (no. of wavelengths )

BE

R

SISO

Optimal spacing: d=λ/4

• For the scenario under consideration, the optimum antenna spacing results in a BER reduction of about two orders of magnitude with respect to the SISO case. Note that the optimum performance is acceptable in spite of the low SNR.

PIN = -30 dBm


80

TimeTime--domain validationdomain validation• Comparison of the MIMO link analysis results produced by our technique with

those generated by time-domain analysis making use of Spectre HDLSpectre HDL. • Very demanding in terms of CPU time since it basically relies upon a time-domain

convolution; moreover, the slow (1.28 Mb/s) modulation of the 2.437 GHz RF carrier generates the need for an unreasonably large number of time-domain integration steps.

-30

-20

-10

0

10

20

30

0 5 10 15 20

time (µµµµs)

(nA

)

This work Time-domain analysis

-30

-20

-10

0

10

20

30

0 5 10 15 20

time (µµµµs)

I(t)

(n

A)


-30

-20

-10

0

10

20

30

0 5 10 15 20

time (µµµµs)

Q(t

) (n

A)


Js1

64-bit time slot

Complex envelope

In-phase

components

Quadrature

components

VERY SATISFACTORY AGREEMENT!Scuola di Dottorato in Scienze ed Ingegneria dell’Informazione

81

Simulation comparisonSimulation comparison

About 100 minutesAbout 100 minutes

Within this budget, about 40% of the time is taken by the EM simulation of the transmitting and receiving antenna arrays, about 45% by the computation of the RT-based field prediction model, and the remaining 15% by the nonlinear analysis of the transmitter and receiver front ends.CPU

time

on a 2.8 GHz PC!

About 22,000 times longer than the About 22,000 times longer than the CAD procedure used in our work!CAD procedure used in our work!

OUR APPROACHOUR APPROACH

TIMETIME--DOMAIN ANALYSISDOMAIN ANALYSIS

Constraints in the number of frequency-domain sampling points for H(ω) and time-domain sampling points in the integration process

Tradeoff between accuracy and CPU time


82

d2x2 MIMO link: same scenario…

Patch antenna as radiating elementPatch antenna as radiating element

… but different optimal distance!

d=λd=3λ/8

-100

-80

-60

-40

-20

0

-2.5 -1.5 -0.5 0.5 1.5 2.5


Norm

ali

zed

pow

er s

pec

tru

m (

dB

)

Input

Output

-100

-80

-60

-40

-20

0

-2.5 -1.5 -0.5 0.5 1.5 2.5


Norm

ali

zed

pow

er s

pec

tru

m (

dB

)

Input

Output


83

AWGN link analysis with enhanced number of symbols by

ANN model

1,500,000 total samples

Modulation format: 16-QAM

PIN = -30 dBm

BER BER -- ResultsResults

Optimal spacing: d=3λ/8

1.E-4

1.E-3

1.E-2

1.E-1

1.E+0

0 0.5 1 1.5 2

Distance (no. of wavelengths)

BE

R

SISO


84

SISO and MIMO SISO and MIMO -- ConclusionsConclusions

• Interactions between subsystems are evaluated through a combination of state-of-the-art nonlinear and EM tools combined with electromagnetic theory.

•• Key aspects:Key aspects: EM-based evaluation of radiated field distribution (both

near-field and far-field) of the antenna array Analysis of transmit/receive front-ends by nonlinear

CAD methods Sophisticated channel model accounting for multiple

reflection, refraction and scattering effects EM field used to establish the actual physical link

between transmitter and receiver

• The work is a starting point for the developement of a new generation of general-purpose software for RF link analysis.


85

33rdrd application: UWBapplication: UWB--receiver receiver analysis in the presence of an analysis in the presence of an

interfering signalinterfering signal


86

MOTIVATIONSMOTIVATIONS

• Due to huge bands ([3.1÷10.6] GHz), UWB systems suffer from active and passive interference.

WLAN – Wi-Fi band

-120

-110

-100

-90

-80

-70

-60

-50

-40

-30

3.0 4.3 5.5 6.8 8.0 9.3 10.5

Frequency (GHz)Scuola di Dottorato in Scienze ed Ingegneria dell’Informazione

87

MOTIVATIONSMOTIVATIONS

Nonlinear interactionsNonlinear interactions

Standard circuit-level approach

Standard circuit-level approach

Time-domain technique

Dispersive effectsDispersive effects

Frequency-domain technique

Problems with huge number of spectral lines

Problems with huge number of spectral lines

• Theoretical signal analysis

• System simulation based on “black-box” models

HB method based on model-order reductionallowing large number of spectral lines to be handled

Efficient circuit-level approachEfficient circuit-level approach

System-level approach

System-level approach


88

EFFICIENT MATEFFICIENT MAT--VEC EVALUATIONVEC EVALUATION

• It is numerically convenient to change summation over vector indexes into summations over one scalar index

• Map properties:

The maximum value of φ(k) for k ∈ S+ (say H) must be minimized (compatibly with previous condition).

Quasi-periodicregime

Quasi-periodicregime

( ) ΩkΩφΩrk i

T

1ii ==∑

=

k

“Equivalent”periodic regime

“Equivalent”periodic regime

1 2 3 4 H( )kϕ

Ω

ω

map φφφφ

k 0 00 0

11

1 1 11 1

1 22 22 -2 -2-1 -1

2 2 2 2k

1

2

ω1ω2

ω

φφφφ----1111

φφφφ

Ωk


89

TRANSMITTEDTRANSMITTED--REFERENCE UWB RxREFERENCE UWB Rx

“0”

24 nonlinear device ports

UWBIN: sequence of frames of DQPSK modulated pulses

(pulse width = 200 ps)

“1”

amplifierandfilterUWB IN

OUT

diode ringmixer

integrator

delayτd

τd = 1 ns

τf = 4 ns


90

-400

-350

-300

-250

-200

-150

-100

-50

0

0 4 8 12 16 20 24 28 32

Frequency (GHz)

Po

wer

Den

sity

(d

Bm

/MH

z) '1' '0'

UWBUWB signal spectrum (sequence of signal spectrum (sequence of ““11”” oror ““00””))

• In this case the time-domain waveform is periodic with

– Period τf = 4 ns

– Fundamental frequency ω1 = ωUWB = 2π • 250 MHz

First 128 spectral lines UWB band

-120

-110

-100

-90

-80

-70

-60

-50

-40

-30

3.0 4.3 5.5 6.8 8.0 9.3 10.5

Frequency (GHz)

Po

wer

Den

sity

(d

Bm

/MH

z)

'1' '0'


91

OUT: in the absence of interfererOUT: in the absence of interferer

UWBIN: sequence of “1”

• Mixer output

– slightly distorted

• Integrator output

– correctly detected

CPU time: 0.55 s (on a 3.8 GHz PC)

-0.5

-0.3

-0.1

0.1

0.3

0.5

0 2 4 6 8 10

Time (ns)

Am

pli

fier

an

d m

ixer

o

utp

ut

(V)

-0.2

-0.1

0

0.1

0.2

Inte

gra

tor

ou

tpu

t (V

)

Amplifier output Mixer output Integrator Output


92

OUT: with a sinusoidal interfererOUT: with a sinusoidal interferer

• Generic IM product:INT2UWB1i

2

1iik ωkωkωkΩ +==∑

= ω2 = ωINT = 2π • 5.18 GHz

|k1| ≤ NH1 = 128

|k2| ≤ NH2 = 5

PINT = PUWB-10 dB PINT = PUWB+10 dB

CPU time ≈≈≈≈ 105 s

-0.5

-0.3

-0.1

0.1

0.3

0.5

0 4 8 12 16 20 24 28 32

Time (ns)

Mix

er o

utp

ut

(V)

-0.2

-0.15

-0.1

-0.05

0

0.05

0.1

0.15

0.2

Inte

gra

tor

ou

tpu

t (V

)

Mixer output Integrator Output

-0.5

-0.3

-0.1

0.1

0.3

0.5

0 4 8 12 16 20 24 28 32

Time (ns)

Mix

er o

utp

ut

(V)

-0.2

-0.15

-0.1

-0.05

0

0.05

0.1

0.15

0.2

Inte

gra

tor

ou

tpu

t (V

)


No. of realunknowns: 67,848

No. of Ωk ≥ 0:1,413


93

OUT: OUT: withwith a WLAN a WLAN modulatedmodulated interfererinterferer• Interfering carrier: ωINT = 2π • 5.18 GHz

– modulated according the 16-QAM format (Br = 16 Mb/s)

– Sequence of 512 bits (8 sampling points per bit)– PINT = PUWB-10 dB

Spectrum of mixer outputCPU time ≈≈≈≈ 50 s per

sampling point

-150

-130

-110

-90

-70

-50

0 4 8 12 16 20 24 28 32

Frequency (GHz)

Po

wer

den

sity

(d

Bm

/MH

z)

-0.5

-0.3

-0.1

0.1

0.3

0.5

0 4 8 12 16 20 24 28 32

Time (ns)

Mix

er o

utp

ut

(V)

-0.2

-0.15

-0.1

-0.05

0

0.05

0.1

0.15

0.2

Inte

gra

tor

ou

tpu

t (V

)

Mixer output Integrator OutputStrong spectralregrowth


94

UWBUWBININ: : randomrandom sequencesequence ofof ““11”” andand ““00””

• Realistic UWB signal by repeating periodically a pseudo-random sequence of NB = 64 couples of pulses

• Period NBτf = 256 ns• Fundamental freq. ω1 = 2π/NBτf = ωUWB/NB ≈ 2π • 3.9 MHz

No. freq. of UWB signal:HUWB = 128.NB+NB/2=8,224

-120

-110

-100

-90

-80

-70

-60

-50

-40

3 4 5 6 7 8 9 10 11

Frequency (GHz)

Po

wer

Den

sity

(d

Bm

/MH

z)

-100

-95

-90

-85

-80

-75

-70

-65

-60

8.75 8.875 9

Frequency (GHz)

Po

wer

Den

sity

(d

Bm

/MH

z)UWB band


95

OUT: in the OUT: in the presencepresence ofof sinusoidalsinusoidal interfererinterferer• ω2 = ωINT = 2π • 5.18 GHz (nearby WLAN)

• |k1| ≤ HUWB = 8,224

• |k2| ≤ NH2 = 5No. of Ωk ≥ 0:

90,469

PINT = PUWB-10 dB PINT = PUWB+10 dB

CPU time ≈≈≈≈ 1,558 s CPU time ≈≈≈≈ 2,005 s

-0.5

-0.3

-0.1

0.1

0.3

0.5

44 48 52 56 60 64 68 72 76

Time (ns)

Mix

er o

utp

ut

(V)

-0.2

-0.15

-0.1

-0.05

0

0.05

0.1

0.15

0.2

Inte

gra

tor

ou

tpu

t (V

)


'0' '1' '0' '0' '1' '0' '1' '1'

-0.5

-0.3

-0.1

0.1

0.3

0.5

44 48 52 56 60 64 68 72 76

Time (ns)

Mix

er o

utp

ut

(V)

-0.2

-0.15

-0.1

-0.05

0

0.05

0.1

0.15

0.2

Inte

gra

tor

ou

tpu

t (V

)


'0' '1' '0' '0' '1' '0' '1' '1'

No. of realunknowns:4,342,536


96

ComparisonComparison withwith commercial simulatorcommercial simulator

0

50

100

150

200

250

300

350

400

0 2000 4000 6000 8000 10000 12000

Number of spectral lines

CP

U t

ime

(s)

New method

Commercialsimulator

•The commercial program in use is only able to handle problems with up to about 6000 frequencies (but this could just be a matter of dimensional settings), while our program could easily reach up to 100,000 frequencies (and even more), as shown above

•The numerical results produced by the two programs are virtually identical


97

UWB UWB -- ConclusionsConclusions

-100

-95

-90

-85

-80

-75

-70

-65

-60

8.75 8.875 9

Frequency (GHz)

Po

wer

Den

sity

(d

Bm

/MH

z)

• In an envelope transient

analysis, the IM products of

the sidebands associated with

different carriers are

disregarded.

• A frequencyfrequency--domain techniquedomain technique, allowing large numbers

of spectral lines to be efficiently handled, appears to

represent the most accurate approach to the circuit-

level nonlinear analysis of UWB systems.

• Envelope-transient techniques carry out a local

multitone harmonic balance analysis at each envelope

sampling instant with a spectrum consisting of the

carriers harmonics only (for the present case, the 128

harmonics of ωUWB).


98

AnyAnyquestionsquestions??


99

THANKSTHANKSFORFORYOURYOUR

ATTENTION!ATTENTION!



ReferencesReferences1. V. Rizzoli, A. Lipparini, D. Masotti, and F. Mastri, "Efficient circuit-level analysis of large microwave systems

by Krylov-subspace harmonic balance", 2001 IEEE MTT-S Int. Microwave Symp. Digest, Phoenix, AZ, May 2001, pp. 25-28.

2. V. Rizzoli, E. Montanari, A. Lipparini, D. Masotti, and F. Mastri, "A fully automatic domain partitioning technique for the efficient circuit-level simulation of large nonlinear microwave subsystems", IEEE Microwave Wireless Comp. Lett., Vol. 11, July 2004, pp. 349-351

3. V. Rizzoli, A. Costanzo, D. Masotti, and P. Spadoni, “Circuit-level nonlinear/electro-magnetic co-simulation of an entire microwave link”, 2005 IEEE MTT-S Int. Microwave Symp. Digest, Long Beach, CA, June 2005, pp. 813-816

4. V. Rizzoli, E. Montanari, D. Masotti, A. Lipparini, and F. Mastri "Domain-Decomposition Harmonic Balance with Block-Wise Constant Spectrum", 2006 IEEE MTT-S International Microwave Symposium Digest (San Francisco), Jun. 2006, pp. 860-863.

5. V. Rizzoli, D. Masotti, P. Spadoni, A. Costanzo, and F. Fuschini "Distortion Analysis of RF Links by Means of Circuit-Level Nonlinear/EM Front-end Simulation and Realistic Channel Description", Proceedings of the 36th European Microwave Conference (Manchester), Sept. 2006, pp. 161-164.

6. V. Rizzoli, A. Costanzo, D. Masotti, P. Spadoni, and A. Neri, "Prediction of the End-to-End Performance of a Microwave/RF Link by means of Nonlinear/Electromagnetic Co-Simulation ", IEEE Transactions on Microwave Theory and Techniques, Vol. 54, No. 12, Dec. 2006, pp. 4149-4160.

7. V. Rizzoli, A. Costanzo, P. Spadoni, F. Donzelli, D. Masotti, and E. M. Vitucci, "A CAD Procedure for MIMO Link Estimation by the Combination of Nonlinear, Electromagnetic and Propagation Analysis Techniques", 2008 IEEE MTT-S International Microwave Symposium Digest (Atlanta), Jun. 2008, pp. 927-930.

8. V. Rizzoli, F. Mastri, A. Costanzo, D. Masotti, and F. Donzelli, "Efficient Circuit-Level Nonlinear Analysis of Interference in UWB Receivers ", Proceedings of the 38th European Microwave Conference (Amsterdam), Oct. 2008, pp. 1465-1468.

9. V. Rizzoli, F. Mastri, A. Costanzo, D. Masotti, "Harmonic Balance Algorithms for the Circuit-Level Nonlinear Analysis of UWB Receivers in the Presence of Interfering Signals”, IEEE Transactions on Computer-Aided Design of Integrated Circuits and Systems, Vol. 28, No. 4, April 2009, pp. 516 - 527.

10. V. Rizzoli, D. Masotti, N. Arbizzani, and A. Costanzo, "CAD Procedure for Predicting the Energy Received by Wireless Scavenging Systems in the Near- and Far-field Region ", 2010 IEEE MTT-S International Microwave Symposium Digest (Anaheim), May 2010, pp 1768-1771.

integration of nonlinear, radiation and propagation analysis techniques · pdf...

Documents