On UWB beamforming

(1)

© Copernicus GmbH 2004

Advances in

Radio Science

On UWB beamforming

T. Kaiser

Duisburg-Essen University, Faculty of Engineering, Department of Communication Systems, Bismarckstraße 81,

47048 Duisburg, Germany

Abstract.

Ultra-Wideband (UWB) communication

sys-tems and Multi-Input-Multi-Output (MIMO) techniques rank

among the few emerging key technologies in wireless

com-munications.

For that reason the marriage of these two

complementary approaches should deserve attention.

Appar-ently, the extremely large ultra-wide bandwidth creates rich

multipath diversity which calls, at a first glance, additional

antenna elements into question. However, another point of

view is as follows. The attenuation by solid materials usually

increases with increasing frequency; e.g. frequencies above,

say, 10 GHz are considered to be blocked by walls etc. Since

UWB can occupy more than 7 GHz of bandwidth (according

to FCC regularisation) the performance of a communication

link can be physically extended only by adding spatial

infor-mation, i.e. multiple antennas, even if such extension may

play a minor role. From this point of view UWB& MIMO

presents an upper physical bound for indoor communications

and is therefore at least worth to be investigated. In order to

see the forest for the trees, we will focus in this limited

con-tribution on beamforming among all alternative MIMO

tech-niques (like space time coding or spatial multiplexing).

1 Introduction

In order to avoid strong interference of conventional

narrow-band transmission systems by ultra-widenarrow-band signals, the

power spectral density of UWB systems is fairly limited,

which leads – despite the enormous bandwidth – to a rather

restricted coverage. This weakness is opposite to one of the

main strengths of MIMO techniques; they are able to

in-crease the range. Such a reversal indicates the potential of

a marriage of these two complementary techniques.

Numerous other benefits can be envisaged. For

exam-ple, the capability of MIMO systems to spatially distinguish

among wavefronts impinging from different directions not

Correspondence to:

T. Kaiser

([email protected])

only facilitates the equalizer design of UWB systems by

re-duction of delay spread, but rather enables a further increase

of data rate – Gbit/s over air becomes feasible. Moreover,

by MIMO techniques, narrowband and broadband interferers

can be spatially suppressed so that the number of concurrent

users might be significantly increased. Last but not least a

reduction of electromagnetic radiation can be expected from

UWB & MIMO, which in turn may also save battery life.

However, a large number of different challenges do resist.

For example, digital beamforming seems to be prevented

due to the extremely high sampling rate. In contrast, analog

beamforming requires adjustable true time delays, such

de-lays exhibit noticeable tolerance and therefore less precision.

Besides these technology barriers, numerous challenges have

to be overcome in fundamental processing of UWB signals

by MIMO techniques.

2 An analogy

Without reinventing the wheel, some ideas can be borrowed

from speech or also from radar processing. The following

table shows the similarities and differences of broadband

beamforming for speech processing and UWB

communica-tion systems.

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164 T. Kaiser: On UWB beamforming

Table 1.

An analogy between speech processing and UWB transmission.

Property

Speech Processing

UWB transmission

bandwidth (rel.)

≈

10 kHz (180%)

≈

10 GHz (110%)

delay spread

≈

100 ms

≈

100 ns

environment

indoor, non-stationary

challenges

highly reverberant

multipath propagation

wavefront shape

spherical or planar

typ. SNR at receiver

moderately positive (6–12 dB)

receiver type

waveform estimation

detection (matched filter!)

type of interferers

broadband

broadband and narrowband

type of noise

correlated (e.g. ventilator)

uncorrelated

other issues

signal duration unknown

signal duration known

be moderately positive, say a 6–12 dB. This can be achieved

either in case of limited range or by spreading techniques.

All these mentioned aspects show the similarities between

speech and UWB spatial processing. The main differences

result from the fact that the UWB receiver knows the

prin-cipal waveform whereas in speech processing not only the

waveform is completely unknown but also when speech

be-gins and when it ends. From this point of view, UWB seems

to be easier to deal with because the transmit signal can be

designed adequately. For example, in order to estimate the

direction-of-arrival

θ

of an impinging wavefront (see Fig. 1),

the transmit signal can be repeated periodically so that at the

receiver the sampling rate can be distinctly reduced by

al-most arbitrary low undersampling techniques. Moreover, for

UWB transmission a matched filter (MF) can be principally

deployed that further boosts up the SNR. However, this

ap-proach tends to be a bit overrated, since in dense UWB

mul-tipath environments numerous reflections occur and each

in-dividual reflection will modify the transmitted impulse shape

simply because of the non-flat frequency response of the

re-flective material. One last major difference concerns the kind

of noise and interferers. While in speech processing

broad-band interferers dominate and the noise is most often

cor-related (e.g. ventilator), in UWB transmission the

interfer-ers can be broadband as well as narrowband and the noise is

mainly of thermal type and hence uncorrelated.

In conclusion, because of its affinity, some concepts – like

broadband beamforming – can be borrowed from speech

pro-cessing.

3 Broadband beamforming

As mentioned previously we will focus on beamforming of

UWB signals. The following figure illustrates a conventional

filter and sum beamformer.

Basically, each filter can be substituted by a delay in order

to compensate for the different signal travel time among the

antenna elements and to coherently summing up all branches.

This so-called array gain enhances the SNR by a factor of

N

(or 10 log

10 (N )

on a decibel scale) under perfect conditions.

Property Speeh Proessing UWB transmission

bandwidth(rel.) 10kHz(180%) 10GHz(110%)

delayspread 100ms 100ns

environment indoor,non-stationary indoor,non-stationary

hallenges highlyreverberant multipath propagation

wavefrontshape spherialorplanar spherialorplanar

typ. SNRat reeiver moderatelypositive(6-10dB) moderatelypositive(8-12dB)

reeivertype waveformestimation detetion(mathedlter!)

typeofinterferers broadband broadbandandnarrowband

typeofnoise orrelated(e.g. ventilator) unorrelated

other issues signaldurationunknown signaldurationknown

Table1: Ananalogybetweenspeeh proessingandUWBtransmission

tiobetweenantennaapertureandtransmitter-reeiver

distane. Inorder to guaranteeauseful transmission,

thesignaltonoiseratioatthereeiverhastobe

mod-erately positive, say a6-12 dB. This anbe ahieved

either in ase of limited range or by spreading

teh-niques.

All these mentioned aspets show the similarities

betweenspeehandUWBspatialproessing. Themain

dierenesresultfromthefatthat theUWBreeiver

knowsthe prinipal waveform whereasin speeh

pro-essing notonlythe waveformis ompletely unknown

but also when speeh beginsand when itends. From

thispointofview,UWBseemstobeeasiertodealwith

beausethetransmitsignalanbedesignedadequately.

Forexample,inordertoestimatethediretion-of-arrival

ofanimpingingwavefront(seeFig. 1),thetransmit

signal anbe repeated periodially sothat at the

re-eiver thesampling ratean be distintly redued by

almostarbitrarylowundersamplingtehniques.

More-over,forUWBtransmissionamathedlter(MF)an

beprinipallydeployedthatfurtherboostsuptheSNR.

However, this approah tends to be a bit overrated,

sine in dense UWB multipath environments

numer-ousreetionsourandeahindividualreetionwill

modifythetransmittedimpulse shapesimply beause

ofits non-atfrequenyresponse. Onelast major

dif-fereneonernsthekindofnoiseandinterferers. While

in speeh proessing broadband interferers dominate

andthenoiseismostoftenorrelated(e.g. ventilator),

inUWBtransmissiontheinterferersanbebroadband

aswellasnarrowbandandthenoiseismainlyof

ther-maltypeandheneunorrelated.

Inonlusion,beauseofitsaÆnity,someonepts

-likebroadbandbeamforming-anbeborrowedfrom

speeh proessing.

3. BROADBAND BEAMFORMING

As mentioned previouslyhere we will fous on

beam-forming of UWB signals. The following gure

illus-tratesaonventionallterandsumbeamformer.

g N

(t) y

N (t)

g 2

(t) y

2 (t)

g 1

(t) y

1 (t)

y(t) x(t)

Figure 1: Alterandsumbroadbandbeamformer

Basially, the lteran be substituted by delay in

ordertoompensateforthedierentsignaltraveltime

among the antenna elements and to oherently

sum-ming up all branhes. This so-alled array gain

en-hanes the SNR by a fator of N (or 10log 10

(N) on

adeibelsale)underperfet onditions. However,

in-terferersannotbesuppressedonlybydelays. Forthat

reason,theuseofltersbeomesjustied. Fig. 2shows

thebeampatterndenedas

B(; 0

)=max t

jy(t;; 0

)j 2

forafamilyofsinusoidalsignals

x(t)=sin(2ft); f =3:1GHz:::10:6GHz

and N =8 antennas, asteering diretion of 0

=0 Æ

,

an antennaspaingd=

=2,where

=

0 =f

,

0 is

speedoflightandf

=6:85GHzistheenterfrequeny

Fig. 1.

A filter and sum broadband beamformer.

However, interferers cannot be suppressed only by delays.

For that reason, the use of filters becomes justified. Figure 2

shows the beampattern defined as

B(θ, θ0)

=

max

t

|

y(t, θ, θ0)

|

2 for a family of sinusoidal signals

x(t )

=

sin

(

2 πf t ),

f

=

3 .

1GHz

...

10 .

6GHz

and

N

=

8 antennas, a steering direction of

θ

0 =

0 ◦

, an

antenna spacing

d

=

λ

c

/

2, where

λ

c

=

c

0 /f

c

,

c

0 is speed of

light and

f

c

=

6 .

85 GHz is the center frequency according to

FCC

1 -regularisation.

Observe that while the location of the mainlobe is

frequency-independent, the locations of the sidelobes and the

nulls are frequency-dependent. This means that broadband

interferers cannot be completely suppressed by a simple

de-lay and sum beamformer. Filters represent a remedy and

al-low an almost arbitrary high interferer cancellation just by

adequately increase of the filter orders. In principle,

conven-tional beamformer techniques (e.g. the minimum variance

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T. Kaiser: On UWB beamforming

165

3

aordingtoFCC 1 -regularisation.

−90

−45

0

45

90

3.1

5

6

7

8

9

10.6 x 10

9 −20

−10

0

10

20

f mainlobe sidelobes B(; 0 ) dB

Figure 2: Beampattern of a delay and sum broadband

beamformer

Observethat while theloationofthemainlobe is

frequeny-independent, the loations of the sidelobes

andthenullsarefrequeny-dependent. Thismeansthat

broadbandinterferersannotbeompletelysuppressed

by asimpledelayandsumbeamformer. Filters

repre-sent a remedy and allow an almost arbitrary high

in-terfereranellationjust by adequatelyinreaseofthe

lter orders. In priniple, onventional beamformer

tehniques (e.g. the minimum variane distortionless

beamformer(MVDR))an bedeployedinorderto

de-signthelterandsumbeamformersimplyby

alulat-ing the weight vetor for a set of suitable frequenies

andtransformingtheresultingweightmatrixintotime

domain.

UWB measurements have shown, at least under

line-of-sight(LOS)onditions,thepropagationof

indi-vidualehoesarrivingatthereeiverin so-alled

lus-ters(seeforexamplethedesriptivevideosat[4℄). Due

to their ultrashort duration, these ehoes are

resolv-ableintimesothat theyalsobeomeresolvablein

an-gle; hene, the diretion-of-arrival an be prinipally

estimated. Moreover, the reorded signals seem tobe

delayedrepliasofeahothersothatbeamforming

be-omesfeasible. Evenforaspaingofafewten

entime-ters,therelevantehoesseemtobestonglyorrelated.

Inaddition,asmallspaing(e.g. 4m)doesnot ause

seriousoupling[3℄.

(Ultra)-broadbandbeamformingoersanadditional

benet opposite to narrowband beamforming.

Nar-rowband beamforming suers from so-alled grating

lobes. They our for antenna spaingsd larger than

=2andtheyleadtoanambiguityofthe

diretion-of-arrival. Forthatreason,ommonnarrowbandantenna

elementsshowaspaingofhalvethearrierwavelenght

1

FederalCommissionforCommuniations

orevensmallerthanthis. Takingintoaountthatthe

mainlobewidthdependsnotonlyonthenumberof

an-tennas but also from the spaing, narrowbandbeams

anonly benarrowedbyinreasingthenumber of

an-tennas. In turn, in (ultra)-broadband proessing also

thespaing an be inreasedfurther without

ambigu-ity. Inordertoillustratethisfat,thefollowinggures

(Fig. 3-6) show the squaredmagnitude of the

beam-former output and the beampattern for an antenna

spaing d =

in ase of two antennas, lower f l

=

3:1GHz and upper ut-o frequenies f u

= 10:6GHz

(!f

=6:85GHz),andaninputsignalx(t)=e j2f

t

(narrowband)or x(t)= e 2((f u f l )t) 2 e j2f t (broad-band). jy(t;)j 2 t=[ns℄

Figure3: Squared magnitudeof narrowbandbeamformer

outputford=,N =2

max t 20log 10 y(t;) max y(t;)

Figure4: Narrowbandnormalizedbeampatternford=,

N =2inlogarithmisale

Itanbeseenthatthenarrowbandbeamformerwill

suerfromthementionedambiguitysineitannot

dis-tinguishamongthe threepossible diretion-of-arrivals

Fig. 2.

Beampattern of a delay and sum broadband beamformer.

distortionless beamformer (MVDR)) can be deployed in

or-der to design the filter and sum beamformer simply by

calcu-lating the weight vector for a set of suitable frequencies and

transforming the resulting weight matrix into time domain.

UWB measurements have shown, at least under

line-of-sight (LOS) conditions, the propagation of

individ-ual echoes arriving at the receiver in so-called

clus-ters (see for example the descriptive videos at Whyless,

www.whyless.org/public/wp5.htm). Due to their ultrashort

duration, these echoes are resolvable in time so that they also

become resolvable in angle; hence, direction-of-arrival

esti-mation can be principally performed. Moreover, the recorded

signals seem to be delayed replicas of each other so that

beamforming becomes feasible. Even for a spacing of a few

ten centimeters, the relevant echoes seem to be stongly

corre-lated. In addition, a small spacing (e.g. 4 cm) does not cause

serious coupling (Sibille and Bories, 2003).

(Ultra)-broadband beamforming offers an additional

bene-fit opposite to narrowband beamforming. Narrowband

beam-forming suffers from so-called grating lobes. They occur

for antenna spacings

d

larger than

λ

c

/

2 and they lead to

an ambiguity of the direction-of-arrival. For that reason,

common narrowband antenna elements show a spacing of

half the carrier wavelength or even smaller than this.

Tak-ing into account that the mainlobe width depends not only

on the number of antennas but also on the spacing,

narrow-band beams can only be further narrowed by increasing the

number of antennas. In turn, in (ultra)-broadband

process-ing also the spacprocess-ing can be increased further without

ambi-guity. In order to illustrate this fact, the following figures

(Figs. 3–6) show the squared magnitude of the beamformer

output and the beampattern for an antenna spacing

d

=

λ

c

in case of two antennas, lower

f

l

=

3 .

1 GHz and upper

cut-off frequencies

f

u

=

10 .

6 GHz (

→

f

c

=

6 .

85 GHz),

and an input signal

x(t )

=

e

−j2

πf

c

t

_{(narrowband) or}

_{x(t )}

₌

e

−2

π((f

u

−

f

l

)t )

2 _e

−j2

πf

c

t

_(broadband).

It can be seen that the narrowband beamformer will

suf-fer from the mentioned ambiguity since it cannot distinguish

aordingtoFCC 1 -regularisation. f mainlobe sidelobes B(; 0 ) dB

beamformer

Observe that whilethe loation of the mainlobeis

byasimpledelay andsumbeamformer. Filters

repre-sent aremedy and allowan almost arbitraryhigh

in-terfereranellationjust byadequatelyinreaseofthe

beamformer(MVDR))anbedeployedinorderto

alulat-ingthe weight vetor fora set of suitable frequenies

domain.

indi-vidualehoesarrivingatthe reeiverinso-alled

resolv-ableintimesothattheyalsobeomeresolvablein

estimated. Moreover, the reordedsignals seemto be

Inaddition,asmall spaing(e.g. 4m) doesnotause

lobes. They our forantenna spaings d larger than

1

an-tennas but also from the spaing, narrowbandbeams

anonlybenarrowedbyinreasingthe numberof

the spaing an beinreased further without

(Fig. 3-6) show the squared magnitude of the

spaing d =

=

= 10:6GHz

(!f

=6:85GHz),andaninputsignalx(t)=e j2ft

(narrowband)orx(t)=e 2((f u f l )t) 2 e j2f t (broad-band).

−90

−45

0

45

90

0

0.5

1

1.5 x 10

−9

0

1

2

3

4

5

jy(t;)j 2 t=[ns℄

Figure3: Squaredmagnitudeofnarrowband beamformer

outputford=

,N =2

max t 20log 10 y(t;) maxy(t;)

Figure4: Narrowbandnormalizedbeampatternford=

,

N=2inlogarithmisale

dis-tinguishamongthe threepossible diretion-of-arrivals

Fig. 3.

Squared magnitude of narrowband beamformer output for

d

=

λ

c

,

N

=

2.

3

aordingtoFCC 1 -regularisation. f mainlobe sidelobes B(; 0 ) dB

beamformer

Observethatwhile theloationof themainlobe is

byasimpledelayandsum beamformer. Filters

repre-senta remedy andallowan almost arbitraryhigh

in-terfereranellationjust byadequatelyinreaseof the

beamformer(MVDR))anbedeployedinorderto

alulat-ing the weight vetor for a set of suitable frequenies

domain.

indi-vidualehoesarrivingatthe reeiverinso-alled

resolv-ableintimesothattheyalsobeomeresolvablein

estimated. Moreover,the reorded signals seem tobe

Inaddition,asmallspaing (e.g. 4m)doesnotause

lobes. They our for antenna spaings d largerthan

1

an-tennas but also from the spaing, narrowband beams

an onlybenarrowedby inreasingthenumberof

the spaing anbe inreasedfurther without

(Fig. 3-6) show the squaredmagnitude of the

spaing d =

=

= 10:6GHz

(!f

=6:85GHz),andaninput signalx(t)=e j2ft

(narrowband)orx(t)=e 2((f u f l )t) 2 e j2f t (broad-band). jy(t;)j 2 t=[ns℄

Figure 3: Squaredmagnitudeof narrowbandbeamformer

outputford=,N =2

−90

−45

0

45

90 −20

−15

−10

−5

0

Figure4: Narrowbandnormalizedbeampatternford=,

dis-tinguish among the threepossiblediretion-of-arrivals

Fig. 4.

Narrowband normalized beampattern for

d

=

λ

c

,

N

=

2 in

logarithmic scale.

among the three possible direction-of-arrivals

−

90

0 , 0

0 and

+

90

0 . In contrast, the broadband beamformer can clearly

resolve the 0

0 -DoA, because of no ringing of the received

impulse-shaped wavefront.

It is also of interest to study the effects caused by

increas-ing the spacincreas-ing and the number of antennas, see Figs. 7, 8.

Observe that extending the spacing leads to a narrowing

of the mainlobe, whereas more antennas not only further

decrease the mainlobe width but also increase the

main-to-sidelobe ratio. For example, in case of

d

=

2 λ

c

,

N

=

4,

the mainlobe width is approximately 15

0 so that with such a

linear array up to 180

0 /

15

0 =

12 spatially seperated users

can be ideally served.

Note also that for

d

=

2 λ

c

,

N

=

2 the array size is

8 .

76 cm, which might be implementable on a terminal. In

turn, for

d

=

2 λ

c

,

N

=

4 the array size becomes 26

.

28 cm,

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166 T. Kaiser: On UWB beamforming

4

−90

−45

0

45

90

0

0.5

1 x 10

−9

0

1

2

3

4

jy(t;)j 2 t=[ns℄

Figure 5: Squared magnitude of broadband beamformer

outputford=,N =2

Figure6: Broadbandnormalizedbeampatternford=,

N =2inlogarithmi sale

90 0 , 0 0 and+90 0

. Inontrast,the broadband

beam-former an learly resolve the 0 0

-DoA, beause of no

ringingof thereeived impulse-shapedwavefront.

Itis alsoof interestto study the eetsaused by

inreasingthespaingandthenumberofantennas,see

Fig. 7,8.

Observethat extendingthespaingleadstoa

nar-rowing of the mainlobe, whereas more antennas not

onlyfurther derease the mainlobewidth but also

in-reasethemain-to-sideloberatio. Forexample,inase

of d = 2

, N = 4, the mainlobe width is

approx-imately 15 0

so that with suh a linear array up to

180 0

=15 0

=12spatiallyseperatedusersanbeserved.

Notealso thatford=2

, N =2the arraysize is

8:76m,whihmight beimplementableon aterminal.

In turn, for d = 2

, N = 4 the array size beomes

Figure7: Broadbandnormalizedbeampatternford=2,

26:28m,eventhisisimplementable-nowonalaptop.

4. CONCLUSION ANDFUTURE WORK

Inthisontribution,wemotivatethemarriageofUWB

and multi-antenna tehnique by foussing on

beam-forming. Beside the omplementary lasses of

multi-antennaapproahes,i.e. spatialmultiplexingand

spae-timeoding,therearenumerousopenissuesinthisnew

andhighlymulti-disiplinaryeld:

adjustablepreiseanalogtruetimedelays(oreven

lters)

diretionof arrival,time delayestimation

beamformingforUWBhannels(model&data)

exploitingmultipathpropagationthanombating

pulseshaping,modulationforUWBmulti-antenna

systems

loalisation, synhronisation with UWB

multi-antennasystems

UWB antenna arrays, where the frequeny

re-sponsesamongtheelementsmaydier,butshould

overlap

broadbandbeamformingwithlownumberof

an-tennas

transmitbeamforming

Fig. 5.

Squared magnitude of broadband beamformer output for

d

=

λ

c

,

N

=

2.

4

jy(t;)j 2

t=[ns℄

Figure 5: Squaredmagnitude of broadband beamformer

outputford=

,N =2

−90

−45

0

45

90 −20

−15

−10

−5

0

90 0 , 0 0 and+90 0

. Inontrast,thebroadband

-DoA, beause of no

ringing ofthe reeivedimpulse-shaped wavefront.

It is alsoof interest tostudy the eetsaused by

Fig. 7,8.

Observethatextendingthe spaingleadstoa

only further dereasethe mainlobe widthbut also

in-reasethe main-to-sideloberatio. Forexample,inase

of d = 2

approx-imately 15 0

180 0

=15 0

=12spatially seperatedusersan beserved.

Note alsothat ford=2

,N =2the arraysize is

8:76m,whihmightbe implementable on aterminal.

In turn, for d = 2

4. CONCLUSION AND FUTURE WORK

lters)

diretionof arrival,timedelayestimation

beamformingforUWB hannels(model&data)

systems

overlap

an-tennas

transmitbeamforming

Fig. 6.

Broadband normalized beampattern for

d

=

λ

c

,

N

=

2 in

logarithmic scale.

4 Conclusion and future work

In this contribution, we motivate the marriage of UWB and

multi-antenna technique by focussing on beamforming.

Be-side the complementary classes of multi-antenna approaches,

i.e. spatial multiplexing and space-time coding, there are

nu-merous open issues in this new and highly multi-disciplinary

field:

–

adjustable precise analog true time delays (or even

fil-ters)

–

direction of arrival, time delay estimation

–

beamforming for UWB channels (model & data)

4

jy(t;)j 2

t=[ns℄

Figure 5: Squared magnitude of broadband beamformer

outputford=,N =2

N =2inlogarithmi sale

90 0 , 0 0 and+90 0

. Inontrast,the broadband

-DoA, beause of no

ringingof thereeived impulse-shapedwavefront.

Itis alsoof interestto study the eetsaused by

Fig. 7,8.

Observethat extendingthespaingleadstoa

only furtherderease the mainlobewidth butalso

in-reasethemain-to-sideloberatio. Forexample,inase

of d = 2

approx-imately 15 0

180 0

=15 0

=12spatiallyseperatedusersanbeserved.

Note alsothatford=2

, N =2the arraysize is

8:76m,whihmight beimplementableon aterminal.

In turn, for d = 2

−90

−45

0

45

90 −20

−15

−10

−5

0 −90

−45

0

45

90 −20

−15

−10

−5

0

4. CONCLUSION ANDFUTURE WORK

lters)

diretionof arrival,timedelay estimation

beamformingforUWBhannels(model&data)

systems

overlap

an-tennas

transmitbeamforming

Fig. 7.

Broadband normalized beampattern for

d

=

2 λ

c

,

N

=

2 in

logarithmic scale.

5

−90

−45

0

45

90 −20

−15

−10

−5

0

Figure8: Broadbandnormalizedbeampatternford=2

,

Of further interest is how the hannel apaity is

af-feted by UWBtransmission. Firstworktowardsthis

relevant topi an be found in [5℄, [6℄. It seems that

the numberof antennashas thesameimpatthanthe

bandwidth, infat, the equation known from

narrow-band MIMOsystemsfor theergodihannelapaity

C e

=BNlog 2

(1+SNR )

alsoholdsapproximatelytrueforUWBhannels. Suh

resultfurthermotivatethemergeofthesetwokey

teh-nologiesinwirelessommuniations.

REFERENCES

[1℄ J.M.Cramer,R.A.SholtzandM.Z.Win,On the

analysis of UWB ommunation hannels, IEEE

Military Communiation Conferene Proeedings

(MILCOM),Vol.2,1999,p.1191-1195

[2℄ H.Lee,H.Haan,Y.Shin,S.Im, Multipath

Char-ateristisofImpulseRadioChannels,Pro.IEEE

VTC, May 15-18, 2000, Tokyo, Japan, pp.

2487-2491.

[3℄ A.SibilleandS.Bories,Spae diversity forUWB

ommuniations, EPMCC, April 22-25, 2003,

Glasgow,UK

[4℄ www.whyless.org/publi/wp5.htm

[5℄ Z.Feng,T.KaiserandA.Czylwik,Onthe

Evalua-tionof Channel Capaityof Multi-AntennaUWB

Case, submitted to IEEE Transations on

Com-muniations

[6℄ Z.Feng,T.KaiserandA.Czylwik,Onthe

Evalua-tionof Channel Capaityof Multi-AntennaUWB

Indoor Wireless Systems{PartII: Frequeny

Se-letive Case, submittedtoIEEE Transationson

Communiations

Fig. 8.

Broadband normalized beampattern for

d

=

2 λ

c

,

N

=

4 in

logarithmic scale.

–

exploiting multipath propagation than combating

–

pulse shaping, modulation for UWB multi-antenna

sys-tems

–

localisation, synchronisation with UWB multi-antenna

systems

–

UWB antenna arrays, where the frequency responses

among the elements may differ, but should overlap

–

broadband beamforming with low number of antennas

(5)