Memory Enhanced PSO-Based Optimization Approach for Smart Antennas Control in Complex Interference Scenario

UNIVERSITY

OF TRENTO

DEPARTMENT OF INFORMATION AND COMMUNICATION TECHNOLOGY

38050 Povo – Trento (Italy), Via Sommarive 14

http://www.dit.unitn.it

M

EMORY

E

NHANCED

PSO-B

ASED

O

PTIMIZATION

A

PPROACH FOR

S

MART

A

NTENNAS

C

ONTROL IN

C

OMPLEX

I

NTERFERENCE

S

CENARIO

M. Benedetti, R. Azaro, and A. Massa

August 2007

proa h for Smart Antennas Control in Complex

Interferen e S enarios

M. Benedetti, R.Azaro, Member, IEEE, and A. Massa, Member, IEEE

Department ofInformation and Communi ationTe hnologies

Universityof Trento, ViaSommarive 14, I-38050Trento - Italy

Tel. +39 0461 882057,Fax +390461 882093

E-mail: andrea.massaing.unitn.it,

{manuel.benedetti,renzo.azaro}dit.unitn.it

proa h for Smart Antennas Control in Complex

Interferen e S enarios

M. Benedetti, R.Azaro, and A.Massa

Abstra t

In the framework of ontrol methods for adaptive phased-arrays, this paper deals

with omplex ommuni ation s enarios by onsidering a memory-enhan ed

ooper-ative algorithm. Compared to existing approa hes where far-eldinterferen es are

takeninto a ount, theproposedanalysis onsiders amore realisti situation where

the jamming sour es are lo ated either in the near-eld or in the far-eld of the

re eiving antenna. In orderto arefully addressthearising hallenges and to

ee -tively dealwithsu h omplexenvironments, anoptimization approa h basedon an

enhan ed

P SO

-based algorithm is used. Theobtained results seem to onrm the

ee tiveness of the proposed te hnique in terms of both signal-to-noise ratio and

omputational ostsand omplexity.

Index Terms:

SmartAntennas,AdaptiveControl,OptimizationTe hniques,Parti leSwarm

The ontinuous evolution of ommuni ation systems requires the development and

us-tomization of te hniques based onthe idea of diversity [1℄. In the frameworkof antennas

design, su h a theory has been applied for developing smart systems able to improve

the quality of the re eived signal and to suppress the ee ts of interfering sour es. The

on ept of spatial diversity [2℄has led tothe ouplingof array theorywith adaptive

on-trol and therefore to the design of antenna ar hite tures able to maximize the system

performan es (i.e., the signal-to-interferen e-plus-noiseratio) by tuning dynami ally the

weights of the array elements.

Themathemati altheoryofadaptivesystemshasbeenoriginallyproposedbyApplebaum

in [3℄ dealing with linear arrays of isotropi sour es in the presen e of far-eld (

F F

)

narrow-band signals (i.e., a desired signal and a set of jammers). The array weights,

adapted for pla ing nulls in the far-eld pattern in the dire tions of interferen e, are

obtained by multiplying the quies ent weights by the inverse of the sampled ovarian e

matrix formed from the omplex signals re eived atea h element inthe array.

Alternatively, the adaptive ontrol has been also re ast as an optimization problem by

dening a suitable ost fun tional to be maximized. Originally, deterministi te hniques

basedongradientmethods(e.g.,theleastmeansquare(

LMS

)algorithmbyWidrowetal.

[4℄[5℄)havebeen proposed,buttheresultingapproa hes werestill hara terizedbyseveral

non-negligibledrawba ks. Be ause ofthe need ofestimating the ovarian ematrix ofthe

desiredsignal fromthe measurementsof there eived signalsatea helementof thearray,

the arraymust haveanexpensivere eiverora orrelatoratea helement. Unfortunately,

most arrays(orthesimplest/ heapest)haveasinglere eiveratthe outputofthesummer

and the re eivers (whenavailable)would requiresophisti ated alibrations. On the other

side, these methods onsider variable analog amplitude and phase weights, but phased

arrays usuallyhaveonlydigitalbeam steeringphaseshifters attheelementsandthe feed

network (xed) determines the amplitudevalues. Therefore, the ontinuous phasevalues

al ulated by the adaptive algorithmsare only approximated and the quantization error

limitsthe nullpla ement.

the total output power measured by the re eiver at the output of the summer has been

investigated[6℄. Asigni antimprovementonthiste hniquehas beenproposedbyHaupt

[7℄ whoused a Geneti Algorithm(

GA

)to adjust someof the least signi antbits of the beam steering phase shifters for minimizing the total output power thus removing the

interferingsignals fromthe outputof the array.

Notwithstandingthe su ess and su essive experimentalimplementation[8℄, su h a

GA

-based approa h did not take into a ount onstantly hanging onditions and the need

of a readaptation to new environments on e the population onverged. Su h a problem

has been over ome in su essive works by Weile and Mi hielssen [9℄ or Donelli et al.

[10℄ by using diploidy and dominan e or ooperative algorithms[i.e., the parti leswarm

optimizer(

P SO

)℄.

In su h a framework, this paper is aimed at assessing the ee tiveness and reliability of

an enhan ed

P SO

-based te hnique in the presen e of more omplex working onditions. In parti ular, the signals impingingonthe array are hara terized by randomly variable

dire tions and generated by ele tromagneti sour es lo ated at dieren edistan es from

the antenna system. More in detail, the sour e of the desired signal is assumed to be

very far from the system, whereas the distan e of the interfering sour es from the array

variesfrom thenear tothe far zone. Su h asituationturnsout to bequiterealisti sin e

it ould model/des ribe an info-mobility s enario where a moving network node (e.g.,

a ar or a pedestrian) ommuni ates with a base station or another node of the mobile

network. In this situation,a neighboring node (i.e., lose to the re eiving system) would

be onsidered as anear-eld jamming sour e.

Inordertoproperlyaddresssu hatopi ,the

P SO

-basedapproa hisaddedwithenhan ed learning apabilities. Similarly to [11℄, the enhan ed strategy is hara terized by the

use of memory-based operators, whi h perform an ex hange of information between the

swarm and a set of referen e solutions(dening the memory of the pro ess) iteratively

updated. Furthermore, the memory me hanism is further exploited (and ustomized

to the ooperative optimizer at hand) by introdu ing a new term in the

P SO

velo ity equation.

wherethe adaptiveantenna ontrolisre astastheminimizationofthetotal powerofthe

array in terms of the quantized phase weights. The optimization pro edure is detailed

in Se t. 3 and the results of a numeri al validation are shown in Se t. 4. Finally, some

on lusions are drawn (Se t. 5).

2 Mathemati al Formulation

Letus onsideranarrayof

N

elements(Figure1). Thenarrowbandsignalre eived bythe

n

-thelement of the array atthe time-step

(1)

_t

ℓ

,

ℓ = 1, ..., L

, an beexpressed as follows

s

(r)

_n

(t

ℓ

) = a

(r)

(t

ℓ

) e

jϕ

(r)

n

_{n = 1, ..., N; l = 1, ..., L}

(1) where

a

(r)

_(t

ℓ

) = h

(r)

(t

ℓ

) e

j2πf tℓ

,

h

(r)

_(t

ℓ

)

and

f

being the slowly-varying envelope of the

re eived signalandthe arrierfrequen y, respe tively. Moreover,

ϕ

(r)

n

isthephaseterm of

there eivedsignal omingfromtheangular oordinates

(θ

r

, φ

r

)

thatidentifythe dire tion-of-arrival(

DoA

) ofthe re eived signal. Under far-eld onditions[12℄, the phase term of (1) turns out tobe

ϕ

(r)

n

=

2π

λ

(u

r

x

n

+ v

r

y

n

+ q

r

z

n

)

(2)

where

u

r

= sin θ

r

cos φ

r

,

v

r

= sin θ

r

sin φ

r

, and

q

r

= cos θ

r

, and

(x

n

, y

n

, z

n

)

are the Cartesian oordinates of the

n

-th element of the array.

By onsidering o- hannelinterferen es,

s

(r)

n

is the resultof the summationof the desired

signal

s

(d)

n

, a set of

I

jammers

n

s

(g)

i,n

; i = 1, ..., I

o

, and an un orrelatedba kground noise

[or noise signal

s

(o)

n

℄ hara terized by an average power equalto

σ

2

,

s

(r)

n

(t

ℓ

) = s

(d)

n

(t

ℓ

) +

I

X

i=1

s

(g)

_i,n

(t

ℓ

) + s

(o)

n

(t

ℓ

)

(3)

(1)

A time-stepisaslotof time,betweentwo onse utivesnapshots(

△t

ℓ

+1

and

△t

ℓ

), hara terized by thepresen eof adesiredsignalandaxed numberofinterferingsignalswith invariant

DoA

s:

t

ℓ

,

where

s

(d)

n

(t

ℓ

) = a

(d)

(t

ℓ

) e

jϕ

(d)

n

and

s

(g)

i,n

(t

ℓ

) = a

(g)

i,n

(t

ℓ

) e

jϕ

(g)

i,n

. Analogously to (2),

ϕ

(d)

n

=

2π

λ

(u

d

x

n

+ v

d

y

n

+ q

d

z

n

)

, while

ϕ

(g)

i,n

=

2π

λ



ρ

i

−

q

(ρ

i

u

i

− x

n

)

2

+ (ρ

i

v

i

− y

n

)

2

+ (ρ

i

q

i

− z

n

)

2



n = 1, ..., N; i = 1, ..., I

(4)

to model [13℄ the phase term of the

i

-th interferen e sour e lo ated at

(ρ

i

, θ

i

, φ

i

)

either in the far-eld orin the near-eld dependingon the value of

ρ

i

(Fig. 2).

Asfarasthe signal

s

(e)

availableatthe theoutputofthesummeris on erned,itappears

that (see Fig. 1)

s

(e)

(t

ℓ

) =

N

X

n=1

W

n

s

(r)

n

(t

ℓ

)

(5) where

W

n

= w

n

e

jβ

n

is the

n

-th omplex weight. Consequently, the total output power

measured by the single re eiveris equalto [3℄[14℄

P (t

ℓ

) = P

ℓ

(W )

,

N

X

n=1

w

n

e

jβn

N

X

p=1

w

p

e

−jβp

Ω

r

p,n

(t

ℓ

)

(6) that is a fun tion of

W = {W

n

; n = 1, ..., N}

,

Ω

r

p,n

(t

ℓ

)

being the

(p, n)

-entry of the o-varian ematrix of the re eived signal.

Inordertominimizethetotaloutputpowerthusremovingtheinterferingsignalsfromthe

output of the array, the array oe ients are iteratively updated for taking into a ount

onstantly hanging (i.e., at ea h time-step) onditions and the need of a readaptation

to new environments. Moreover, a time-varying phase-only ontrol is implemented to

redu e the omplexity and the osts of the adaptive system. In parti ular, the following

optimization problem

β

opt

_(t

ℓ

) = arg

n

min

β

[P (t

ℓ

)]

o

(7)

issolvedbymeansoftheenhan ed

P SO

-basedstrategy(Se t. 3)todeterminetheoptimal

settingofthephases,

β = {β

n

; n = 1, ..., N}

,sin eamplitude oe ients

{w

n

; n = 1, ..., N}

arexedquantities(e.g.,uniformamplitudesordistributeda ordingtoDolph-Cheby hev

3 Memory Enhan ed

P SO

-based Optimization (

P SOM

)

3.1 Stru ture of the Binary

P SO

Optimization

The

P SO

[16℄[17℄ has been introdu ed by Eberhartand Kennedy inthe lastde ade [18℄. It isamultiple-agentoptimizationapproa hbased onthe imitationofthe so ialbehavior

of groupsof animalsin sear h of food. A swarm of

P

parti les, whi h models a set of

P

trialsolutions,isdened and itsevolutionin the solutionspa eis ontrolledby means of

a set ofupdating equationsthattakeinto a ountand exploitthe history of the swarm.

In this paper, following the implementation guidelines of the

P SO

-based strategy pro-posed in [10℄ and on erned with

N

-sized phased-arrays in the presen e of simplied far-eld interferen es, the solutionspa e is binarized forallowingthe use of digitalbeam

steering phase shifters. The traje tories of ea h parti le in the binary spa e are

deter-mined by evaluatingthe hanges inthe probability that a oordinatewill take on azero

or one value.

Be auseofthe omplexityofthes enarioathand,thelearning apabilitiesoftheapproa h

have been enhan ed by dening a memory me hanism as well asan innovative updating

relationship aimed at exploiting the history of the optimization for speeding up the

onvergen etotheoptimalsolutionandtheadaptabilityofthe ontroltothetime-varying

onditions.

Asfarasthemappingbetweentheproblemathandandtheswarmstru tureis on erned,

let us refer to a phased-array ontrolled by

B

-bits digital phase shifters. Therefore, the

p

-thtrialsolution turns out tobethe sequen e of the quantized phasevalues [10℄

B

p

= {β

b,p,n

∈ {0, 1} ; n = 1, ..., N; b = 1, ..., B} .

(8)

Con erning the parti le des ription,

B

p

denes the position of the

p

-th element of the swarm in the solution spa e and the velo ity

V

p

models the apa ity of the parti le to y from a given position

B

kℓ

p

to another position

B

kℓ+1

_p

ofthesolutionspa e,

k

ℓ

beingtheiterationindexatthe

ℓ

-thtime-step

t

ℓ

. Moreover,

V

b,p,n

is the probability that

β

b,p,n

takes value

1

.

The swarm samples the solution spa e by means of a binary

P SO

-based strategy. At ea h iteration

k

ℓ

(

k

ℓ

= 1, ..., K

) of every time-step

t

ℓ

, the

P

trial solutions are ranked a ording to their tness to the environmental s enario by omputing (6) in

orre-sponden e with

B

kℓ

p

,

P

kℓ

p

= P B

kℓ

p

. Su h an operation leads to the denition of the

personal best parti le

ξ

ℓ

p

=

arg



min

hℓ=1,...,kℓ

P B

h

ℓ

p



and of the global best parti le

ζ

ℓ

=

arg

n

min

p=1,...,P

h

P



ξ

ℓ

_p

io

. Startingfromtheinitialpopulationrandomlygenerated aroundthedesiredsignalparti le(i.e.,

B

kℓ

p

=

n

β

k

ℓ

b,p,n

su h that

β

n

= ϕ

(d)

n

; n = 1, ..., N

o

,

k

ℓ

= 1

and

p = 1

), the set ofsolutionsiteratively evolves by modifyingthe parti les posi-tions a ording to the binary-positionupdating equation[10℄:

β

_b,p,n

kℓ+1

=











1 if r

k

ℓ

b,p,n

< ℑ



V

k

ℓ

b,p,n



0

otherwise

(10)

where

ℑ ( . )

is the sigmoid fun tion

ℑ



V

_b,p,n

kℓ



=

1

1 +

exp



−β

k

ℓ

b,p,n



(11)

r

_b,p,n

kℓ

beingarandomnumberdrawnfromanuniformdistributionbetween

0

and

1

. Asfar asthe velo ityupdate is on erned,itisobtained by applyingthe ThresholdingOperator

Λ (·)

tothe result

X

kℓ

b,p,n

ofthe Memory-Based Velo ity Operator

U {·}

(13)

V

_b,p,n

kℓ

= Λ

n

X

_b,p,n

kℓ

o

=























−V

max

X

b,p,n

kℓ

< V

max

X

_b,p,n

kℓ

−V

max

≤ X

b,p,n

kℓ

≤ V

max

V

max

X

_b,p,n

k

ℓ

> V

max

.

(12)

Duringatimestep

t

ℓ

,theiterativepro essstopswhenamaximumnumberofiterations

K

is rea hed,

k

ℓ

= K

,(i.e., when themaximum rea tiontime

T

resp

of the system iselapsed,

T

resp

= K × T

kℓ

,

T

kℓ

being the iteration

CP U

-time) or if the optimality riterion of the

system performan e is attained [i.e.,

P ζ

ℓ

_{≤ γ}

opt

,

γ

opt

being a user-dened threshold℄.

Whatever the termination ondition,

ζ

ℓ

is assumed as the problem solution on erned

with the

ℓ

-thtime-step,

t

ℓ

.

3.2 Memory-Based Learning and Updating Strategy

Inordertodeneafastrea tion ofthe ontroltotheenvironmental hanges,a

ustomi-zedandintegratedstrategybasedonamemoryme hanismhasbeenimplementedthrough

the denition of suitable operators a ting during the iterative pro edure (

k

ℓ

= 1, ..., K

) and in the whole time-varying pro ess (

t

ℓ

;

ℓ = 1, ..., L

).

Thememoryme hanismliesonthedenitionofasystemmemory omposedbya

nite-length buer

M = {ς

m

_{; m = 1, ..., M}}

(

M

being the buer length). At ea h time-step, the Storage Operator allows an ex hange of informationfrom the swarm to the memory

of the system. In orresponden e with a new time-step (

t

ℓ

← t

ℓ+1

), the solutions stored in

M

areranked a ording totheir tnessvaluessu hthat

P

ℓ+1

ς

1

≥ ... ≥ P

ℓ+1

ς

M

.

Then, at the end of the time-step, the system memory is updated as follows:

ς

1

= ζ

ℓ+1

if

P

ℓ+1

ζ

ℓ+1

_{< P}

ℓ+1

ς

₁

. In a omplementary fashion, the operator

Π {·}

ontrols the exploitation of the system memory to improve the swarm rea tionto the hanges of the

interferen e s enario. Unlike [11℄, a simpler a tivation me hanism is implemented by

dening a user-xed lower bound for the system performan es,

γ

wor

. More in detail, when

P ζ

ℓ

_{> γ}

wor

then the worst parti le isrepla ed by the best solutionstored in

M

(

γ

ℓ+1

_{← ς}

M

, being

γ

ℓ+1

_{= arg}

_max

p=1,...,P

P B

kℓ+1

p



).

Althoughsu halearningstrategyee tivelyusesthe availableinformationonthesystem

history, ertainlythe exploitationof the information ontainedin

M

atea h iteration

k

ℓ

of the swarm evolution would allow a more pun tual and immediate use of the a quired

knowledgeonthebehaviorof theenvironment. Towards thispurpose,the Memory-Based

Velo ity Operator

U {·}

is dened asthe ompositionof four terms

X

_b,p,n

kℓ

= I

n

V

_b,p,n

kℓ

−1

o

+ S

n

β

_b,p,n

kℓ

, ξ

ℓ

b,p,n

o

+ G

n

β

_b,p,n

kℓ

, ζ

ℓ

b,n

o

+ A

ς

m

b,n

; m = 1, ..., M .

(13)

I

n

V

_b,p,n

kℓ

−

1

o

= αV

_b,p,n

kℓ

−

1

.

(14)

It models the tenden y of a parti le to ontinue in the same dire tionit is traveling. In

general,theinertialweight

α

takesa onstantvalue[19℄oritde reasesduringtheiterative pro ess to favor alo alsear hing atthe end of the optimization[20℄[21℄.

The se ond term is alled self-knowledge and it auses the attra tion of the parti le

to-wards thebest positionpreviouslyrea hed foranamountproportionaltoaxed onstant

oe ient

c

1

( ognition oe ient)andarandomnumber

r

1

fromanuniformdistribution between

0

and

1

S

n

β

k

ℓ

b,p,n

, ξ

ℓ

b,p,n

o

= c

1

r

1



ξ

b,p,n

ℓ

− β

k

ℓ

b,p,n



.

(15)

Complementary to the self-knowledge omponent, the group-knowledge term models a

linear attra tion towards the optimalposition a hieved sofar

G

n

β

_b,p,n

kℓ

, ζ

ℓ

b,n

o

= c

2

r

2



ζ

ℓ

b,n

− β

kℓ

b,p,n



(16)

c

2

being the so ial oe ient and

r

2

∈ [0, 1]

.

Be ause ofthetime-varyings enarioandthe needtoredu ethe rea tiontimetaking into

a ount the similaritiesamong the environmental onditions at dierent time-steps, the

fourth velo ity omponent (indi ated as ambient-knowledge) is a ordingly dened as

follows

A

ς

m

b,n

; m = 1, ..., M

= c

3

r

3

P

M

m=1

h

ς

m

b,n

e

−H

(m−1)

M

i

M

(17)

H

,

c

3

beingtwo onstantweightingparametersand

r

3

isanotherrandomnumber. Insu h a manner, the parti le velo ity is inuen ed by a histori al term related to the optimal

solutionsatdierenttime-stepsandin orresponden e withvariousinterferen es enarios.

4 Numeri al Validation

In this se tion, the results of several numeri al tests are reported in order to assess the

deals with the alibration of the

P SO

-based pro edure and it is aimed at dening the optimal ongurationof the key parameters of the optimization algorithm. The latter is

on erned with the des ription of the performan es of the adaptive ontrol in omplex

s enarios hara terizedby the presen e of near-eld interferen e sour es, aswell.

4.1 Calibration of the Optimization Algorithm

The key parameters of the optimizationalgorithmhave been sele ted through numeri al

simulations. Theyhavebeenxedtothosevaluesthatallowafavorabletrade-obetween

therateof onvergen e towardsasuitablesolutionandthe apabilityofusefullyexploring

thewholesolutionspa e. Moreover,duetotheintrinsi statisti alnatureoftheapproa h,

ea htest aseorexperimenthasbeenrunseveraltimestoassessthequalityofthesolution

as wellas its statisti alsigni an e.

The referen e geometry onsisted of a linear array of

N = 20 z

-oriented and

λ/2

-spa ed dipoles lying on the

x

-axis. The amplitudes of the array weights have been hosen a - ording to the Dolph-Chebyshev distribution. In the following, su h a geometry will be

referred to aslinear array.

The inertial weight

α

has been heuristi ally tuned by verifying the ee tiveness of the adaptive ontrol in orresponden e with dierent rules of variation or setting. Towards

this end, an interferen e s enario hara terized by jamming signals with dire tions

ran-domlydistributedandarrival-timesmodeledbymeansofaPoisson'spro ess[11℄hasbeen

onsidered. Withreferen e to Fig. 3, where arepresentative sample of a sto hasti

real-izationof the interferen e generation pro ess is pi toriallydes ribed, arandomnumber

I

of jammingsignals[Fig. 3(a)℄with

DoA

suniformlydistributedin

φ ∈ [0; 180]

[Fig. 3(b)℄ has been onsidered (Poisson's s enario). The power of the jamming sour es has been

xed to

30 dB

above the power of the desired signal (the power of ba kground noise has been assumed equal to

σ

2

_{= −30 dB}

). Moreover, the positions of the jamming sour es

have been randomly hosen between

5 λ

and

100 λ

. In su h a noisy environment, the hoi e of a swarm of

P = 30

parti les is a good trade-o between onvergen e rate and quality ofthe adaptive ontrolas onrmed byFig. 4wherethe plot ofthe averagevalue

a quality rating of the algorithmperforman e

(2)

.

Dierent hoi es of

α

have been analyzed (Tab. I) taking into a ount the guidelines suggested in the referen e literature. Firstly, adynami law has been used by de reasing

theinertialweightfrom

0.9

upto

0.4

intherangeofiterations(

k

ℓ

= 1, ..., K

,

K = 1000

)of a time-step

t

ℓ

. In general,su ha hoi e allows abetter balan ebetween global and lo al exploration during the minimization en ouraging the global and the lo al sear h at the

start and atthe end of the optimization, respe tively. However, when solving (7) and as

onrmed by the indexes inTab. I and relatedtothe

SINR

averaged over

L

time-steps, better performan es have been attained by hoosing a small and onstant value of the

inertial weight (

α = 0.1

). Su h a hoi e usually favors the rea tion and the adaptability of the ontrol to the environmental hanges thus improving the onvergen e rate of the

algorithm. Consequently, thefaster the ontrolrea hes aset ofsuitableweightsthe lower

be omes the response time with a redu tion of the amount of iterations needed for ea h

time-step without penalizing the ee tiveness of the optimization pro ess. Therefore,

starting from su h an indi ationand after an exhaustive and statisti ally relevant set of

numeri altests,

K

has been set to

20

iterationswhatever the interferen e s enario.

Asfarasthetuningoftheself-knowledge,ofthegroup-knowledgeandoftheam

bient-knowledge terms is on erned, a large number of simulations has been performed by

onsidering the guidelines re ommended by the

P SO

literature [16℄[17℄ as referen es and by taking into a ount other experimentations in similar optimization frameworks

[22℄[19℄[23℄. The hyperspa e of possible setups of the parameters

c

1

,

c

2

,

c

3

, and

H

has beensampledto ndthe most suitablesettingtoallowane ient

P SO

-based optimiza-tion. As a representative example, let us refer to Fig. 5 where the plot of the averaged

SINR

along asli e of the

P SO

parameters hyperspa e (

H = 10

and

c

1

= 2.0

) isshown. The maximum value of su h a quality index is situated at

c

2

= 2c

3

= 2.0

and su h a parameters ongurationhas been assumed inthe followinganalyses/experiments.

Finally,the ontrolparametersof the memoryme hanism havebeen tuned. Be ause of

the noveltyofthe proposedimplementation,noindi ations areavailable. Thus, three

dif-(2)

Unfortunately,the

SI N R

annotbeusedbythe ontrolalgorithmtoranktrialsolutions,butonly asaqualityindex. As amatterof fa t,thereisnowayto al ulatethesignal-to-interferen e-plus-noise ratio for the system ar hite ture assumed in this paper (Fig. 1). Therefore, the total output power measuredbythere eiverisusedastheindex ofthetnesstotheenvironmentofea hparti le.

and ustomized interferen e ongurations have been generated to verify the

ee tive-ness of the approa h in fully exploiting similarities and o urren es of jamming signals.

The former (intermittent s enario) oin ides with that proposed by Weile et al. in [9℄.

The latter (deterministi s enario) onsiders a luster of interferen es whose

DoA

s are supposed to beinvariantduring alarge numberof iterations(Tab. II).

Inordertoevaluatethesensitivityofthesystemtothe memorydimension(i.e.,thebuer

length

M

),let usanalyze the behavior of the followingindex

∆ =

hSINR

M

=Y

i − hSINR

M

=0

i

hSINR

M

=0

i

× 100

(18)

where

Y

is the urrent value of

M

and the operator

h . i

stands for the average value. Con erning the deterministi s enario, the obtained results are summarized in Tab. III.

As it an be noti ed, the e ien y of the ontrol improves in orresponden e with an

in rease of the dimension of the buer, until a saturation veries when

M ≥ 20

(i.e.,

M

P

= 0.67

). As a matter of fa t,

M = 20

seems to be the best hoi e sin e it allows a non-negligible improvement in the ontrol apabilities (

∆ = 39.7

) without signi antly ae tingthe omputationalburden. Tofurther onrmsu ha on lusion,theanalysishas

been extended to the whole set of s enarios. Figure 6shows the plots of the

SINR

with (

M = 20

) and without(

M = 0

) memory versus

t

ℓ

(

ℓ = 1, ..., L

;

L = 900

). As expe ted, the mostrelevantenhan ementholds forthedeterministi onguration,eventhoughthe

learning apabilities of the approa h impa ts in a non-negligible way in orresponden e

with the intermittent onguration and the Poisson's s enario, as well. Moreover, the

obtained results onrm that the introdu tion of a memory buer and of an enhan ed

strategy for the velo ity updating turns out in a fully exploitation of the existing (when

negligibleor limitedtoo) orrelationsamong dierenttime-steps.

4.2 Testing of the Optimization Algorithm

Byassumingtheoptimalsettingofthe

P SOM

parametersdened afterthe  alibration phase,thissub-se tionpresentstheresultsofastudyaimedatevaluatingtheperforman e

omparative assessment, as well. As a matter of fa t, the enhan ed

P SO

-based ontrol hasbeen omparedwithotherstate-of-the-artpro eduresintermsofbothqualityindexes

and omputational osts.

The rst analysisis devoted at evaluatingthe dependen e of the adaptive ontrolonthe

lo ations of the interferen e sour es and the re eiving system ar hite ture. As a result,

it appears that the performan es of the

P SOM

are notably ae ted fromthe number of bits

B

of the digital phase shifters espe iallyin orresponden e with small values of the distan e

ρ

i

. Su haneventispointed outinFig. 7(a)wherethe behaviorof

Φ

av

versus

B

fordierentvaluesof

ρ

i

issummarized(Poisson'ss enario).

Φ

av

isaqualityindexdened as

Φ

av

=

hSINR

F ull

i − hSINR

F F

i

hSINR

F F

i

× 100

where the subs ripts

(F ull)

and

(F F )

indi ate that the

SINR

has been omputed with the array weights determined by minimizing (6) and using (4) or (2) for modeling the

jammers, respe tively.

As expe ted and onrming the ee tiveness of the Full formulation in dealing with

near-eld interferen es,

Φ

av

in reases when

ρ

i

be omes smaller and smaller. Moreover, the value of

Φ

av

grows as

B

in reases up to

B = 8

. As a matter of fa t, when

B ≥ 10

the binary-solution-spa e onsiderablyenlargesand itappearstobetoolargeforallowing

fast onvergen e and reliable results.

For omparison purposes, Figure7(b) shows the results obtained setting

B = 8

with the

P SOM

approa h,theApplebaum-basedidealmethod[3℄,theApplebaumte hniquewith dis retephases(

DP A

),theLeastMeanSquarealgorithm(

LMS

),the

LMS

withdis rete phases (

DP LMS

), the

P SO

-based approa h proposed in [10℄ (

P SO

), and the learned real-time

GA

[24℄ (

LRT GA

). As it an be noti ed, the proposed approa h outperforms both

DP LMS

and

LRT GA

, as well as the

P SO

. Moreover, its behavior turns out to be quite lose to that of the

DP A

whatever the jammers lo ations, despite a lower ar hite tural omplexity. Furthermore, the

P SOM

a hieves better signal-to-noise ratios than

LMS

when

ρi

λ

< 400

, whilefor farther interferen es the

LMS

allows slightlybetter performan es, but with multiplere eivers one atea h array element.

As a representative example, Figure 8 shows the behavior of the

SINR

for a realization of the Poisson'ss enario (

L = 900

) underthe assumptionthat

ρ

i

is randomlydistributed in the range

[5λ, 100λ]

and the interferen es do not hange in

K

(P SOM )

_{= 20}

iterations.

Moreover, the ontrol methods have been arrested after the same

T

resp

. Consequently,

K

has been xed to

3000

when using the

LMS

algorithm sin e the number of om-plex oating point operationsper iterationis

O (N)

, while the oating point operations needed by

P SOM

/

P SO

/

LRT GA

are of the order of

O (P

2

_{× B × N)}

. As far as the

LRT GA

is on erned,itisofabout

4

times omputationallyheavierthanthe

P SO

-based methods(Tab. IV). Therefore, ea h

GA

-basedoptimization loophas been terminated at

K

(LRT GA)

₌

K

(P SO)

4

.

In Figure 8(a), the results obtained with the

F F

formulation are given in terms of the signal-to-interferen e-plus-noise ratio (

SINR

F F

), whereas Fig. 8(b) shows the

SINR

behaviorwhenusingthe ompleteformulation(

SINR

F ull

). Ex ept fortheidealapproa h and whateverthe ontrolte hnique,the systemperforman eimprovesby resortingtothe

Full formulation as outlinedby the plot of the index

Φ

[Fig. 9( )℄ given by

Φ =

SINR

F ull

− SINR

F F

SINR

F F

× 100.

On the otherhand, the

P SO

-basedapproa hes generallyoutperform otheroptimization methods as well as the

LMS

-based te hniques. Furthermore, they turn out to be very lose orbetterthanthe

DP A

approa h[Fig. 8(b)℄. Asamatteroffa t,

SINR

P SOM

F ull

 =

29.90

and

SINR

P SO

F ull

 = 28.82

versus

SINR

DP A

F ull

 = 27.05

(Tab. V).

These ondtest asedealswiththesames enarioofFig. 8,butwithalowerresponsetime

T

resp

. As a matter of fa t, the optimization loops have been terminated at

K

(P SOM )

₌

K

(P SO)

_{= 5}

,

K

(LRT GA)

_{= 2}

, and

K

(LM S)

_{= 750}

, respe tively. Unlike both Applebaum

and

LMS

-based approa hes, the results from sto hasti strategies signi antly hange. Whatever the formulation, the average values of

SINR

redu e of about

3 ÷ 6 dB

as indi ated inTab. Vand Tab. VI. However, the

P SOM

stillfavorably ompares withthe other digital optimization methods (i.e.,

DP LMS

,

P SO

, and

LRT GA

) [Figs. 9(a)-( ) and Tab. VI℄.

arrayof

N = 61 z

-orientedand

λ/2

-spa eddipoles [11℄withuniformamplitudes. Atea h time-step

t

ℓ

, a random number of

I

jamming signals with Poisson-modeledarrival-times and

DoA

s uniformly distributed in

θ ∈ [0; 180]

and

φ ∈ [0; 180]

(

3D

-Poisson s enario) impinges on the array. Likewise the Poisson's s enario, ea h jammer is hara terized by

a power of

30 dB

above the desired signal power and the lo ations of the interferen e sour es are random variablesuniformlydistributed between

5 λ

and

100 λ

.

Figure10(a)shows theplotofthe

SINR

valueinawindowof

L = 100

time-steps. As ex-pe ted,the ompleteformulationallowsamoreee tiveadaptive ontrol(

SINR

P SOM

F ull

 =

38.02

vs.

SINR

P SOM

F F

 = 26.84

). As far as the omparative assessment is on erned, Figure10(b) pointsout that on average the e ien y of the

P SOM

tends tothat of the

DP A

(

SINR

P SOM

F ull

 = 38.02

vs.

SINR

DP A

F ull

 = 38.31

)anditover omesthe

LMS

-based strategies, the

P SO

as well as the

LRT GA

(

SINR

LM S

F ull

 = 31.31

,

SINR

DP LM S

F ull

 =

28.62

,

SINR

P SO

F ull

 = 31.63

, and

SINR

LRT GA

F ull

 = 29.43

).

For ompleteness, Figure 11 shows the olor level representations of the quies ent beam

pattern [Fig. 11(a)℄ and both near-eld [13℄ [Fig. 11(b) -

ρ

oss

= 25 λ

, Fig. 11( )-

ρ

oss

=

59 λ

℄andfar-eld[Fig. 11(d)℄distributionsgeneratedbytheadaptiveplanararray atthe

ℓ = 28

-thsnapshotwhentwointerferen esour eslo atedat

(θ

1

= 62

o

_{, φ}

1

= 89

o

, ρ

1

= 25 λ)

and

(θ

2

= 42

o

_{, φ}

2

= 39

o

, ρ

2

= 59 λ)

radiates. 5 Con lusions

Thispaperhasinvestigatedboththetheoreti alandnumeri alaspe tsoftheuseofdigital

phase-shifters onlyweighting for adaptive nullsteeringin omplex interferen e s enarios.

It has demonstrated the appli ation of a

P SO

-based ontrol equipped with enhan ed memory features for the adaptation of the antenna array to minimize the total output

poweratthere eiver. Themathemati alformulationoftheapproa handthealgorithmi

sequen e of the enhan ed adaptive ontrolhave been arefully des ribed. The numeri al

validation has been arried out by onsidering dierent array geometries and various

interferen e ongurations.

•

an enhan ed e ien y of the adaptive ontrol (Full vs. FF formulation);

•

a favorabletrade-o amongar hite tural omplexity ofthe re eiver, omputational load, and fast readaptationto hanging environmental onditions;

•

a robustness toboth near-eld and far-eld interferen es.

As far as the main novelties of this paper are on erned, they an be summarized as

follows:

•

the mathemati alformulationof the smart ontrolable to modeltime-varying s e-narios hara terized by randomly lo ated jammingsour es;

•

the enhan ed

P SO

-basedapproa h,whi hhas been suitably designed toprotably exploit the memory me hanism.

Future developments and resear ha tivities willbe aimedatimprovingthe modelof the

interferen e s enario. Forexample, by onsideringthe presen e of s atterers in the

lose-ness of the antennaordierentstatisti aldes riptions. Moreover, it would beinteresting

to study the performan e of the adaptive ontrol under onditions when array elements

are expe ted to fail [25℄. In prin iple, no hanges to the proposed algorithm would be

[1℄ C. B. Dietri h, W. L. Stutzman, K. Byung-Ki, and K. Dietze, Smart antennas in

wireless ommuni ations: base-station diversity and handset beamforming, IEEE

Antennas Propagat. Mag., vol. 52,pp. 142-151, O t. 2000.

[2℄ M. Chryssomallis, "Smart antennas," IEEE Antennas Propagat. Mag., vol. 42, pp.

129-136, Jun. 2000.

[3℄ S. P.Applebaum, "Adaptive arrays," IEEE Trans.Antennas Propagat., vol. 24,pp.

585-598, Sep. 1976.

[4℄ B. Widrow, P. E. Mantey, L.J. Griths, and B. B. Goode, "Adaptive antenna

sys-tems," Pro . IEEE, vol. 55,pp. 2143-2159, De . 1967.

[5℄ L. C. Godara,Improved LMS Algorithmfor Adaptive Beamforming, IEEE Trans.

Antennas Propagat., vol.38, pp. 1631-1635, O t. 1990.

[6℄ C.A.BairdandG.G.Rassweiler,Adaptivesidelobenullingusingdigitally ontrolled

phase-shifters, IEEE Trans. Antennas Propagat.,vol. 24,pp. 638-649,Sep. 1976.

[7℄ R. L. Haupt, "Phase-only adaptive nulling with a geneti algorithm," IEEE Trans.

Antennas Propagat., vol.45, pp. 1009-1015, Jun. 1997.

[8℄ R. L. Haupt and H. Southall, "Experimental adaptive nulling with a geneti

algo-rithm," Mi rowave J., vol. 42,pp. 78-89, 1999.

[9℄ D. S.WeileandE.Mi hielssen,"The ontrolofadaptiveantennaarrayswithgeneti

algorithms using dominan e and diploidy," IEEE Trans. Antennas Propagat., vol.

49, pp. 1424-1433, O t. 2001.

[10℄ M. Donelli, R. Azaro, F. De Natale, and A. Massa, An innovative omputational

approa h based on a parti le swarm strategy for adaptive phased-arrays ontrol,

IEEE Trans.Antennas Propagat., vol.54, pp. 888-898,Mar. 2006.

[11℄ A.Massa, M.Donelli,F.DeNatale, S.Caorsi,andA.Lommi,Planarantennaarray

ontrol with geneti algorithmsand adaptive array theory, IEEE Trans. Antennas

[13℄ A. J. Fenn, Evaluation of adaptive phased array antenna far-eld nulling

perfor-man e in the near-eld region, IEEE Trans. Antennas Propagat., vol. 38, pp.

173-185, Feb. 1990.

[14℄ L. C. Godara,Smart Antennas.Bo aRaton: CRC Press, 2004.

[15℄ R.T. ComptonJr.,Adaptive Antennas.EnglewoodClis,New Jersey,Prenti eHall,

1988.

[16℄ J.Kennedy,R.C. Eberhart,and Y.Shi, Swarm Intelligen e.San Fran is o: Morgan

Kaufmann Publishiers, 2001.

[17℄ J. Robinson and Y. Rahmat-Samii, Parti le swarm optimization in

ele tromagnet-i s, IEEE Trans.Antennas Propagat., vol. 52,pp. 397-407,Feb. 2004.

[18℄ R. Eberhart and J. Kennedy, "A new optimizer using parti leswarm theory, Pro .

Sixth Int. Symp. Mi ro-Ma hine and Human S ien e (Nagoya, Japan), pp. 39-43,

1995.

[19℄ M. Donelliand A.Massa, Computationalapproa h basedona parti leswarm

opti-mizer for mi rowave imagingof two-dimensional diele tri s atterers, IEEE Trans.

Mi rowave Theory Te hn., vol. 53,pp. 1761-1776,May 2005.

[20℄ R. C. Eberhart and Y. Shi, Comparing inertia weights and onstri tion fa tors in

parti leswarm optimization, inPro . CongressonEvolutionary Computation2000,

Pis ataway, USA, pp. 84-88, 2000.

[21℄ Y. Shi and R. C. Eberhart, Empiri al study of parti le swarm optimization, in

Pro . Congress on Evolutionary Computation 1999, Washington, USA, pp.

1945-1950, 1999.

[22℄ D. W. Boeringer and D. H. Werner, Parti le swarm optimization versus geneti

algorithms for phased array synthesis, IEEE Trans. Antennas and Propagat., vol.

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[24℄ S. Caorsi, M. Donelli, A. Lommi, and A. Massa "A real-time approa h to array

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36, pp. 235-238,Feb. 2003.

[25℄ B.-K. Yeo and Y. Lu, Array failure orre tion with a geneti algorithm, IEEE

•

Figure 1. Ar hite ture of the adaptive array with a single re eiver at the output of the summer.

•

Figure 2. Geometry of the s enario undertest.

•

Figure 3. Poisson'sinterferen e s enario. (a)Numberofinterferen e signals

I

and (b) distributionof the anglesof arrival of the jammers versus the time-step index.

•

Figure 4. Calibration Phase. Averaged

SINR

fordierent sizes of the swarm,

P

.

•

Figure 5. Calibration Phase. Behavior of the averaged

SINR

versus

c

2

and

c

3

(

c

1

= 2

,

H = 10

).

•

Figure 6. Calibration Phase. Behavior of the

SINR

versus the time-step index for dierentinterferen e s enarios with (

M = 20

) and withoutmemory me hanism (

M = 0

).

•

Figure 7. Testing Phase (Poisson's interferen e s enario). Behavior of

Φ

av

versus

ρ

i

for (a) dierent values of

B

(

P SOM

) and in orresponden e with (b) dierent ontrolte hniques (

B = 8

).

•

Figure 8. Testing Phase (Poisson's interferen e s enario,

ρ

i

∈ [5λ, 100λ]

- Linear Array). Plots of (a)

SINR

F ull

, (b)

SINR

F F

,and ( )

Φ

versus the time-step index for dierent adaptive ontrolmethods[

K

P SOM

_{= 20}

℄.

•

Figure 9. Testing Phase (Poisson's interferen e s enario,

ρ

i

∈ [5λ, 100λ]

- Linear Array). Plots of (a)

SINR

F ull

, (b)

SINR

F F

,and ( )

Φ

versus the time-step index for dierent adaptive ontrolmethods[

K

P SOM

_{= 5}

℄.

•

Figure 10. Testing Phase (Poisson'sinterferen e s enario,

ρ

i

∈ [5λ, 100λ]

-Planar Array). (a)Plotsof

SINR

F ull

and

SINR

F F

versusthe time-stepindexwhenusing

P SOM

. (b) Comparison between dierent ontrol methods.

•

Figure 11. Testing Phase (3D Poisson's interferen e s enario,

ρ

i

∈ [5λ, 100λ]

-Planar Array). (a) Quies ent beam pattern. Beam patterns generated at the

•

Table I. Calibration Phase. Impa t of the inertialweight setting

α

on the system performan e (

∆

).

•

Table II. Des riptive parametersof the Deterministi S enario.

•

TableIII.Calibration Phase. Impa t ofthe dimension

M

of thememorybuer on the system performan e (

∆

).

•

TableIV. Computational ostsofthe digitaloptimizationapproa hes (

CP U Intel

P 4

,

2.8 GHz

,

512 MB

RAM).

T

,

T

_kℓ

min

(

T

_kℓ

)

.

•

Table V. Testing Phase (Poisson's interferen e s enario,

ρ

i

∈ [5λ, 100λ]

- Linear Array). Average values of

SINR

F ull

and of

SINR

F F

for dierent adaptive ontrol methods[

K

(P SOM )

_{= 20}

℄.

•

Table VI. Testing Phase (Poisson's interferen e s enario,

ρ

i

∈ [5λ, 100λ]

- Linear Array). Average values of

SINR

F ull

and of

SINR

F F

for dierent adaptive ontrol methods[

K

(P SOM )

_{= 5}

1

s

(r)

W

1

W

2

W

₃

Σ

Antenna

_{Adaptive Weights}

Elements

(r)

2

s

(r)

3

s

(r)

_N

s

W

N

PSOM

s

(e)

Total

Measurement

Output Power

θ

1

θ

2

θ

d

far−field

approximation

N

1

2

n

0

...

ρ

2

ρ

1

x

z

jammer 2

jammer 1

desired signal,

0

2

4

6

8

10

0

100

200

300

400

500

600

700

800

900

Number of Interferers, I

Time-steps, t

_l

(a)

0

20

40

60

80

100

120

140

160

180

0

100

200

300

400

500

600

700

800

900

Direction of Arrival (DoA),

φ

[deg]

Time-steps, t

_l

(b)

15

20

25

30

35

1

3

10

30

100

300

1000

<SINR> [dB]

P

0

c

2

4

2

c

3

0

20

SINR [dB]

30

-10

0

10

20

30

40

50

60

70

0

100

200

300

400

500

600

700

800

900

SINR [dB]

Time-steps, t

_l

M=20

M=0

Determinist scenario

Poisson scenario

[6], scenario 1

-5

0

5

10

15

20

25

30

35

40

45

50

1

10

100

1000

10000

Φ

av

ρ

i

/

λ

Near Field Region

Fresnel Region

Far Field Region

B = 4

B = 6

B = 8

B = 10

(a)

-10

0

10

20

30

40

50

60

70

1

10

100

1000

10000

Φ

av

ρ

i

/

λ

Near Field Region

Fresnel Region

Far Field Region

Applebaum

DPA

LMS

DPLMS

PSOM

PSO

LRTGA

(b)

10

15

20

25

30

35

40

45

50

55

60

0

100

200

300

400

500

600

700

800

900

SINR [dB]

Time-steps, t

_l

Applebaum

DPA

LMS

DPLMS

PSOM

PSO

LRTGA

(a)

10

15

20

25

30

35

40

45

50

55

60

0

100

200

300

400

500

600

700

800

900

SINR

full

[dB]

Time-steps, t

_l

Applebaum

DPA

LMS

DPLMS

PSOM

PSO

LRTGA

(b)

0

20

40

60

80

100

0

100

200

300

400

500

600

700

800

900

Φ

Time-steps, t

_l

Applebaum

DPA

LMS

DPLMS

PSOM

PSO

LRTGA

( )

10

15

20

25

30

35

40

45

50

55

60

0

100

200

300

400

500

600

700

800

900

SINR [dB]

Time-steps, t

_l

Applebaum

DPA

LMS

DPLMS

PSOM

PSO

LRTGA

(a)

10

15

20

25

30

35

40

45

50

55

60

0

100

200

300

400

500

600

700

800

900

SINR

full

[dB]

Time-steps, t

_l

Applebaum

DPA

LMS

DPLMS

PSOM

PSO

LRTGA

(b)

0

20

40

60

80

100

0

100

200

300

400

500

600

700

800

900

Φ

Time-steps, t

_l

Applebaum

DPA

LMS

DPLMS

PSOM

PSO

LRTGA

( )

10

15

20

25

30

35

40

45

50

55

60

0

20

40

60

80

100

Time-steps, t

_l

l = 28

SINR

_full

[dB]

SINR

_FF

[dB]

(a)

10

20

30

40

50

60

70

0

20

40

60

80

100

SINR

Full

dB

Time-steps, t

_l

Applebaum

DPA

LMS

DPLMS

PSOM

PSO

LRTGA

(b)

−1

q

1

−1

q

1

1

u

−

1

1

u

−

1

0

G(u, q) dB

− 200

0

G(u, q) dB

− 200

(a) ( )

−1

q

1

−1

q

1

1

u

−

1

1

u

−

1

0

G(u, q) dB

− 200

0

G(u, q) dB

− 200

(b) (d)

α

hSIN Ri [dB]

0.4 → 0.9

13.81

0.9

13.73

0.4

13.86

0.1

13.93

0.01

13.84

ℓ

θ

1

φ

1

ρ

1

[λ]

0

→ 330

90 165

5

330

→ 660 90 120

10

660

→ 990 90 42

7

M

∆

5

10.9

10

27.3

20

39.7

40

41.1

Control Algorithm

T

kℓ

[ms]

T

P SOM

1.62

1.02

P SO

1.59

1.0

LRT GA

6.48

4.07

hSIN R

F ull

i [dB] hSIN R

F F

i [dB]

Applebaum

42.80

42.52

DP A

27.05

20.44

LM S

25.82

20.09

DP LM S

23.54

19.82

P SOM

29.90

23.25

P SO

28.82

22.81

LRT GA

25.56

22.87

hSIN R

F ull

i [dB] hSIN R

F F

i [dB]

Applebaum

42.80

42.52

DP A

27.05

20.44

LM S

25.82

20.09

DP LM S

23.54

19.82

P SOM

24.48

21.24

P SO

21.98

20.07

LRT GA

21.84

20.55