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1 INTRODUCTION
Theexistingmodelofmarineradarshasahighpeak
poweroftheradiation,whichworsensthequalityof
themainlobeandleadstoharmfulemissionintothe
environment and worsens the property of the
electromagnetic compatibility. To improve the
effectiveness of the radar must be developed
radar
withareducedpulseradiationpower,whichisactual
topicnowadays.
Thebasisofalmostallmethodsfordetectingand
identifying target objects is the use of complex
probingsignalswithoptimizedcorrelationproperties.
Knowledgeisneededtoimprovethecontrastofradar
images. Tasks can be solved by
determining the
phase‐frequencypropertiesofthesurfaceoftheta rget
object. The fixed conditions are necessary for the
analysis of phase and amplitude distortions of the
probe signal at different frequencies [1]. Therefore,
theuseofadaptivefiltrationincombinationwiththe
radar processing method makes it possible to
establish,
with sufficient accuracy, the phase‐
frequency characteristics of probe radar signals,
directly for each sensing period. Get radar
information about the target object based on the
adaptivefilterineachsensing period.Theprocedure
istoadaptthefilteratthetimeofreceivinganecho‐
signal.Furtheranalysisof
theerror(rejectionofecho
andprobe signals)is atransient characteristicof the
adaptive filter after its adaptation. For each target
objectinonesensingperiod,aseparatealgorithmfor
adaptivefiltrationmustbeformed.
The Development of Iteration Method for Optimization
of Pair "Signal-filter"
V.M.Koshevyy&I.Y.Gorishna
NationalUniversity“OdessaMaritimeAcademy”,Odessa,Ukraine
ABSTRACT:Thispaperisdevotedtotheimprovementoftheworkingmethodsoftheʺsignal‐filterʺpairusing
aniterativeproceduretomaximizethesignal‐to‐noiseratio,namely,tohighlighttheusefulsignalstoprovide
information about the environment during the adaptive radar
sensing in the conditions of obstacles. An
algorithmfordeterminingtheoptimalfilterforsuppressing undesiredside lobesis proposed,which allows
improvingtheprocessofdetectionandidentificationthetargetobjects.
Qualitative characteristics and the stages of space‐time signal processing in the radar were justified under
correlationconditions
(ССF)betweenthereceivedand expectedsignals.The usingofprobingradarsignals,
shortened intheirdurationwereproposed in order to reduce the power of reflections from the underlying
surfaceandincreasethecontrastoftheradarimage.
A simulation test of the developed methodology was carried out in
order to confirm the reliability of the
proposed algebraic expressions using a mathematical model implemented in the Matlab programming
environment,andaconclusionisdrawnaboutthepracticalqualityofthetechnicalsolutionsdevelopedonthe
basisoftheiterationmethod.
http://www.transnav.eu
the International Journal
on Marine Navigation
and Safety of Sea Transportation
Volume 12
Number 3
September 2018
DOI:10.12716/1001.12.03.13
542
From the point of view of increasing resolution
andaccuracy(i.e.,radarinformativity),itisnecessary
to extend the frequency band of the probe signal,
which, for example, is achieved by decreasing the
duration of the sounding pulses or using special
complexsignals[2].
Further we consider it with more
details. The
Ambiguity Function (AF) corresponds to the time‐
frequency response function that is observed on the
output of the filter. One of the most important
characteristics of the AF is the level of side lobes,
which in most cases are trying to reduce. Phase‐
manipulated (PM) signals aresequence
of radio
pulses, phases of which vary according to a given
law. The complex envelope of such PM signals is a
sequence of positive and negative pulses [3, 4].
Almost always is the same shape of pulses and in
mostcasesitisrectangular.Arectangularpulsewith
unitamplitudeand
durationwrittenas:
0
() 1pt ,at
0
0.t
(1)
Let the amplitude of the n‐th pulse in the video
PMsignalisequalto+1or‐1,whichcorrespondsto
theinitialphasesof0 or
inradioPMsignal.With
thisdefinitionthePMsignaliswrittenasfollows:
00
1
() [ ( 1) ].
N
n
n
St Sp t n
(2)
One of the important characteristics of the cross
ambiguity function (CAF) is the level of side lobes,
which in most cases are trying to reduce. Choice of
formofCAF,thatisactuallyaformofprobingsignal
depends primarily on the purpose of radar station,
interferenceenvironment,the
formandnatureofthe
objectives,parametersofmovement,etc.
In general, the expression for the CAF phase‐
manipulatedradiopulsecanbewritten:
0
2
*
0
1
(,) ,
N
j
nfT
sw n n k
n
fWSe
(3)
where
nk
j
nk
Se
thecomplexamplitudeofsignal;
*
n
n
We
thecomplexamplitudeoffilter;
The analysis of CAF phase‐manipulated signals
with different phase modulation law leads to the
conclusionthatthelevelofsidelobesofCAFofmany
peaks or many crest structure without the use of
special measures has significant value,
commensurable, sometimes, with a maximum
value
ofCAF.Applyingofweightprocessingwiththeuse
of quasi optimal weighting coefficients allows to
reduce the side lobes level between peaks, but
inevitablyistheexpansionofpeaks,this,initsturn,
affectstheperformanceofaccuracyandambiguityof
targetcoordinatesestimationandtheirreliability.
Substituting into
the expression (3)
0
1
,
4
f
NT
then the expression for the CAF phase‐manipulated
radiopulsecanbewritten:
n
2
*
4
0
1
(,) .
l
N
j
N
sw n n k
n
fWSe
(4)
Using formula (5) were calculated optimal filter
weightingcoefficients:
1
WRS
, (5)
where
R
‐thecorrelationmatrixofsimilartosignal
obstacle.
2 ITERATIONMETHOD
Theiterationprocedureofoptimizationofthesignal
and filter to find the maximum of signal/(noise +
interference)ratioattheirvariousdimensionsliesin
sequentialsolutionofintegralequationsforthefilter
and the signal at the fixed
norm of the signal and
filter[5].
Atthefirststep,foragiveninitialsignalvectoris
beingsolvedequation,determiningthefilterimpulse
response, then for the thus‐obtained filter is being
solvedequationdefiningthesignal,etc.
Thus, each value of the found filterorthe signal
passes
normalizationprocess.Themethodsofjoined
optimizationofthesignalandfilterwereconsidered
earlier,takinginto accountadditional restrictionson
the permanent resolution of time, the amount of
lossesinthesignal/noiseratioandmethodsofsignal
and filter optimization at a fixed amplitude signal
modulation. The research of
their efficiency is being
consideredinthispaper
Inthecalculationsweusedtheiterationprocedure
of maximizing the signal/noise ratio, taking into
account the restrictions on losses in the signal/noise
ratio and a constant resolution in time where the
signal/noiseratiowasconsideredas[6]:
2
*
22
0
()S(t)dt
,
() (,0) (,0)
sw
Wt
Wt dt d
(6)
where
0
1
2
*
0
(,f) (, )
N
infT
sw n n k
n
fWSe
ambiguity function,
0
T
elementary pulse duration
inthe signal,
f
Doppler`s frequency,N– number
of pulses in the signal,
0
NT
period of signal (in
periodic mode of work),
nk
i
nk nk
sse
nk
iφ
nk nk
SSe
the
complexamplitudeofsignal,delayedonkpositions,
nk
phase of signal,
*
n
w
complex amplitude of
bearing signal (filter),
0
the coefficient, which
describes reflected properties of interference
,
(,0)
‐ the range‐velocity distribution of
interfering reflections,e parameters that determine
therestrictionsonlossesofsignal/noiseratio(
)and
a constant restriction on time resolution (
).
Expressionofconstanttimeresolutionisasfollows[1,
3]:
543
2
2
*
22
*
()S(t )
(,0)
.
(0,0)
W()S(t)dt
sw
R
sw
Wt dtd
d
T
t
(7)
The constant time resolution
R
T has the best
value,whenallthesidelobesofthecross‐correlation
functionsarezero.Thesolutionoftaskwillbefound
for the values of parameters
0,
1.N
In fact,
we consider the problem of maximizing the
signal/noiseratio(thenoisewithspectraldensity
0
N
)
with restriction on constant time resolution. On the
firstiteration,wearelookingforafilterthatprovides
for the chosen parameters
и
3
0
10N
almost
completesuppressionofsidelobes.Thisisconnected
to the fact that the problem of digital signals
corresponds to suppress
1N
side lobes, which
corresponds to the condition of the zero zone [7].
Zoneswithcompletesuppressionofsidelobes.
Theexpressionoflossesinsignal/noiseratioisas
follows:
2
*
**
.
WS
WS
WS
(8)
Inthefirststepmaybealargelossesinthesignal/
noise ratio. Therefore, we shall use the procedure
abovetoselectthesignalsandfilters,whichallowto
obtainminimallossesinthesignal/noiseratio.
Programdevelopmentusingtheiterativemethod
In the Matlab
was developed a program that
allows to realize the iteration process of joint
optimizationoffilterandsignalandreceivegraphics
withCAF‐sections
0
4
l
f
NT
givenbelow(figures1‐7).
In this case, as the initial approximation we
consideredadiscretesignalsequencewithN=10with
thefollowingforms=[1;1;1;1;‐1;‐1;1;1;1;‐1],Inthe
resultoftheiterationprocesswereceivedacoupleof
signal and filter,
which ensures a constant value of
time resolution
1
R
T (it means complete
suppression of the side lobes in L=0) and
1,
which no lossesinsignal/noise ratio (figure 1б) and
correspondstotheagreedtreatment.
Figure1. The shape of CAF and her sections at l=0…9 of
periodicsignals=[1;1;1;1;‐1;‐1;1;1;1;‐1].Thevalueof
optimalfilter:Wn=[2.1943;0.4389;0.0878;0.7900;‐0.6145;‐
1.6676; 0.4389; 0.0878; 0.7900;‐0.6145] and optimal signal
Snorm = [1.0002; 1.0000; 0.9999;
1.0000;‐1.0000;‐1.0001;
1.0000; 0.9999; 1.0000;‐1.0000]. The value of losses in
signal/noiseratio
=0.5967.
Figure2. The shape of CAF and her sections at l=0…9 of
periodicsignals=[1;1;1;1;‐1;‐1;1;1;1;‐1].Thevalueof
optimal filter: Wn = [2.1938; 0.4395; 0.0883; 0.7907;‐
0.6150;‐1.6669; 0.4395; 0.0883; 0.7907;‐0.6150] andoptimal
signal Snorm = [1.0018; 0.9996; 0.9991;
1.0000;‐0.9998;‐
1.0012;0.9996;0.9991;1.0000;‐0.9998].Thevalueoflosses
insignal/noiseratio
=0.5980.
Figure4. The shape of CAF and her sections at l=0…9 of
periodicsignals=[1;1;1;1;‐1;‐1;1;1;1;‐1].Thevalueof
optimalfilter:Wn=[2.1431;0.4944;0.1388;0.8500;‐0.6620;‐
1.5995; 0.4944; 0.1388; 0.8500;‐0.6620] and optimal signal
Snorm = [1.1593; 0.9598; 0.9182;
1.0013;‐0.9799;‐1.0963;
544
0.9598; 0.9182; 1.0013;‐0.9799]. The value of losses in
signal/noiseratio
=0.6101.
Figure5. The shape of CAF and her sections at l=0…9 of
periodicsignals=[1;1;1;1;‐1;‐1;1;1;1;‐1].Thevalueof
optimalfilter:Wn=[2.1431;0.4944;0.1388;0.8500;‐0.6620;‐
1.5995; 0.4944; 0.1388; 0.8500;‐0.6620] and optimal signal
Snorm = [1.1593; 0.9598; 0.9182;
1.0013;‐0.9799;‐1.0963;
0.9598; 0.9182; 1.0013;‐0.9799]. The value of losses in
signal/noiseratio
=0.7126.
Figure6. The shape of CAF and her sections at l=0…9 of
periodicsignals=[1;1;1;1;‐1;‐1;1;1;1;‐1].Thevalueof
optimalfilter:Wn=[1.8697;0.6954;0.4119;0.9789;‐0.8035;‐
1.4108; 0.6954; 0.4119; 0.9789;‐0.8035] and optimal signal
Snorm = [1.6835; 0.7814; 0.5702;
0.9927;‐0.8681;‐1.3477;
0.7814; 0.5702;0.9927;‐0.8681].The value of losses in
signal/noiseratio
=0.9888.
Figure7. The shape of CAF and her sections at l=0…9 of
periodicsignals=[1;1;1;1;‐1;‐1;1;1;1;‐1].Thevalueof
optimalfilter:Wn=[1.8166;0.7225;0.4595;0.9854;‐0.8233;‐
1.3914; 0.7225; 0.4595; 0.9854;‐0.8233] and optimal signal
Snorm = [1.7456; 0.7548; 0.5198;
0.9898;‐0.8482;‐1.3690;
0.7548; 0.5198; 0.9898;‐0.8482]. The value of losses in
signal/noiseratio
=0.9984.
Furthermore,calculationswereperformedwithN
=3,8,9,12fortheperiodiccasewheresimilarresults
were obtained and also for aperiodic case. Using
obtained signals for different N (N1, N2,…Np) new
signalsmaybeconstructedwiththemethodbasedon
element‐wisemultiplicationofsignalswithmutually
prime
periods[7].Inparticularwecangetresultant
signal due to the product of two signals: N= N1N2
(for example N1=3, N2=4; N1=5, N2=4; N1=7, N2=9;
andothers).Alsocanbeusedproductsofthree,four
signalsandsoon.
Considered in this article method of signal‐filter
pair synthesis
can also be used for range‐velocity
distributions of the interfering reflections, which
contain a few cross ‐sections CAF with different
Dopplershifts.
3 CONCLUSIONS
Thesidelobesuppressionhelpstoreducethelevelof
harmfulradiation tothe surroundingspace. Alsoan
important part is to reduce the level of background
noise in the antenna, as it is created due to the
differencesoftheamplitudesandfrequenciesofside
lobesfromthemainlobe.
In this paper we considered the the task of
maximization of signal/noise ratio with additional
restrictions in it and restrictions on constant time
resolution. The results
of calculations confirmed the
effectiveness of the considered iteration procedure
allowingattheappropriatechoiceoftheinitialsignal
to get known globally optimal solutions. Therefore,
we will consider the tasks with the help of this
procedure to suppress of interfering reflections with
random range‐velocity distribution of preventing
reflections,the
bestsolutionsofwhichareunknown.
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