125
Due to the fact that the sensitivity to the Doppler
frequency shifts is an important indicator for
selectingsignalsformarineradarsitisofinterestto
considercontinuoussignalswithlowsensitivityto
the Doppler frequency shifts. Continuous signals
reducesignificantlythepeakpowerofradiationand
improveenvironmental
ecologyandelectromagnetic
compatibilitywithotherradioelectronicdevicesona
vessel.
One of the possible approaches to the choice of
such signals has been considered in [1]. Since the
search and rescue transponder (SART) has no
compression filter, for its work in the class of
continuous signals it is
required amplitude
modulation and peak factor other than one, in
particular, a class of binary signals has been
presentedin[2]andhastheform:
012 1
N
ssss s abb b
Onthebasisofthisstructureitwasbuiltaclassof
signals, which ensures to co‐operate CW radar and
SART.
For the work of marine radar the signals with
idealcorrelationpropertiesareofinterest.Thishelps
improve immunity of signals against interference
suchasclutter.
Therefore, within
the continuousdiscrete signals
with non‐uniform structure there were considered
signals with zero side lobe level of periodic
autocorrelationfunction(PAF)whicharedefinedas
follows[2]:
2
2
a
i
N
aae
,where
2N
(1)
1
b
i
bbe
Suchsignalshaveapeakfactor:
The Selection of Signals for Continuous Wave Radar
which Reduce the Sensitivity to Doppler Shift of
Frequencies
V.M.Koshevyy,I.V.Koshevyy&D.O.Dolzhenko
OdessaNationalMaritimeAcademy,Odessa,Ukraine
ABSTRACT:Thesignalswithidealcorrelation properties areofinterestforcontinuouswaveradar.Atthesame
timeit’simportanttoprovidelowsensitivitytoDopplershiftsoffrequencies.Therewereconsideredsignals
withspecialstructureduetoamplitudemodulationwhichprovidecapabilityofradarwork
withSearchand
RescueTransponder(SART).Becausetheamplitudemodulationhasadrawback–notefficientuseofsignal
energy,inaclassofproposedsignalstherewereconsideredsignalswithuniformamplitude.Themismatched
filteringmaybeusedbymeansspecial weightingfunctionsforobtainingthenecessarycorrelationproperties.
http://www.transnav.eu
the International Journal
on Marine Navigation
and Safety of Sea Transportation
Volume 10
Number 1
March 2016
DOI:10.12716/1001.10.01.14
126
2
2
max
2
2
1
0
(2)
(2)4(1)
n
N
n
n
S
NN
H
S
NN
N
(2)
In order to reduce the peak factor there was
proposed a method in [3, 4] based on the known
property of element‐wise multiplication of signals
with mutually prime periods[5]. This increases the
coherence of the resulting signal. In particular, an
examplewaspresented,wheretheresultantsignal
is
obtained due to the product of two signals (1) and
12
21 4 84; NNN the peak factor has a
value
17H
(accordingtotheleftpartof(2)).
a)
b)
c)
Figure1. Sections of AF of
signal
12
21484NNN:а)l=0;b)l=1;c)l=2.
Expression for the calculation of Periodic cross‐
ambiguityfunctionhastheform
2
1
*
4
0
,
nl
N
i
N
n
nk
n
kl ws e
, (3)
where
k is the discrete interval of time and l is
discrete of frequency with step
0
1
Δ;
4
f
NT
0
T
is elementary pulse duration;
n
w is the filter
coefficient.
Below in Fig. 1 plots of three sections of the
periodic ambiguityfunction (AF) of the signal with
12
21 4 84NNN
areshown.
a)
b)
c)
Figure2.SectionsofAFofsignal
:а)l=0;b)l=1;c)l=2.
127
As it can be seen from the figure, a periodic
autocorrelation function has ideal correlation
properties. But the product of two signals has a
drawback–notenoughdecreasingthevalueofpeak
factor
5.9H which leads to a noticeable
sensitivity to Doppler frequency shift, which is
undesirable. Therefore we consider the option, in
whichwecanfurtherreducethepeakfactor.To do
this, we can choose the smaller parts for
product
123
347 84NNNN . This will
decrease the peak factor (according to (2)) of the
signal to a value
7.4H . At the same time, it is
expectedtoreducethesidelobesofthecrosssections
ofAFwithaDopplerfrequencyshift.
а)
b)
c)
Figure3. Sections of AF of signal
1234
4 5 7 9 1260NNNNN :а) l=0; b)
l=1;c)l=2.
As it’s expected and seen in Fig. 2 above,
sensitivity to the Doppler frequency shift was
reduced.
The presented approach is effective and can be
used for obtaining signals with long periods.
Consider, for example, a signal in the form of a
product of four signals:
1234
4 5 7 9 1260 NNNNN
(AF is on
Figure3)andpeakfactorisequalto
5
H .
Itwas confirmedthat wehave receivedperiodic
signaloflongdurationwithasmallpeakfactorand
lowsensitivitytotheDopplerfrequencyshifts.
Thus, we can widely modify the peak factor of
signals (1), obtaining anideal correlation properties
in the AF zero section, and with an increase
in the
coherent part of the signal we can reduce the side
lobesofAF.
Furtherincreasingofsegmentsofresultingsignal
will lead to an increase in the peak factor. For the
individual modes of radar let’s consider the case
whenthepeakfactorisone:
1
H
.Inthiscase,the
formofthesignalisdeterminedaccordingto:
abb b ,where
1, 1ab
. (4)
Thus to provide ideal properties of periodic
autocorrelation function it can be used mismatched
processing that is development of an approach
described in [4]. The filter coefficients can be
calculatedaccordingtotheexpressionfound:
0
12 2
; 1
1
n
aa N a N
ww
a
(n=1
1N
). (5)
Arisingsomelossesinsignal‐to‐noiseratiocanbe
foundfromthefollowingexpression:
2
2
2
2
12 2 11
12 2 11 1
aaa N a N N a
aa N a N N a a N
(6)
If
2
2
N
a
, then there has no losses in
signal‐to‐noiseratio
1
.
If
1; a
thenthelossesinsignal‐to‐noiseratio
canbecalculatedfromtherelation:
2
2
42
31
N
NNN
(7)
Asanexamplethereisasignal(4)whenN=9,and
on the Figure 4 there is cross‐ ambiguity function
(CAF)ofit.
128
Figure4.CAFofsignal(2)N=9
а)
b)
c)
Figure5. Sections of AF of signal
1234
4579NNNNN: а)l=0;b)l=1;c)l=2
Here is an example where the resulting product
signal is composed of signals (4) with relatively
prime periods
1234
4 5 7 9 1260NNNNN
.
The value of the loss in signal‐to‐noise ratio for
the resulting signal will be a product of the values
of its component signals [6]:
1234
1 0.9 0.65 0.5 0.29
.
Across‐ambiguityfunctionofproductofthefour
signals
4579N
in the casewhen the signals
havetheform
1 1 1 1aa
isillustratedbelow
inFigure5.
On Fig.6 there is CAF of product of signals (4)
whenN=45.
0
10
20
30
40
50
1
2
3
4
5
0
0.2
0.4
0.6
0.8
1
k
l
X
Figure6.TheCAFofproductofsignals(4),N=45
However, increasing N increases the losses in
signal‐to‐noise ratio. Thus, when N> 11, the
effectiveness of such signals will fall, because of
significant losses in the signal‐to‐noise ratio. As
possible solutions is using the additional classes of
signals, including Barker codes. For example,
consider a signal
1234
45713NNNNN
whichincludesaBarkercode
4
13N .
The presence of positive side lobes of the
correlation function at the Barker code gives low
lossesinsignaltonoiseratio
0.96
[7].Resulting
=0,57.
BelowinFig.7CAFofsuchsignalispresented.
However, the continuous mode has some
difficulty in the practical implementation, since it
requires the availability of two antennas on the
vessel.
As a solution, we can use a quasi‐continuous
mode [8], when the entire signal is
superimposed
another signal with intervals of zeros. A
disadvantage of such signals is that they are not
suitableforallrangesofelements.
Anotherwayistouseperiodicsignalsofacertain
duration[1],buttheyhave adisadvantagewhichisa
significantside‐lobelevelofAFequal
1
N
.
129
а)
b)
c)
Figure7. Sections of MAF of signal
1234
45713NNNNNwithBarkercode:а)
l=0;б)l=1;в)l=2.
Thethirdapproachis thefollowing: toradiate a
certain signal in each period and due to
complementarity zero side lobes of resulting
aperiodiccross‐correlationfunctionwillbeprovided.
Thus, based on the considered signals there are
constructed composite signals of arbitrary length
with suitable correlation properties and different
peak
factors,andinparticularequaltounity.These
signalsprovidelowsensitivitytotheDopplershiftof
frequencies.
REFERENCES
[1]V. M. Koshevyy, D. O. Dolzhenko. The Selection of
Signals which Enable Continuous Wave Radar in
Conjunction with Existing SART [in Russian],
Navigation (Судовождение), Odessa: ONMA,№21,
2012,pp124‐129.
[2] V. M. Koshevyy, D. O. Dolzhenko. The Synthesis of
PeriodicSequenceswithGivenCorrelationProperties//
Proc. of
IEEE East–West Design & Test Symposium
(EWDTS’11), Sevastopol, Ukraine, September 9–12,
2011.–P.341–344.
[3]V.M.Koshevyy,D.O.Dolzhenko. SelectionofSignals
for Continuous Wave Radar [in Russian], Automation
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63‐73.
[4]V. M. Koshevyy, D.
O. Dolzhenko, The Signals of
Marine Continuous Radar for Operation with SART,
10thInternationalNavigationalSymposiumon”Marine
NavigationandSafetyofSeaTransportation”TRANS‐
NAV2013,Gdynia.
[5]R. C. Titsworth, Correlation properties of cyclic
sequences,Ph.D.Thesis,Calif.Inst.Tech.,1962.
[6]V. P. Ipatov, Periodic Discrete
Signals with Optimal
CorrelationProperties,RadioISvyaz,Moscow,1992.
[7]V. M. Koshevyy, A. O. Shapovalova,Optimization of
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