IMPROVING THE DETECTION OF THE SMALL, WEAK REFLECTIVE TARGETS ON THE BACKGROUND SURFACES USING POLARIZATION-DOPPLER METHOD Текст научной статьи по специальности «Медицинские технологии»

ТЕХНИЧЕСКИЕ НАУКИ

Pham Trong Hung

Ph-D, Military TechnicalAcademy,Vietnam

IMPROVING THE DETECTION OF THE SMALL, WEAK REFLECTIVE TARGETS ON THE BACKGROUND SURFACES USING POLARIZATION-DOPPLER METHOD

DOI: 10.31618/ESSA.2782-1994.2023.2.87.332 Abstract. The article focuses into the construction of the Polarization - Doppler response function of the radar target and performs a comparative evaluation of the energy efficiency when using the Polarization - Doppler response function compared to when using the conventional Doppler method. From this, a method is proposed to improve the detection of small, weak reflective targets on the background surface based on the Polarization -Doppler response function.

Keywords - Doppler radar, small-target detection on the sea, moving target detection, circular polarization.

THE PROBLEM

The problem of detecting moving targets on the background surface (ground, sea surface...) is usually done by Doppler processing. It is a classical method in radar signal processing, popular in many documents. However, when the target is small, the ability to detect these targets will be limited because the signal power reflected from the small moving target is not enough for detection. The polarization parameter treatment measures in the target detection problem on the background surface (especially small targets) give many good results, increasing the detection ability [1, 2]. In the process of calculating the polarization parameter function for the ground surface and the fluctuating target [3], it is found that: the polarization parameter of the target is no longer a constant quantity but also fluctuates with time. [4]. The cause of this fluctuation is the disturbance of the target (ground surface or target). Since the polarization ratio function [4, 5] in the circular polarization base is time dependent, it is possible to use the transformation of the polarization parameter function on the time domain to the frequency domain to exploit information about the degree of polarization Doppler frequency shift. The Doppler processing method then is the same as the usual Doppler processing methods, so it can be temporarily called the Polarization - Doppler method. This method can increase the ability to detect small

where & is the eigenvalue of the moving point target, h(t), h(t) is the eigenvalue of the fluctuations in the SM of the background surface; Qd is the Doppler frequency corresponding to the target's velocity V.

targets moving on the ground surface. The article will follow this research direction: fully exploit the target polarization parameter, combining the Doppler processing to increase the detection ability. Specifically, the study of energy efficiency when using the Polarization-Doppler method compared to the conventional Doppler method. Then performing the FFT transform of the Doppler polarization response function to see the difference in the energy spectral function of the mixed target (background surface + small target) in the case of non target and the case with moving target on the background surface. The structure of the article is as follows: Part II presents the calculation and construction of the Polarization-Doppler response function based on circular polarization. Part III is a comparison of the energy efficiency using conventional Doppler and Polarization-Doppler processing. Part IV is the conclusion.

BUILDING THE RESPONSE DOPPLER FUNCTION OF THE COMBINED RADAR TARGETS ON THE BASIS OF CIRCULAR POLARIZATION

Assuming a mixed radar target consists of a spread surface and a small target (point target). Each target is characterized by its own scattering matrix. In the circularly polarized basis, these scattering matrices (SM) have the form [1, 3]:

(1)

Assuming that the eigenvectors of these targets are the same. Then the SM of a mixed target in a circularly polarized base can be written as:

)- ФJ H&t) + Ф

j )+/&ощ - )- )щ

%)i; 1 \mt 2

Г- & J jf+ ^fc

J jj&+ & - jj&- ^

exp {j w/ }

i

2

u .J

(t J = IS» (t )|| + IS» (t J =

II lis N linen N llm?

= 1 &) - l&t) + (&- &xp {jWt} j {l&(t) + l&(t) + (&+ x»exp {jWt}} 2 j {l&(t) + l&(t) + (&+ X»exp {jWt}} - t) - l&(t) + (&- x»)exp {j Wt}}

(2)

When the transmitted wave is circularly polarized,

0

Er (t)

px

will be:

[3], the reflected signal from the mixed target

El (t) 0 _ 1

Er (t) = lr (tIs • th Er (t) 2 px

j {f»t) + &)!+ ^)- & yg §

kp {jWt}} \xp {W }}

(3)

The circular polarization ratio of the reflected wave from the mixed target has the form:

jH j(^)- &^ &tp{jWt})

s # ^t) + &&$xp {jWt}

(4)

We see that the above circular polarization ratio is the background surface and the small, weakly reflective the average sum of the two target components including spot target moving on the background surface:

P& (t ) =

j(

+ (t) + f + && (t)exp {jW })

+ &)g+ iX&+ &$xp {jW}

(5)

where & (t) = )- lf), P& (t) =

nen v ' iXt, . . iXts . 7 nen v '

& reflected from the background surface and the 2 6 corresponding target. According to [4] these

l&t) + l&t)" nen^ g&

+ ^ parameters are exactly equal to the complex is the ratio of the circular polarization of the wave polarization am^topy coefficient °f the target:

P& (t )= t& (t), P& (t ) =

nen ^ y nen v y ' mt v y

(6)

2

target to the RCS of the background surface. We can let a&t) = ¡^ - corresponds to the ratio rewrite expression (5) in the form:

of the radar cross section (RCS) of the small point

j(]&en (t) + &)exp {j Wt ] (t)) (7)

(t ) =

1 + a&t )exp {j Wt}

we write the denominator of expression (7) in the 1 + &)exp {jW} = 1 + && with

form:

a&= & )exp {j Wt}

With the condition |i&< 1, it can be:

N

Rr" 1

(1+ Z&-1 = e (- 1Y& = 1- z&+ Z&- Z& + ...+ (- 1)"Z&

n =0

Here, the solution of analytic expansion of the (i.e. in case the reflected signal from the background Polarization-Doppler response function of the mixed surface is larger than the reflected signal from the point

target (expression 5) is used for the condition |a&< 1 target of smaU size). Keeping only the first part of the

expanded expression we get:

if (t) = j(1 - z&pnn(t) + a&t)exp {jW(t)°= j § - &)exp {jWt Jj*(t) + &)exp {jWt }P&t(t)£

(8)

From this equation, it is possible to propose a method to detect targets with weak reflections on the background surface. Expanding expression (8) and removing the extra components, combining the

condition (6) obtains the Polarization-Doppler response function in the form of a narrow band stochastic process:

*)= KWp, - & (' m„ - «L «¡j

CO, ji + jjf ) + j a (t)£

For a target with a small size with weak reflectivity, then |a&<< 1 (the signal reflected from the target is much smaller than the signal reflected from the

ground surface). Small-sized targets often have a simple structure, so they can be considered as polar isotropic targets with zero polarization anisotropy (fmt = 0). Then we can reduce the expression (9) to:

*i(t)= M |«L (t)\cOS W + jm(t) + ja (t)j

That represents the change that the weak reflective target introduces into the signal reflected from the background surface. They are determined by the Doppler shift within the Polarization-Doppler response function of the mixed target and take the form of a random process. Thus, for a target with a small size, weak reflections moving on the ground surface cannot be detected by conventional Doppler methods, but the "polarization trace" of that target can be detected in the response function of Polarization - Doppler. When using the spectrum analysis both the energy function c(t) and the response function Polarization - Doppler S1(t) can see the difference in the energy spectrum of these functions. This will increase the efficiency in detecting small-sized moving targets with weak

reflections on the background surface compared to conventional Doppler method.

THE COMPARISON OF THE ENERGY EFFICIENCY OF POLARIZATION DOPPLER AND CONVENTIONAL DOPPLER PROCESSING Consider two signals:

Ul(t)= alcos(wlt + j j) va

U2 (t) = acos - W)t + j 21 are the signals

reflected from the ground surface and the moving radar target on the ground surface, where Qd is the Doppler frequency of the moving target. It is possible to approximate the total reflected signal by the expression:

U s(t ) = U(t ) + U 2(t ) »

- ^ n n

'a2 + al r 11 + , 1 2 , cosW/icos g^t + j (t

m

2

al + al

with the condition a2 << ai (i.e. the signal reflected from the target is many times smaller than the signal reflected from the ground surface in a radar cell).

Signal (11) is amplitude modulated. We can rewrite the expression in the form:

Us (t) = Um(1 + M cosWj)coswt + j (t

(12)

where the amplitude modulation factor M is calculated as:

M =

U - U

U + U

(13)

a 2 + al

mm 1 2

The average power of the signal (12) is:

P )= (p ) + ÎP ) + (P № — +

\ AM I \ w / J w -W/ \ w + W/ ¿j 2

U2 M2

(14)

From this expression it is possible to calculate the components (^ ± Wd ) compared to the power at the relative power ratio of the external frequency 1 d

main frequency component rai:

(Pw -W+ (pw1+W M2

K) ' ~

(15)

Substituting the expression (13) into (15) we get:

p =m 2 _ i if aa g _ i

2 2 a a2

1 K2

(16)

2 2 Ua2 + a\ & 2(a2 + a¡)2 2(1 + K2)

With K = — is the ratio of the radar cross *2

section (RCS) of the moving target to the RCS of the ground surface.

Combining expression (10) and expression (12), we can compare the ratio of signal reflected from small moving target to signal reflected from the ground surface when using conventional Doppler processing method (12) and Polarization - Doppler (6).

From Figure 1, it can be seen that the relative ratio of the reflected signal from the target to the reflected signal from the background surface has increased significantly when using the Polarization-Doppler method. Specifically, when the ratio of RCS of the target to the background is 0.1, the ratio of signal reflected from the target to the signal reflected from the background surface is 0.005 in the case of conventional Doppler and equal to 0.01 in the case of Polarization-Doppler processing. That is, the ratio of energy has increased 2 times (3dB). If the RCS of the target to the background is 0.15, the ratio of the relative power of the reflected signal from the target to the signal reflected from the background surface increases from

0.01 to 0.023, that is the ratio of energy has increased by 2.3 times (3,6dB).

Figure 2 is the spectrum of the conventional Doppler, for a small moving target, the reflected energy from the target is very small (a2/a1=0.001 - i.e. the signal reflected from the background surface compared to the signal reflected from a moving target is 1000 times), it is difficult to distinguish the target from the background surface. Figure 3 is the Polarization-Doppler processing method with a2/a1=0.001, here it is seen that: the spectral function at the Doppler frequency of the small target is clearly shown at the Doppler frequency. Figure 4 is the spectrum of the Polarization-Doppler function in the case of non moving target on the background surface (a2/a1=0) giving a zero spectral. The comparison between Figure 3 and Figure 4 immediately shows the difference when there is non moving target on the background surface and there is a moving target on the background surface in the Polarization-Doppler spectral function. This is the basis for the detection of small moving target on the ground surface when conventional Doppler method is ineffective. Thus, small moving targets on the surface of the background that would be difficult to detect by

2

conventional Doppler methods can be detected by Polarization-Doppler processing through the change of polarization traces of target within a radar cell.

0.09 0.08 0.07 -a 0.06

D

f 0.05

03 -Q

L

^ 0.04

CD

ro

0.03 0.02 0.01 0

Comparison of conventinal Doppler and Polarization Doppler

Polarization \ /

Doppler / /

*

—

/ /

/

..... Conventinal Doppler

0

0.3

0.05 0.1 0.15 0.2 0.25

RCS of target/RCS of background a2/a1

Figure 1. Comparison of the energy efficiency of conventional Doppler processing and Polarization-Doppler processing

2 1.8 1.6 1.4 1.2 1

0.8 0.6 0.4 0.2 0

Spectrum of Conventinal Doppler

- —

- —

— —

100

400

200 300

f(Hz)

Figure 2. Spectrum of the conventional Doppler function

200 300

f(Hz)

Figure 3. Polarization-Doppler spectral function

200 300

f<Hz}

Figure 4. Spectrum of the Polarization-Doppler function in the absence of a moving target

CONCLUSION

The article has proposed a new method in improving the ability to detect small, weak reflective, moving targets on the background surface. When using Doppler processing on the polarization response function of mixed targets (including small moving weak reflective targets and the background surface), it allows to increase the contrast of small moving targets compared to the surface background (increased power ratio compared to conventional Doppler processing, significantly improving detection of small targets moving on the background surface (with targets that

conventional Doppler processing cannot). In addition, the comparison results of the energy spectrum function also show that, when the background surface is stable (i.e, the polarization parameter of the background surface is constant, invariant over time) if there is a target. Small motions on that background surface will give clear results in the energy spectrum function of the polarization - Doppler response function.

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Targets, IEEE 1999 International Geoscience and Remote Sensing Symposium, vol II, pp 1387- 1389, Hamburg, Germany, 1999

[2]. Козлов А.И.,Татаринов В.Н.,Татаринов С.В.,Кривин Н.Н. "Поляризацион-ный след при рассеянии электромагнитных волн составными объектами" М.: Научный вестник МГТУ ГА, 2013 г., № 189. - С. 66 - 73.

[3]. Татаринов В.Н., Татаринов С.В., Лигтхарт Л.П. "Введение в современную теорию поляризации радиолокационных сигналов // Поляризация плоских ЭМВ и её преобразования". -

Томск: изд-во Томского государственного университета, 2006. -Т. 1.

[4]. Tatarinov V, Ligthart L P, Tatarinov S, "An Introduction to the Statistical Theory of Polarization Parameters of Fields Scattered by Complex Radar Objects", Proc. MIKON2000, vol 2, ISBN 83-30 906662 - 0-0, pp 351- 354, Wroclaw, Poland 2000.

[5]. Tatarinov V.N., Tatarinov S.N., Krivin N.N. "Innovations in radar technologies: Polarization invariant parameter utilization for the problem of radar object detection and mapping", IICST 2011, pp 62-68, Tomsk, Russia, 2011.