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Polarization Filtering Based Interference Suppressions for Cooperative Radar Sensor Network Bin Cao, Qin-Yu Zhang, Yan-Qun Zhang, Shou-Ming Wen, and Dong Liang Communication Engineering Research Center, Department of Electronics and Information Engineering, Shenzhen Graduate School, Harbin Institute of Technology, Shenzhen, Guangdong, P.R. China, 518055 Email: {caobin, zqy, zhangyanqun, wenshouming, liangdong} @hitszcerc.org

Abstract—The radar members are likely to interfere with each other if their waveforms and polarized states are not orthogonal in radar sensor network (RSN). In this paper, we propose the oblique projection polarization filtering (OPPF) based interference suppressions for RSN where each radar member is equipped with the orthogonally dual-polarized antenna (ODPA). In our discussed cooperative environment, under which radar members share their polarized states, members radiate EM waves using the same waveform but different polarized states, however, their polarized states are not needed to be orthogonal. Doppler-Shift and its uncertainty are not involved due to the independence from the polarized state, which makes the proposed method simple and effective. The results demonstrate that, after passing through the proposed OPPF scheme, each radar member can effectively suppress the echoes from the others while keep its own amplitude and phase unchanged, which improves the target detection performance of the RSN. Theoretical analysis is done, and the simulation results are illustrated, both showing the proposed method suitable for suppressing interferences for RSN.

towards the target simultaneously. Taking the ith radar member for an instance, it receives its own return (black color) scattered by the target, while it also receives other members’ returns, such as the 1st and the Nth members (blue and red colors) shown in Fig. 1. These signals are interferences for the ith radar member, and the interferences degrade the detection and cognition performance of the RSN. In order to suppress these interferences, much attention has been paid to the waveform design [3-6], [8]. If the waveform of each radar member is orthogonal, the interferences can be eliminated. Coding can also be used to suppress the interferences in the RSN, and some novel coding schemes were proposed [3], [8].

Radar N

I. I NTRODUCTION For the single radar system, its detection and recognition performance is limited by several issues, such as manmade and natural interferences, deceptive jamming, and stealth target. A slow fluctuations of target radar cross section (RCS) also results in radar target fades, and this is a main factor degrading the detection and recognition performance for single radar. Meanwhile, hidden targets, such as tactical weapons, aircraft, ships, spacecraft, vehicles, and people, are also challenges for the single radar system. The single radar system encountering above-mentioned problems boosts radar researchers and engineers to exploit the new schemes, therein, the radar sensor network (RSN) appears [2-8]. In the RSN, radar members are networked together in an ad-hoc fashion, and this makes the RSN not limited by any preexisting infrastructure [7]. The RSN holds lots of advantages over the single radar, since the radar members can send the information about the target to the central processor via wireless channel. Then the target information can be processed in the central processor by using the sensor data from each radar member in the RSN. In the RSN, the radar members are likely to interfere with each other if the waveforms are not orthogonally designed [36], [8]. Fig. 1 depicts the block diagram of the RSN. There are N members in the RSN and they are detecting an aircraft target. The N members are transmitting the detecting signals

T arget

Radar i Fig. 1.

Radar 1

Block diagram of the RSN detecting the target

In this paper, we perform some theoretical studies on the interference suppressions for RSN based on the application of polarization information. We discuss a cooperative RSN where each radar member is equipped with the orthogonally dualpolarized antenna (ODPA), and the radar members share their polarized states in the RSN. Based on these conditions, the extension result of the oblique projection polarization filtering (OPPF) previously proposed in [13-16], is introduced into the RSN for suppressing the interferences coming from other members. In the discussed RSN, radar members radiate EM waves using the same waveform but different polarized states, and their polarized states are not needed to be orthogonal. Theoretical analysis and the simulation results demonstrate that, after passing through the proposed OPPF scheme, each

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radar member can effectively suppress the echoes from other members while keep its own amplitude and phase unchanged, which improves the target detection performance of the RSN. The remainder of this paper is organized as follows. System model and fundamentals of the OPPF are introduced in Section II. The OPPF based interference suppressions for the cooperative RSN is discussed in Section III. Detailed analysis and simulation results are done and illustrated in Section IV. Finally, Section V concludes this paper. II. S YSTEM M ODEL AND THE O BLIQUE P ROJECTION P OLARIZATION F ILTERING A. System Model We assume that the RSN consists of N radar members together in a self-organizing fashion like shown in Fig. 1. Each radar member radiates EM waves in different polarized states, and when representing the completely polarized waves using Jones vector in a right-handed Cartesian coordinate system with the z coordinate representing the direction of propagation and the orthogonal basis defined by a pair of x and y representing the horizontal (H) and the vertical (V) components, ignoring the absolute phase of the horizontal ˆ si (t) of the component, the transmitted modulated waveform S ith radar member can be modeled as cos εsi SˆsiH (t) E E ˆ ˆ si (t) = = Ss (t) cos(ωt) S jδ si Tp SˆsiV (t) Tp sin εsi e (1) where 0 < t < Tp , and Tp is the time duration for radar pulses and each oscillator; Sˆs (t) is the constant amplitude E/Tp is a normalization factor to let pulse envelope; Tp ˆ { E/T (t) cos(ωt)}dt = 1, wherein, E is the energy S p s 0 of the waveform; ω is the center frequency, εsi and δsi are its polarization parameters with εsi denoting the polarized angle, and δsi the phase difference in polarized angle. The polarized state is determined by the amplitude and phase relationship between the two components received by the ODPA. Taking the polarization of the ith radar member as an instance, the polarized angle and the phase difference in polarized angle are calculated as εsi = arctan{

|SˆsiV (t)| } |SˆsiH (t)|

(2)

δsi = arg{SˆsiV (t)} − arg{SˆsiH (t)}

(3)

where arg{x} indicates the argument of vector x. As depicted in Fig. 1, a point moving target at an instant range is taken into our consideration. The two-way time delay for the ith radar member is denoted as τi . Due to the movement of the target, the absolute value of the Doppler-shift denoting as ωdi is introduced. Hence, the back-scattered radiation of the ith radar member from the target is written as cos εri E ˆ ˆ ri (t) = Sri (t) cos[(ω ±ωdi )(t−τi )] (4) S Tp sin εri ejδri

where Sˆri (t) is the amplitude of the return for the ith radar member; εri and δri are the polarization parameters of its return. If the target is a fluctuating one, the most popular and reasonable model for |Sˆri (t)| is the Swerling2 model, thus |Sˆri (t)| follows the Rayleigh distribution [1]. We can easily formulate (4) as ˆ ri (t) = Hθ S

(5)

where H = [cos εri , sin εri exp(jδri )]T denotes the polarization subspace ofthe signal, and the superscript T is the vector transpose. θ = E/Tp Sˆri (t) cos[(ω ± ωdi )(t − τi )]. Since all radar members are transmitting signals, the received signals of each radar member are mixed signals containing its own desired back-scattered signal and the scattered signals generated by others. Then the signals received by the ODPA of the ith radar member can be modeled as ri (t) =

N

ˆ rk (t) + ni (t) S

(6)

k=1

where ni (t) is the additive white Gaussian noise (AWGN) with mean value zero and variance σi2 . Rewrite (6) as the form of (5), we can get the representation as follows: ri (t) = Hθ +

N

Sk ζk + ni (t)

(7)

k=1,k=i

where Sk is the polarization of the kth member’s return received by the ith member, and ζk holds the similar form to θ while the specific parameters are different due to different propagation paths. The form of equation (7) indicates the linear subspace representation of the RSN. B. Oblique Projection Polarization Filtering The oblique projection operator along the subspace B onto the subspace A is defined as [17] † AH AH A AH B (8) EAB = [A 0] H B A BH B BH where the superscript symbols of † and H indicate the pseudoinverse and the Hermitian transpose of a matrix, respectively. The properties of the oblique projection operator EAB are as follows [17]: EAB A = A,

EAB B = 0

(9)

Polarization filtering (PF) is an effective method of interference suppressions for radar and wireless communication systems, and its development and applications can be found in [9-16]. Based on the previous theory of PF, we proposed the oblique projection polarization filtering (OPPF) scheme [13-16], and the proposed method is the extension to the conventional PF and the NPSPF. By introducing the oblique projection theory, the OPPF can cancel the interference effectively and keep amplitude and phase of the target unchanged. Once the polarized states of the target and the interference are different, the OPPF is valid.

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In order to suppress multi-interference by using the PF, the multi-notch logic product (MNLP) based PF have been proposed [11], [12]. The MNLP method processes the filtering in the frequency domain by setting up the N independent filters to cancel N interferences [12]. The complexity of the implementation of the MNLP based scheme is considerably high. And the OPPF proposed in [13-15] is a single interference suppression system due to the system model of the oblique projection. Since the polarization matrix of two signals is a 2-by-2 matrix, then for more signals the matrix is not a full column rank one. In this paper, we propose a single notch system that can suppress multi-interference. III. OPPF IN THE C OOPERATIVE S CENARIO We perform the analysis of the proposed scheme to suppress the interferences coming from other radar members. In order to make the deduction simple and clear, we assume that there are three radar members in the RSN. When there are more radars, the results can be extended straightforwardly. Firstly, for the received signal of the first radar member, we rearrange equation (7) as the form of matrix ⎡ ⎤ θ ⎢ ⎥ (10) r1 (t) = H, S1 , S2 ⎣ζ1 ⎦ + n1 (t) ζ2 where the polarization parameters for the desired radar member are εr , δr , and the polarization parameters for the interfering radar members are εr1 , δr1 and εr2 , δr2 , respectively. It is obviously that the size of matrix [H, S1 , S2 ]T is 2by-3. In order to meet the requirement of using the oblique projection, the matrix augmentation should be done. We adopt the polarization vector transformation (PVT) to generate new components that are independent with the original signals, then the system can be a full column rank matrix. We use the PVT to convert the received target signal to be a vertically polarized wave, and the PVT matrix can be obtained as M = ×

1 2

2

2

W=

W1 W2

V1 V= V2

(15)

where a1 = sin εr cos εr1 and a2 = sin εr cos εr2 . We can add the u(t) as the third component of the signal r1 (t) ˆr(t) = (16) u(t) Therefore, the system model can be constructed as ⎡ ⎤ cos εr1 , cos εr2 cos εr , ⎢ ⎥ Z = ⎣ sin εr ejδr , sin εr1 ejδr1 , sin εr2 ejδr2 ⎦ 0, sin εr cos εr1 , sin εr cos εr2 ⎡ ⎤ θ ⎢ ⎥ ˆr(t) = Z⎣ζ1 ⎦ ζ2

and

(17)

(18)

It can be verified that if these three radar members hold different polarized states, then the matrix Z is a full-rank one, i.e., rank(Z) = 3. We further define ˆ = [cos εr , sin εr exp(jδr ), 0]T H and

(19)

⎡

⎤ cos εr1 , cos εr2 ⎥ ˆ=⎢ S ⎣sin εr1 exp(jδr1 ), sin εr2 exp(jδr2 )⎦ sin εr cos εr1 , sin εr cos εr2

ˆ −1 H ˆ H Pˆ ⊥ ˆ ˆ H ˆ ⊥ H) EH ˆS ˆ = H(H PS S

(20)

(12)

Let W = H, and V = [0, exp(jδr )]T , i.e., V denotes the vertical polarization vector. It is easy to obtain that MH = V. Then after the transformation, the returned target signal of the 1st user is a vertically polarized wave. After the transformation by M, equation (10) is obtained as (13)

ˆ H ˆ −1 ˆ H

(21)

ˆ S S) S , and I is the unit matrix. It where PSˆ = I − S( ˆ ˆ ˆ is easy to verify that EH ˆS ˆ Hθ = Hθ and EH ˆS ˆ S = 0, which shows the interferences embedded in the received signal are suppressed totally while with the amplitude, the phase and the polarized state of the target signal unchanged. It can be found that the proposed method uses one filtering operator to suppress two interferences. If there are more interferences, the proposed scheme can be extended straightforwardly. Taking three interferences for an example, the original system is a 2-by-4 matrix, and we should add at least two new independent components and construct a 4-by-4 matrix. It can be implemented as follows: the first component can be chosen like the above analysis, for the ⊥

Mr1 (t) = Vθ + MS1 ζ1 + MS2 ζ2 + Mn1

u(t) = a1 ζ1 + a2 ζ2

(11)

W 1 V 2 − V 1 W 2 , V 1 W 1 + W2 V 2

where

where ap , bp , cp , and dp (p = 1, 2) are the parameters after transformation by M. If we select the real part of the transformation result in (14), and take the first array of the transformation result of the received signal, then it can be obtained as

According to the OPPF in [13], we can get the filtering operator of the OPPF as

2

(| W1 | + | W2 | )(| V1 | + | V2 | ) W1 V 1 + W2 V 2 , W 2 V 1 − V 2 W 1

We focus on the polarization changes of other two radar members. It can be achieved that a1 + b1 j a2 + b2 j MS2 = (14) MS1 = c1 + d1 j c2 + d2 j

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When adopting the MNLP based PF scheme to suppress multi-interference, the constraint is that all of the signals are assumed not overlapped in the frequency domain then the MNLP based PF can suppress the multi-interference, and this assumption is really unreasonable in practice. Meanwhile, it needs multiple filters to fulfil the goal of interference suppressions, which renders a considerably high complexity of implementation. It is evident that the Doppler-Shift and its uncertainty are independent from the polarization information, and this shows that after the processing of the OPPF, the information of the Doppler-Shift and its uncertainty are unchanged. Then we can process the signal in the Doppler domain or the distance domain after interference suppressions by using the OPPF. Moreover, after the operation by the OPPF, the target signal is still a polarized format, i.e., with its original polarization information, unlike the conventional PF and the NPSPF after which the output is a scalar. This shows we can still process the output of the OPPF in the polarization domain, for example, implementing another oblique projection polarization filtering processing. This shows that the OPPF based multi-interference suppressions uses one filtering operator, and this scheme is simpler than the waveform based system and the MNLP based PF. Since the polarization information remains the same after the OPPF, the polarization diversity can be used to further enhance the detection and cognition performance for RSN.

IV. D ETAILED A NALYSIS AND S IMULATION R ESULTS In this section, some simulation results by M atlab are given and analysis about these results are done to show the performance of interference suppressions when using the OPPF for RSN. 6 4 Amplitude /mV

second component, we can firstly convert one interference to be a vertically polarized wave, then do the same process as above mentioned. The basic principle of matrix augmentation is that the new components should be independent with the original ones, then the composite system can be a full column rank one.

2 0 −2 −4 −6 0

Received Signal Output of OPPF Output of NPSPF 0.2 0.4 0.6 0.8 Observation Window /second

1

Fig. 3. Filtering performance comparison when using the OPPF and the NPSPF for interference suppressions when both the signals are vertically polarization

Firstly, we compare the OPPF and the NPSPF. Fig. 3 shows the filtering performance comparison between the proposed OPPF and the NPSPF. The target signal is a linear frequency modulation (LFM) type with the amplitude 1.5mV. The interferences are two LFM signals with amplitudes 3mV and 2mV, and they overlap with the target in the frequency domain. We let both the target and the interferences be the vertical polarization. The signal-to-noise ratio (SNR) is 10dB. The black line is the received signal. The filtering result of the OPPF is illustrated in the form of the red line. It can be C o mb inatio n r i (t) Mi clearly seen that the interferences are suppressed effectively, O P P F Devic e O u tpu t and the original LFM type target signal appears after the Signal operation of the OPPF. The blue line is the filtering result ODP A SP S of the NPSPF, since both the target and the interferences EPS are vertically polarized, they are canceled simultaneously by the NPSPF. This simulation result shows that the application Fig. 2. Block diagram of the radar member scope of the proposed OPPF is wider than the NPSPF when introducing the PF into RSN for interference suppressions. The block diagram of the radar member is given in Fig. In order to fully validate the effectiveness of the OPPF for 2. The signal received by the ith radar member’s ODPA is RSN, we consider there are three radar members in the RSN. fed to the Transformer Mi and the Combination Device, and The polarized states are as follows: εr = 30o , εr1 = 45o , the parameters of Mi are selected from the Set of Polarized εr2 = 60o , δr = 0, δr1 = 45o , and δr2 = 70o . The expected States (SPS) which contains all radar members’ polarized returned signal without AWGN is shown in the subplot (a) states. Each radar member is equipped with the Estimator of of Fig. 4. The interferences coming from other two radar Polarized State (EPS). After transformation by Mi , the results members are simulated as follows: the first interference is one are fed to the Combination Device, and the Combination radar member’s scattered signals, and the second interference Device combines the true signals and the virtual signals as is the transmitted signal of the other radar member and this a new signal. Finally, the new signal is fed to the OPPF and transmitted signal is modulated with the Gaussian envelope, the OPPF suppresses other radar members’ signals. and the SNR is 5dB. Subplot (b) is the received signal of the

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V. C ONCLUSION

(a)

0 −10 −20 0

1

2

3

4

5

3

4

5

2 3 4 Observation Window / second

5

Power /dB

(b)

5 0 −5 −10 −15 0

1

2 (c)

−10 −20 0

1

In this paper, we analyze the interferences from radar members by exploring the polarization information of the electromagnetic (EM) waves. Then, we propose the oblique projection polarization filtering (OPPF) based scheme to suppress the interferences while keeping the amplitude and phase of its own return unchanged in RSN, even if the polarized states of the radar members are not orthogonal. Another advantage of this method is that the Doppler-shift and its uncertainty are independent of the polarization information, which contributes that the interferences can be suppressed without the utilization of the spatial, the temporal, the frequency, the time-delay and the Doppler-shift information. Theoretical analysis and simulation results show that the proposed scheme is a valid and simple implementation. ACKNOWLEDGMENT

Fig. 4. Performance of interferences suppressions when using the OPPF for RSN

This work was supported by the National Basic Research Program of China under Grant 2007CB310606. Special thanks also go to Dr. Hong-Yang Chen in the University of Tokyo for his useful suggestions and help to our work.

(a)

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R EFERENCES

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[1] Skolnik M., “Introduction to Radar Systems,”, 3rd ed, New York, McGraw Hill, 2001. [2] Lubczonek J., and Stateczny A., “Aspects of spatial planning of radar sensor network for inland waterways surveillance,” Pro. Radar Conference 2009, pp. 501-504, 2009. [3] Xu L., and Liang Q., “Radar sensor network using a new triphase coded waveform: theory and application,” Pro. ICC 2009, pp. 1-5, 2009. [4] Liang Q., “Radar sensor networks for automatic target recognition with delay-Doppler uncertainty,” Pro. MILCOM 2006, pp. 1-7, 2006. [5] Liang J., Liang Q., and Zhou Z., “Radar sensor network design and optimization for blind speed alleviation,” Pro. WCNC 2007, pp. 26432647, 2007. [6] Liang Q., “Waveform design and diversity in radar sensor networks: theoretical analysis and application to automatic target recognition, ” Pro. SECON 2006, pp. 684-689, 2006. [7] Pescosolido L., Barbarossa S., and Scutari G., “Radar sensor networks with distributed detection capabilities,” Pro. Radar Conference 2008, pp. 1-6, 2008. [8] Liang J., and Liang Q., “Orthogonal waveform design and performance analysis in radar sensor networks ,” Pro. MILCOM 2006, pp. 1-6, 2006. [9] Poelman A., “Virtual polarisation adaptation-a method of increasing the detection capability of a radar system through polarisation-vector processing,” Pro. IEE Pt. F, vol. 128, no. 5, pp. 261-270, 1981. [10] Giuli D., “Suboptimum adaptive polarisation cancellers for dualpolarisation radars,” Pro. IEE Pt. F, vol. 135, no. 1, pp. 60-62, 1988. [11] Poelman A., “Polarisation-vector translation in radar systems,” Pro. IEE Pt. F, vol. 130, no. 2, pp. 161-165, 1983. [12] Mao X., and Liu Y., “Null phase-shift polarization filtering for highfrequency radar,” IEEE Trans. on AES., vol. 43, no. 4, pp. 1397-1408, 2007. [13] Cao B., Liu A., Mao X., and Zhang Q., “An oblique projection polarization filter,” Pro. WiCOM 2008 Proceedings, pp. 1893-1896, 2008. [14] Zhang Q., Cao B., Wang J., et.al., “Polarization filtering technique based on oblique projections,” Science in China, Series F: Information Sciences, vol. 2010, no. 53, pp. 1056-1066, 2010. [15] Cao B., Zhang Q., Liang D., et.al., “Blind adaptive polarization filtering based on oblique projection,” Pro. ICC 2010, pp. 1-5, 2010. [16] Wang J., Zhang Q., and Cao B., “Multi-notch polarization filtering based on oblique projection,” Pro. GMC 2009, pp. 1-5, 2009. [17] Behrens R., and Scharf L., “Signal processing applications of oblique projection operators,” IEEE Trans. on Signal processing, vol. 42, no. 6, pp. 1413-1424, 1994.

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(b)

1 0 −1 0

0.5 (c)

0.5 0 −0.5 0

0.5 1 Observation Window /second

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Fig. 5. Performance of interferences suppressions when using the OPPF for RSN

radar member. After filtering by the OPPF, the returned signal suffering attenuation for the radar member is shown in the subplot (c) of Fig. 4. In Fig. 5, there are two radar members in the RSN, and the received signal for the desired radar member is shown in the subplot (b). The polarized states of the two radar members are allocated as follows: εr = εr1 = 90o , δr = 0, δr1 = 45o . It can be seen that the returned signals of the two radar members overlap in the pulse-width distance, and SNR is 10dB. After the processing by the OPPF, the returned signals for the desired radar member is shown in the subplot (c). In subplot (a), the expected returned signal without AWGN is plotted. It can be seen that the output of the OPPF contains no interfering components from the other radar member.

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