II. SIGNAL MODELS OF RADAR TARGET AND ACTIVE JAMMING

In a horizontal and vertical polarization coordinate system, electromagnetic wave signal transmitted by radar can be described as

(1) $${\bi e}_{\bi t}({\bi t}) = g\sqrt {\displaystyle{{P_t} \over {4\pi L_t}}} e^{j2\pi f_ct}s(t){\bi h}{\rm,}$$

where g is the gain of radar antenna, P _t is the peak power of transmitted signal, L _t is the comprehensive loss, f _c is the carrier frequency, s(t) is the modulation function of radar signal, and h  = [h _H  h _V ] is the polarization form of the antenna. For convenience of description, the transmitted signal can be simplified as

(2) $${\bi e}_{\bi t}({\bi t}) = gA_t{\bi h}{\rm,}$$

where $A_t = \sqrt {(P_t/4\pi L_t)} e^{j2\pi f_ct}s(t)$ .

So at the receiving port of radar antenna, the backscattering echo from a target can be described as

(3) $${\bi e}_{\bi i}({\bi t}) = \displaystyle{g \over {4\pi R^2}}A_t(t - \tau )e^{j2\pi f_d(t - \tau )}{\bi hS}{\rm.}$$

Here R represents the slant range between the radar and the target; f _d represents the Doppler frequency caused by target motion; τ = 2R/c represents the delay time of target echo, c represents the speed of light;

$${\bi S}\;{\rm =}\;\left[ {\matrix{ {S_{HH}} & {S_{HV}} \cr {S_{VH}} & {S_{VV}} \cr}} \right]$$

denotes the polarization scattering matrix (PSM) of the target.

While the signal from active jamming at the receiving port of radar antenna can be described as

(4) $${\bi e}_{\bi J}({\bi t}) = J(t){\bi h}_{\bi J}{\rm.}$$

where h _J  = [h _jH  h _jV ] denotes the polarization form of active jamming, which is usually circular polarization; J(t) is the modulation signal of active jamming.

As is mentioned above, the practical signal received by radar consists of that from the target and that from active jamming. It can be expressed as

(5) $$E_r(t) = \displaystyle{{k_{RF}g} \over {L_r}}\left[ {{\bi e}_{\bi i}({\bi t}) + {\bi e}_{\bi J}({\bi t})} \right]{\bi h}^{\bi T} + n(t){\rm,}$$

where k _RF represents the RF amplification coefficient of radar receiver, L _r is the loss of the receiver, and n(t) is the receiver noise that always obeys normal distribution.

III. CHARACTERISTIC OF DUAL-POLARIZATION RADAR

Formulated by Sinclair, PSM can absolutely denote the polarization characteristic of a target, which is able to be obtained by full polarization radar [Reference Lee and Pottier16]. It is defined as

(6) $${\bi S} = \left[ {\matrix{ {S_{HH}} & {S_{HV}} \cr {S_{VH}} & {S_{VV}} \cr}} \right] = e^{j\omega} \left[ {\matrix{ { \vert S_{HH} \vert} & { \vert S_{HV} \vert e^{j(\emptyset _{HV} - \omega )}} \cr { \vert S_{VH} \vert e^{j(\emptyset _{VH} - \omega )}} & { \vert S_{VV} \vert e^{j(\emptyset _{VV} - \omega )}} \cr}} \right]{\rm,}$$

where S _HV denotes the vertical polarization backscattering coefficient of the target irradiated by horizontal polarization wave, S _HH , S _VH , and S _VV are the same definition as S _HV , ω is the phase of S _HH , $\emptyset _{HV}$ , $\emptyset _{VH},$ and $\emptyset _{VV}$ are respective phases of S _HV , S _VH , and S _VV .

In practical engineering applications, dual-polarization radars are commonly used. They have the ability of single polarization transmission, but dual-polarization channels receiving simultaneously. Taking vertical polarization transmission for example, only half PSM of the target can be obtained, and it is simplified as

(7) $${\bi S} = [\matrix{ {S_{VH}} & {S_{VV}} \cr} ]{\rm.}$$

Here S _VV represents the co-polarized component that includes the same echo information as the conventional single polarization radar; S _VH represents the cross-polarized component, which denotes the converting polarization ability of the target and is the main polarization characteristic obtained by dual-polarization radars.

For typical radar targets, such as aircrafts, warships, tanks, buildings, and so on, the polarization form of their backscattering electromagnetic wave is greatly related to that of the incident electromagnetic wave. It means that the polarization form of their backscattering electromagnetic wave is mainly as the same as that of the incident electromagnetic wave. In other words, their co-polarized ability is much greater than the converting polarization ability. So the value of S _VV is much greater than S _VH , and that is to say |S _TVV | ≫ |S _TVH | [Reference Dai17]. Here S _TVV and S _TVH are respectively S _VV and S _VH of the targets.

For active jamming, it is usually of circular polarization. Thus, its polarization form can be expressed as h _J  = [j.sinwt coswt] or h _J  = [j.sinwt coswt], which respectively denote left- and right-hand circular polarizations. The powers received by vertical- and horizontal polarization antennas from active jamming with standard circular polarization are equal, but they are 3 dB lower than that received by the matching circular polarization antenna. If active jamming is considered as a special target, it is evidently |S _JVV | = |S _JVH |, and the difference between S _JVV and S _JVH is just the phase [Reference Dai, Wang and Li2]. Here S _JVV and S _JVH are respectively S _VV and S _VH of active jamming. Therefore, the method of polarization cancellation can be introduced to suppress active jamming. Note that the polarization form of active jamming in practical engineering is not usually a standard circle, so the axial ratio of the circle is just close to but not 1. That is to say, it is usually |S _JVV | ≈ |S _JVH | in practical engineering.

According to Section II, the signal models for dual-polarization radars should be developed as follows. When the radar is being interfered with by active jamming, the signal received by vertical polarization channel can be described as

(8) $$E_v(t) = \displaystyle{{k_{vRF}g_v} \over {L_{vr}}}\left[ {{\bi e}_{\bi i}({\bi t}) + {\bi e}_{\bi J}({\bi t})} \right]{\bi h}_{\bi v}^T + n_v(t){\rm,}$$

where k _vRF is the RF amplification coefficient of vertical polarization channel, g _v is the gain of vertical polarization antenna, L _vr is the receiver loss of vertical polarization channel, h _v is the polarization form of vertical polarization antenna, and n _v (t) is the noise of vertical polarization channel.

Substituting equations (3) and (4) into (8), equation (9) can be obtained.

(9) $$\eqalign{ E_v(t) &= \displaystyle{{k_{vRF}g_v} \over {L_{vr}}} \cr & \quad \left[ {\displaystyle{{g_v} \over {4\pi R^2}}A_t(t - \tau )e^{j2\pi f_d(t - \tau )}S_{TVV} + S_{JVV}J(t)} \right] \cr & \quad+ n_v(t).}$$

In the same way, the signal received by horizontal polarization channel can be expressed as

(10) $$\eqalign{ E_h(t) &= \displaystyle{{k_{hRF}g_h} \over {L_{hr}}} \cr & \quad \left[ {\displaystyle{{g_v} \over {4\pi R^2}}A_t(t - \tau )e^{j2\pi f_d\left( {t - \tau} \right)}S_{TVH} + S_{JVH}J(t)} \right] \cr & \quad + n_h(t),}$$

where k _hRF is the RF amplification coefficient of horizontal polarization channel, g _h is the gain of horizontal polarization antenna, L _hr is the receiver loss of horizontal polarization channel, and n _h (t) is the noise of horizontal polarization channel.

IV. ADAPTIVE POLARIZATION CANCELLATION OF ACTIVE JAMMING

A) Principle of adaptive polarization cancellation

From equations (9) and (10), the signals obtained by vertical- and horizontal channels differ in both amplitude and phase. To make the active jamming be completely cancelled, the amplitude and phase of active jamming signals obtained by the two channels should be made consistent. So the weight coefficient of polarization cancellation can be defined as

(11) $$\varphi = \displaystyle{{k_{vRF}g_vL_{hr}S_{JVV}} \over {k_{hRF}g_hL_{vr}S_{JVH}}} = \displaystyle{{k_{vRF}g_vL_{hr}} \over {k_{hRF}g_hL_{vr}}}\alpha e^{ - jw_{vh}}.$$

Here α = |S _JVV |/|S _JVH |, represents the axial ratio of circular polarization; w _vh is the phase difference between S _JVV and S _JVH .

Then, the polarization cancellation method can be described as

(12) $$z(t) = E_v(t) - \varphi E_h(t).$$

Substituting equations (9) and (10) into (12), It can be developed as

(13) $$\eqalign{z(t) = & \displaystyle{{k_{vRF}g_v^2} \over {4\pi R^2L_{vr}}}A_t(t - \tau )e^{j2\pi f_d(t - \tau )}[S_{TVV} - S_{TVH}\alpha e^{ - jw_{vh}}] \cr & + \left[ {n_v(t) - \displaystyle{{k_{vRF}g_vL_{hr}} \over {k_{hRF}g_hL_{vr}}}n_h(t)\alpha e^{ - jw_{vh}}} \right].}$$

From equation (13), active jamming can be completely eliminated in theory, but the signal power received from the target is changed. It will reduce the angle-measuring accuracy of monopulse radars with sum and difference patterns of amplitude, because the method of monopulse angle measurement is sensitive for the amplitude of the target signal [Reference Barton18, Reference Skolnik19].

In practical engineering, both amplitude difference and phase difference between vertical and horizontal channels of the dual-polarization radar caused by the hardware system can be adjusted easily as was described in prior publications [Reference Gu, Liang and Yu20, Reference Jeffrey21]. So the weight coefficient of polarization cancellation can be simplified as

(14) $$\varphi = \displaystyle{{E_{Jv}(t)} \over {E_{Jh}(t)}} = pe^{ - jw_{vh}},$$

where E _Jv (t) represents the signal of active jamming obtained by vertical channel, E _Jh (t) represents that obtained by horizontal channel, and

$$p = \displaystyle{{k_{vRF}g_vL_{hr} \vert S_{JVV} \vert} \over {k_{hRF}g_hL_{vr} \vert S_{JVH} \vert}} $$

represents the amplitude ratio of the signals obtained by the two orthogonal polarization channels. When the dual-polarization radar does not emit electromagnetic wave, its received signal must be only from active jamming. So E _Jv (t) and E _Jh (t) can be easily obtained.

In equation (12), E _h (t) = E _Jh (t) + E _Th (t), where E _Th (t) is the horizontal component of the target echo, thus it is regarded as jamming signal and eliminated in error. To improve angle-measuring accuracy, the target signal power after polarization cancellation should be adjusted as

(15) $$z(t) = E_v(t) - \varphi E_h(t) + \varphi (E_h(t) - E_{Jh}(t)) = E_v(t) - E_{Jv}(t).$$

For monopulse radars, equation (15) must be used in both sum signal and difference signal simultaneously. Eliminating most active jamming signal and adjusting the power change introduced by polarization cancellation, the method will greatly improve the angle-measuring accuracy. But E _v (t) and E _Jv (t) are not obtained at the same time, so it may introduce extra phase difference and the target signal after it cannot retain coherent perfectly.

Therefore, equations (12) and (13) should be chosen to counter active jamming when the radar needs coherent integration. Because the same value of φ is used in the whole integration period, the phase of target signal will keep consistent and the polarization cancellation method will not reduce the gain of coherent integration. In addition, the co-polarized component is much greater than the cross-polarized component for typical radar targets and the axial ratio of active jamming is usually close to 1, so the signal power after polarization cancellation received from the target is just made a little change. It has little influence for subsequent signal processing besides monopulse angle measurement.

The proposed method above needs not any parameters of active jamming in prior, and can adaptively obtain the weight coefficient of polarization cancellation in time. Then, it adaptively does different cancellation processing according to requirements, equation (12) for coherent integration and equation (15) for monopulse angle measurement.

B) Influence factors of polarization cancellation

According to equation (12), the weight coefficient φ is unquestionably a key factor related to the efficiency of polarization cancellation. In the process of adaptive polarization cancellation, φ is obtained from the actual environment in real time, then it will be used for the following echo pulses. So there are some errors between the obtained φ and the real φ of every pulse, certainly the loss of polarization cancellation will be introduced.

In this paper, the gain of signal-to-interference-and-noise ratio (G _SINR ) is defined as the improvement factor to evaluate the efficiency of polarization cancellation. It is expressed as

(16) $$G_{SINR} = SINR_{out} - SINR_{in},$$

where SINR _in represents signal-to-interference-and-noise ratio (SINR) of input signal, and SINR _out represents SINR of output signal. In addition, SINR is defined as

(17) $$SINR = 10\;{\rm log}\displaystyle{{P_S} \over {P_I + P_N}},$$

where P _S represents the power of the target signal, P _I represents that of interference, and P _N represents that of noise.

When SINRs of two input signals are −7 and −3 dB, their three-dimensional diagrams of G _SINR after polarization cancellation with the change of amplitude and phase errors of φ are respectively shown in Figs 1 and 2. Here, the x-axis denotes the amplitude error Δp, the y-axis denotes the phase error Δw _vh , and the z-axis denotes G _SINR . It is evidently that G _SINR is extremely sensitive to Δp and decays rapidly with the increase of Δp, but not sensitive to Δw _vh .

Fig. 1. G _SINR with the change of amplitude and phase errors of φ, when SINR = −7 dB.

Fig. 2. G _SINR with the change of amplitude and phase errors of φ, when SINR = −3 dB.

On the other hand, noise and interference are surely influence factors of polarization cancellation. Thus, the influence of SINR is also analyzed in Fig. 3, where the x-axis represents SINR of the input signal, and the y-axis represents G _SINR . The diagram shows that G _SINR increases with the increase of SINR, and G _SINR reaches the peak when SINR is approximately 10 dB, then decays slowly. Note that SINR most depends on the radar system and the practical scene, so it is difficult to be improved.

Fig. 3. G _SINR with the change of SINR.

In the two simulations, the radar signal is linear frequency modulation signal, and the ratio of co-polarized-to-cross-polarized component of the target signal is 6. According to the analysis above, it is obviously that the amplitude value of φ is the most sensitive factor, so ensuring real time update of φ and reducing its error is very important in the process of polarization cancellation.

V. EXPERIMENTAL RESULTS AND ANALYSIS

In order to prove the effectiveness of the proposed method for countering active jamming, real experimental data obtained by the dual-polarization radar in millimeter wave band is analyzed. In the experiment, an angle reflector is used as the target, and it is approximately 1000 range units far from the radar, then an active blanket jammer and an active deception jammer are respectively used to emit interference signal at the radar.

Their results after the proposed adaptive polarization cancellation for active blanket jamming are shown in Figs 4–6. In which, Fig. 4 is the one-dimensional range profile obtained by vertical polarization transmission and vertical polarization receiving (VV) channel of the dual-polarization radar, Fig. 5 is that obtained by vertical polarization transmission and horizontal polarization receiving (VH) channel, and Fig. 6 is the result after polarization cancellation. From them, the target has been completely drowned by interference signal in the VV channel, but the interference signal is perfectly eliminated and the target is effectively retained after polarization cancellation. Figures 7–9 are the same meaning as above for active deception jamming. Although they are difficult to distinguish from the real target in the VV channel, the deception decoys are also completely eliminated with the retaining of the real target after polarization cancellation.

Fig. 4. Range profile of the VV channel for active blanket jamming.

Fig. 5. Range profile of the VH channel for active blanket jamming.

Fig. 6. Polarization cancellation result for active blanket jamming.

Fig. 7. Range profile of the VV channel for active deception jamming.

Fig. 8. Range profile of the VH channel for active deception jamming.

Fig. 9. Polarization cancellation result for active deception jamming.

In addition, the comparison of monopulse angle measuring value is given in Table 1. In the experiment, the target and the active deception jammer are located at the same azimuthal direction of −0.5° off the boresight of the radar, while the active blanket jammer is nearly located at 1.5°. Making the angle estimation value acquired by the monopulse method without jamming as the standard value of the real target angle, it is obviously that the method proposed in this paper for countering active jamming can improve the angle-measuring accuracy greatly; and the result is also much better than the method in [Reference Varga and DeWolf15].

Table 1. Comparison of monopulse angle measuring value.

It is important to note that, the projection effect of geometry on the polarization vector is neglected in this paper, but the experimental results show that the proposed method is also quite meaningful.

VI. CONCLUSION

In this paper, a countering method for active jamming is proposed based on dual-polarization radar seeker. Both active blanket jamming and active deception jamming can be eliminated perfectly, and the angle-measuring accuracy of monopulse radars is also improved greatly. Since it needs not any other hardware source more, the proposed method is in the vantage of size and complexity, which is significant for guidance radars. In addition, it can be realized before pulse compression, and does not affect the subsequent signal processing, such as coherent integration and imaging, so it is of a high value for engineering applications.