Bistatic radar with the separate transmitter and receiver has some attractive merits, thus obtaining many attentions. However, in a traditional bistatic radar system, there are still many problems that hinder it from practical applications. Here we introduce a bistatic radar scheme using a well-designed optical chaos system, from which the analog chaos signal could be determined by generated random binary sequence. The broad bandwidth analog signal is used as surveillance signal and the digital signal are transmitted to the receiver by optical fibers. Finally, high spatial and velocity resolutions of radar system could be obtained by using the analog chaos signal. A high-quality regeneration of the reference signal at different locations can be established by transmitting the digital sequence. Moreover, the mutual interferences could be concealed since the analog surveillance signal and the transmitted digital sequence are delivered by different paths. These could be advantageous for radar applications.
© 2018 Optical Society of America under the terms of the OSA Open Access Publishing Agreement
Bistatic radar with separated transmitter and receiver gains considerable concern in recent years [1–4]. This flexible physical configuration makes it superior in dealing with jamming and electronic counter-countermeasures (ECCM) compared with monostatic radar. However, there are still some problems that restrict its performance and practical application. In traditional bistatic radar systems, a replica of the transmitted signal is required as the reference signal in the receiver, which is obtained using a pair of reference antennas through the direct-path between the transmitter and receiver. Howbeit, a wireless channel could be degraded heavily by obstacles and environmental conditions . Hence, it is difficult to obtain the reference signal with a high signal-to-noise ratio (SNR) in the receiver which is necessary for acquiring a high cross-correlation value between the reference signal and the echo signal. Another severe problem comes from mutual interferences [6,7]. Since the reference signal is a delay version of surveillance signal, they could interfere mutually when transmitted through the same channel. The reference signal, through the direct-path or multi-path transmission, could be detected by the side lobe of surveillance receiver antenna, which is considered as the clutters for the target echo waveform. This phenomenon could cause a significant influence on the radar detection because the power of the direct signal is far larger than echo signal. To tackle with the problem, many algorithms are proposed to conceal the interference from reference signal [6–8]. However, none of them could conceal the interference entirely but would largely increase calculation complexity of the receiver.
On the other hand, using noise as the transmitted signal has been proved to be a suitable choice for radar [9–11]. Owning broadband and random properties of noise signals, this kind of radar could have many valuable advantages, such as high range resolution, unambiguous estimation of range, high immunity to channel noise, low probability of intercept, and ideal ‘thumbtack’ ambiguity function (AMF). Chaos systems, generating stochastic waveforms in the time domain, have been a popular method to obtain noise-like signals [12–14]. With broad and flat spectrum, excellent correlation properties and sensitivity to system parameters, chaos signal could match the requirements of radar system well. Meanwhile, under the requirement of higher characteristics of spatial and velocity resolutions, traditional RF generation methods of radar systems have faced a great challenge. Recently, numerous efforts have been devoted to the implementation of radar system on basis of photonic way because of the ultra-wide bandwidth of optical devices [15–20]. By means of optical generation method, chaos system can maximum its broadband property. Indeed, optical chaos system has been used in various radar applications Monostatic and multi-input-multi-output radar based on optical chaos systems have been discussed widely [21–29]. Beside the optical sources, optical fiber line is also a promising choice for bistatic radars, owning the stable channel characteristic, low attenuation and precise delay-management properties. The off-the-shelf optical communication network could be utilized to transmit the reference signal [27,28].
In this paper, we propose a novel optical chaos system which contains an analog-digital hybrid feedback loop. Both analog chaos signal and random binary digital sequence can be generated simultaneously. Beside the common properties, the generated analog chaos signal could be directly determined by the corresponding digital sequence. This extra characteristic makes it propitious to be applied in the bistatic radar system. Compared with the typical system, the digital sequence could be used as the reference signal instead of delivering a replicate analog signal directly. Digital signal is more robust to channel noise and easy to control, reconstruct, and reshape. The analog signal can be easily regenerated by using the digital sequence at the receiver. A high correlation value between the transmitted analog signal and the regenerated analog signal could be acquired both in simulation and experiment. It means a high quality of reference signal can be guaranteed at different locations. Thus, the SNR of the reference signal can get improved, which could be helpful in the detection of targets. Simultaneously, as the reference signal is transmitted through an optical fiber, the mutual interference could be concealed entirely. Benefiting from the optical channel, in the receiver, the SNR of the reference signal and surveillance signal could be enhanced further.
2. Analog-digital hybrid chaos system
2.1 The structure of chaos system
The scheme of chaos system is sketched in Fig. 1. As shown in the diagram, the system consists of four parts: shift registers (SR), phase-to-intensity conversion module (PICM), the nonlinear transformation module (NLTM) and the sampling-quantification module (SQM). SR module outputs electric on-off keying signal to drive the PICM.
The generated electric signal s(t) is carried in the phase dimension of an optical continuous-wave emitted from a laser diode (LD) by using a phase modulator (PM). The obtained optical signal E(t) could expressed by
Then a dispersion media is used to perform the phase modulation to intensity modulation conversion of the phase-modulated carrier. In the simulation, the function of the dispersion media is realized by a fiber Bragg grating (FBG). Due to the different conversion efficiency at different frequencies , the PICM could be considered as a generalized microwave photonics filter, thus the dichotomous sequence could be transformed to continuous analog signal. The transfer function of FBG in frequency domain is given as
It seems that the PICM implement the intensity modulation of signal, so could it be replaced by a simple intensity modulator (IM)? In fact, by inducing the phase modulation to intensity modulation conversion mechanism, the binary OOK signal turns out to be noise-like in the temporal waveform . If the PICM is substituted by an IM, the output will still be an OOK signal, whose state distribution mainly focuses on the level ‘1’ and ‘0’. Under the close-loop configuration, the dynamical system will enter the fixed point state according to our simulation, and chaotic output cannot be observed. Therefore, it might be unfit for this system to use only an IM to replace the PICM. An IM and an optical filter could be a feasible choice. Howbeit, its realization is too complicated as demonstrated in .
After being reflected from the dispersion media, the output optical field can be written as E1 = E(t)◦h(t), where “◦” denotes the convolution operation and h(t) corresponds to the time-domain expression of H(ω). The obtained intensity signal is then post-processed by the NLTM. The NLTM is made up of two photo-detectors (PD), a radio frequency amplifier (RFA), an IM, an optical coupler (OC) and a LD. The generated chaos signal could be described by33]. After the nonlinear transformation induced by the NLTM, the spectrum of the input signal could be flattened . Sequentially, the signal is delivered to the SQM. In this module, the signal is quantized by an 8-bit analog-digital converter (ADC). Finally, the least-significant bit of quantized signal is extracted and fed back into the SR to close the loop, where the SR performs the function of digital time delay. These processes could be depicted by following equations:
The whole system could be divided into two parts: the analog part and digital part. The analog part consists of PICM and NLTM and the digital part is constituted by the SR and SQM. The digital signal is generated from the analog part, meanwhile, the analog signal originating from the digital part. The function of digital part could be easily executed and set by field programmable gate array. As the calculation complexity is low as that of shift-register, a high output rate of field programmable gate array could be achievable. Here the length of SR is selected as 30 and the time of unit shift-register is 0.1ns. By virtue of advantages of the analog and digital subsystems [31,32], a broadband and robust chaos signal could be acquired.
2.2 Properties of the generated chaos signal
The theoretical model of this chaos system is investigated by means of simulation software MATLAB 2013a and VPItransmission 9.0. The simulation step is set as 1/(160e9) s. Figures 2(a) and 2(b) show the temporal waveform and spectrum of the generated chaos signal. The signal turns to be chaotic in temporal domain and a non-periodic waveform could be obtained, which can help suppress the range ambiguity and reduce the probability of intercept and interference of radar systems . A flat spectrum of the generated chaos signal is displayed in Fig. 2(b). A peak located at 10GHz could be observed in the spectrum, which corresponds to the clock frequency of the OOK signal generated by SR. The corresponding effective bandwidth measures 12.4GHz, where the effective bandwidth is defined as the frequency including the range between DC to the frequency that contains 80% of the whole spectrum power . In this hybrid system, the generated analog chaos signal could be fully determined by the digital sequence, since the transformation between sn and x(t) is deterministic. An identical analog signal could be recovered at a different place by transmitting the corresponding digital sequence. The cross-correlation function between the digital and analog signals is displayed in Fig. 3. The maximum value of their cross-correlation coefficient is only 0.14, which indicates a very low correlation relationship between the digital sequence and the analog chaos signal. It could have the potential to help reduce the mutual interferences of the direct-path signal and the transmitted signal when they are transmitted through the same transmission path.
The characteristic of a radar system is usually evaluated by the AMF. As for the broadband noise signal, the AMF could be expressed by :
The 2-D AMF of the generated chaos signal is calculated and displayed in Fig. 4. In order to reduce the computational complexity, the generated chaos signal is resampled at the rate of 10GHz. The integral interval is adopted as 8ms. As can be seen, there is only a main peak appearing at the center of AMF, which is close to an ideal thumbtack shape. This indicates the generated chaos signal is endowed with an excellent ability in the unambiguous detection. Figures 5(a) and 5(b) show the one dimension curves of the AMF at “zero-doppler cut” and “zero-delay cut”. As depicted in the figures, the full-width at half maximum of the peaks corresponding to the delay and delay rate axes are about 0.2ns and 5e-8 respectively. An equivalent range and range rate resolution could be calculated as 3 cm and 7.5 m/s. The range rate resolution could be further improved by lengthening the integral time T. Hence, high spatial and velocity resolutions could be brought by the chaos system when applied in radar applications.
Another major concern in radar systems is ECCM. Chaos signal usually owns an excellent correlation property, thus being considered as a promising choice. In order to inspect the ECCM capability of the proposed chaotic system, the cross-ambiguity function (CMF) is performed by correlating two chaos signals shown in Fig. 2(a), which are generated at different times. As shown in Fig. 6, there is no distinguishable peak appearing at the surface of 2-D AMF, indicating the non-repetitive characteristic of generated chaos signal. Moreover, the CMF of chaos signals is plotted in Fig. 7, when the initial values of SR are of a little difference, designated as “010110001110100100110101100100” and “110110001110100100110101100100” respectively. As can be seen, no distinguishable ripple is observed in Fig. 7. In other words, uncorrelated chaos signals could be easily obtained by changing the initial values of SR. In view of the characteristics discussed above, the proposed chaos system could be a good candidate in radar applications.
2.3 Experiment results of the chaos system
Here, an experiment of the proposed chaos system is conducted to verify its properties further. The experiment system is constructed according to the simulation setup shown in Fig. 1. A tunable laser with four-channel outputs (CoBriteDX4) is used to perform the functions of LD1 and LD2. The LD1 emits an optical continuous wave with the average power of 13dBm and center wavelength of 1550.14nm. Then the optical carrier is sent to a PM (KG-PM-15-10G-PP-FA-FA) and a dispersion media which is performed by a segment of DCF. The half-wave voltage of the PM is 4.5V and the accumulate dispersion value of the DCF is 800ps/nm. After the dispersion induced PM-to-IM conversion, the obtained optical signal is processed by the NLTM, which consists of a PD1 (PT10GCB), a RFA2 (OA4MVM3), a LD2 (CoBriteDX4), an IM (JDSU-X5), and a PD2 (PT10GCB). The responsivity of PD is 750V/W and the 3dB bandwidth is 16GHz. The half-wave voltage of IM is about 5V. The small signal gain of RFA2 is 29dB, where the saturated output voltage is 7.5V. Then the output of PD2 is sampled and quantized by an ADC acquisition board (EV10AQ190). The digital signal is then sent to a FPGA (XC7K325T-2FFG900C) to perform the SR function, where the length of SR is set as 30 and the time of unit shift-register is 0.1ns. It is worth noting that the applicable sample rate of the ADC is only 2.5GHz. Therefore, a parallel-to-series transformation is needed in the FPGA. After performing the parallel-to-series transformation, four lower significant bits of the ADC could be used as the feedback bit of system, replacing the least significant bit selected in the simulation. As a result, 10GHz outputs of binary sequences could be obtained in FPGA. Finally, the output of FPGA is amplified by a RFA1 (OA4SMM5) and used to drive the PM to complete the system feedback. The generated analog signal is captured and stored by the PD3 (PT10GCB) and a 100GSa/s digital sampling oscilloscope (DSO, DSA72504D), respectively. Although the obtained experiment result may have a little difference with the simulation result because of the change in the signal sampling process, the main conclusions in this paper still could be maintained.
The obtained chaos signal waveform is shown in Fig. 8(a), where the input optical power of PD2 is −4dBm. A non-periodic stochastic waveform could be acquired in Fig. 8(a). Figure 8(b) shows the flat spectrum of generated chaos signal. Its effective bandwidth is 8.75 GHz. A high spatial resolution could be brought by the broadband properties of chaos signal when applied in radar systems.
The 2-D AMF of the generated chaos signal is also evaluated and displayed in Fig. 9. The generated chaos signal is resampled at the rate of 10GHz to reduce the computational complexity. The integral interval is adopted as 1.5 ms, which is limited by the data record length of the DSO. As depicted in Fig. 9, only a main peak appears at the center of AMF. The one dimension curves of the AMF at “zero-doppler cut” and “zero-delay cut” are shown in Figs. 10(a) and 10(b). The full-width at half maximum of the peaks corresponding to the delay and delay rate axes are calculated as 0.2ns and 2e-7 respectively. Thus, an equivalent range resolution of 3 cm and range rate resolution of 60 m/s could be obtained. The range rate resolution could be improved further by increasing the correlation interval.
The ECCM capability of the chaos system is assessed by the CMF. Figures 11(a) and 11(b) show the CMFs of the chaos signals generated at different times and generated with different initial values of SR, which are experimental results corresponding to Figs. 6 and 7. The generated chaos signal owns good correlation properties. As discussed above, experiment results agree with simulation results well, which can verify the feasibility of the hybrid chaos system. With these mentioned advantages, the chaos system could be a good choice of the surveillance signal generator in radar systems.
3. Bistatic radar system
3.1 Typical bistatic radar system
In a typical bistatic radar system, a reference antenna and a surveillance antenna are in need to transmit reference signal and surveillance signal. The prior is aimed at the surveillance area for searching the targets and the latter is directed to the corresponding receiver antenna to build a direct path channel for the reference signal. The schematic diagram is demonstrated in Fig. 12. As for the transmitted chaos signal, considering the multi-path and direct-path interference of reference signal, the following equation is usually adopted to express the received echo signal by many literatures [6–8]:
The first term represents the direct-path interference received by the side lobe of surveillance antenna. d(t) is the complex envelope of the direct-path signal, and β0 is the complex amplitude. The second term is the multi-path interference of reference signal reflected from obstacles or ground, βi and τi represent the complex amplitude of the ith target (i = 1, 2...) and the corresponding time delay (with respect to the direct signal). The third term denotes the echo signal from static targets, μj and τj represent the complex amplitude of the jth target (j = 1, 2…). The fourth term describes the reflected signal from moving targets. γm, τm, and fdm are the complex amplitude, time delay (with respect to the direct signal) and the Doppler frequency of the mth target (m = 1, 2…) respectively. When using broadband signal as the surveillance signal, the echo signal reflected from the moving target often contains both a time delay and “Doppler stretch” compared with the original signal [36–38]. α denotes the time scale factor induced by the “Doppler stretch”, which is approximate to 2υ/C. ηe(t) denotes the thermal noise contribution at the surveillance antenna.
At the receiver site, the reference signal is obtained by the reference antenna. Besides, the replicas of the reference signal through the reflection of ground could be detected by side lobe of the reference antenna. Neglecting the other interferences, the received reference signal could be expressed by:
In order to assess the performance of radar system, a simulation based on MATLAB is conducted by using Eqs. (10) and (11). The generated chaos signal in Fig. 1 is used as the transmitted signal, which is resampled at the rate of 10GHz to reduce the computational complexity. The received echo signal contains direct signal with the direct signal to noise ratio of 40dB. Six static targets and four moving targets are considered in the simulation. The relative distance with respect to direct-path, radial velocity and the signal-to-direct signal ratio (SDR) of targets are listed in Tables 1 and 2. Besides, the echo signal contains a multipath replica of direct signal with SDR of −10dB. The reference signal consists of direct signal with the direct reference signal to noise ratio of 50 dB, two multipath replicas with multipath signal to direct reference signal ratio of −10dB and −15dB respectively.
The CMF between the surveillance and the reference signal is shown in Fig. 13. As can be seen, there is one main peak corresponding to the direct-path signal located at the center that could be observed. Only the strong echo targets could cause the subtle ripples and others are masked in the background noise. It could be attributed to that the power of reference signal is far larger than other echo signals, thus causing severe direct path interference (DPI) and multi-path interference (MPI). Meanwhile, the MPI could lead to the false identification of targets. Lots of efforts are devoted to proposing effective algorithms to suppress the strong degradations brought by DPI and MPI. However, software based methods could bring about additional computational complexity as well as the processing time. Yet the interferences cannot be concealed entirely.
3.2 Bistatic radar system based on hybrid chaos system and optical fiber
Figure 14 displays an example of bistatic radar using the proposed chaos system and optical fiber line. In the transmitter, the generated optical chaos signal is detected by a PD and then transmitted by the surveillance antenna. The corresponding electrical binary sequences generated in SQM are used to drive a direct-modulated laser (DML). The obtained optical signal is sequentially delivered by optical fiber to the receiver. Here, the distance between the transmitter and receiver is assumed as 120km. The attenuation and dispersion of the fiber are set as 0.2dB/km and 16 ps/(nm·km) respectively. The dispersion and attenuation of transmission fiber are compensated by dispersion compensation fiber (DCF) and erbium doped fiber amplifier (EDFA). In the receiver, a precise matched PICM and NLTM are constructed to regenerate the reference signal.
The simulated waveforms of surveillance signal (x1) and the regenerated reference signal (x2) are displayed in Figs. 15(a) and 15(b). The correlation relationship between them is shown in Fig. 15(c), with a high correlation coefficient of 0.99. The correlation coefficient is measured by using the following equation31]. In another word, an exactly replicated transmitted signal could be provided at the receiver. This could benefit the radar system for enhancing the SNR of target detection .
The CMF between the echo signal and the reference signal is shown in Fig. 16. The mutual interferences between them could be concealed totally on account of their transmission through separate physical channels. As displayed in Fig. 16, there are nine peaks that could be distinguished from the background noise. In order to describe clearly, these targets are marked with numbers 1 to 9, where the corresponding positions are (15, 0), (33.3, 0), (68.3, 1), (110, 0), (120, 0), (150, −1.33), (150, 1.8), (176.7, 0) and (240, 2) respectively. As can be seen, the peaks with labels of number 1, 2, 4, 5 and 8 reflect the five static targets listed in the Table 1. The received signal of the sixth static target is covered by the background noise due to its low SDR. On the other hand, the peaks with labels of number 3, 6, 7 and 9 correspond to the four moving targets. The fourth moving target could result in a subtle ripple over the surface of CMF even with a low SDR of −24dB. It can be seen that a better detection performance can be obtained in our scheme.
It should be noted that the power consume in our scheme could be decreased significantly since attenuation of the optical fiber is only 0.2dB/km. A high power antenna prepared for reference signal could be saved in fiber based scheme. Therefore, it is a more environmental-friendly method to deliver the reference signal by using optical fiber. Besides, wireless channel is unstable and severely influenced by the temporary environmental condition. This makes the transmission duration of reference signal fluctuating, which could affect the measure of target distance. Literature  has demonstrated the feasibility of using optical fiber link to synchronize clock between the transmitter and receiver by transmitting a frequency signal. A stable transmission and precise time-delay management of reference signal could be implemented via the optical fiber, accompanied by a high accuracy of measurement.
Meanwhile, different from the traditional noise radar, the analog noise signal is not transmitted directly as the reference signal in the proposed scheme. Because the analog chaos signal is determined by the digital states, the reference signal could be regenerated easily in the receiver using the digital sequences. Compared with analog noise, using digital signal could bring about lots of advantages. Firstly, the digital signal is robust to channel noise and fiber dispersion, and therefore suitable for long-haul transmission. The distortion of the digital signal is easier to correct, which could ensure the high similarity of two digital signals in different places. Moreover, for the digital signal, it could be easily compatible with transmission formats of the current optical communication network. Thus, the off-the-shelf optical fiber network could be exploited to transmit the signal. The digital signal is also easy to store and process in digital signal processors, hence convenient for delay scanning in the receiver. With such advantages discussed above, the proposed scheme might perform better in the practical bistatic noise radar applications. As can be seen, the differences between our scheme and the existing ones mainly focus on the type of transmitted signal and transmission method of the direct-path signal. In our scheme, the analog chaos signal is used as the surveillance signal, and the digital signal is used as the direct-path signal which is delivered by the optical fiber. The fact that broadband analog chaos signal could be a good choice of surveillance signal has been confirmed in literatures [22,27]. Utilizing optical fiber to transmit digital signal in OOK format has also been a mature technology. Moreover, we have demonstrated the experimental realization of the proposed chaos source in section 2.3. Therefore, our scheme seems to be feasible based on these key technologies. In practical applications, the characteristic of the proposed system is mainly restricted by the synchronization degree of chaos signals at the transmitter and receiver. With a high synchronization degree, the transmitted chaos signal could be recovered from the digital signal at different places. The synchronization degree of chaos system is mainly influenced by the parameter mismatch between the transmitter and receiver. We have discussed the issue in this section and . In view of the discussion above, the proposed model could be feasible, although we are not able to establish a full scale experiment due to the lack of some devices.
In this paper, we introduce a novel bistatic radar system based on the optical hybrid chaos system. The transmitted signal is generated through the well-designed chaos system where the analog chaos signal could be determined by the corresponding internal digital sequence. As long as the sequences keep the same, a chaos signal with high similarity could be recovered at different places. It means the analog noise signal could be replaced by digital sequences to be transmitted to the receiver. The reference signal could be regenerated using the digital sequences. Since the digital signal is more robust to the channel degradation, it could be extremely propitious to be applied in the bistatic radar system. Here the surveillance signal and reference signal are delivered by wireless channel and optical fiber respectively. Compared with the traditional bistatic radar, different transmission path could obviate the mutual interferences between the echo and reference signal. Hence it can bring about both a high SNR of the echo signal and the reference signal in the receiver site. Moreover, the optical fiber is a stable transmission media. It could provide low attenuation transmission, stable channel property, precise time-delay management, and many other advantages. These are essential factors for the transmission of the reference signal. The proposed scheme could provide a promising choice for bistatic noise radar application.
Although we mainly focus on the situations that the reference signal is transmitted by using optical fiber, it could also maintain a good performance in the situation of wireless transmission. For the digital signal are connected with the analog chaos signal by a nonlinear non-invertible process, the correlation value between them is very low as investigated in section II. In other words, effects brought by the mutual interference between the surveillance signal and reference signal may be minor. Meanwhile, it is nearly impossible to regenerate the reference signal by capture the direct signal without the information of the chaos system. Such characteristic could endow the bistatic radar system with the ability to resist hostile camouflage jamming. We will discuss this in our future works.
As demonstrated in the section 2, the initial values of the proposed chaos system are determined by SR. The dynamic process could be easily changed by resetting the values of SR. Meanwhile, chaos signal or periodic signal could be obtained by changing the length of SR, as discussed in . All these works can be performed through software. Reconfiguration and soft-define process could be available in our system. These might provide some advantages in practical applications.
National Natural Science Foundation of China (NSFC) (61505061, 61675083, 61377073, 61471179); Fundamental Research Funds for the Central Universities’, HUST (2017KFYXJJ034, 2017KFXKJC002); Key project of R&D Program of Hubei Province (2017AAA046).
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