1 2 3 4 5 6 7 8 9 10 11 High-Resolution Radar Ranging Based on Ultra-Wideband Chaotic Optoelectronic Oscillator ZIWEI XU,1 HUAN TIAN, 1 LINGJIE ZHANG,1,2,* QINGBO ZHAO,1 ZHIYAO ZHANG1,2 SHANGJIAN ZHANG,1,2 HEPING LI1,2 , AND YONG LIU,1,2 1State Key Laboratory of Electronic Thin Films and Integrated Devices, University of Electronic Science and Technology of China, Chengdu 610054, P. R. China 2Advanced Research Center for Microwave Photonics (ARC-MWP), School of Optoelectronic Science and Engineering, University of Electronic Science and Technology of China, Chengdu 610054, P. R. China *[email protected] 12 13 14 15 16 17 18 19 20 Abstract: A high-resolution radar ranging scheme is proposed and demonstrated based on ultra-wideband chaotic optoelectronic oscillator (OEO). Through biasing the electro-optic intensity modulator near its minimum transmission point, high-dimensional chaotic signals with flat spectra and low time-delayed signatures can be generated in the OEO, which are favorable for increasing the ranging resolution and the confidentiality. In the experiment, the optimized broadband OEO generates a high-dimensional chaotic signal with a flat spectrum in the frequency range of 2 GHz to 16 GHz and a high permutation entropy of 0.9754. This chaotic signal is used to achieve multiple target ranging, where a ranging resolution of 1.4 cm is realized. 21 22 © 2023 Optica Publishing Group under the terms of the Optica Publishing Group Open Access Publishing Agreement 23 1. Introduction 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 Chaotic signals, which are characterized by noise-like waveform, wide spectrum and low power spectral density, are promising for radar and communication applications due to their benefits for security, anti-interference and suppression of range-Doppler coupling effect [1]. The common methods for generating chaotic signals are using electrical circuits [2-4] or function iterations [5-7]. Nevertheless, due to the limited cut-off frequency of the triode, the bandwidth of the generated chaotic signal is generally below a few gigahertz, which cannot meet the everincreasing requirement of high-resolution radars and broadband secure communications. Nonlinear feedback systems based on semiconductor lasers or optoelectronic oscillators (OEOs) are powerful candidates to solve the bandwidth limitation problem of chaotic signal generation [8]. Broadband chaotic signals can be generated through disturbing the active layer of a semiconductor laser via the delayed optical signals [9]. The main problem of this scheme lies in that the spectrum flatness is poor, which is attributed to the relaxation oscillation effect in the laser resonant cavity [10,11]. Continuous-wave (CW) optical injection is an effective method to enhance the spectrum flatness, which has been widely researched in past years [12,13]. However, the chaotic source based on a semiconductor laser is sensitive to external disturbance [14], where a slight perturbation of working temperature or injected light intensity will result in the instability of the chaotic state. Nonlinear feedback systems based on broadband OEOs exhibit rich dynamic behaviors due to the nonlinearity induced by the optoelectronic devices in the cavity, which can be used to generate various broadband and complex signals such as periodic signals, pulse packages, chaotic breathers and hyper-chaos [15-20]. For example, a hyperchaotic signal with a Lyapunov dimension of about 3700 and a bandwidth over 10 GHz has been generated in a broadband OEO with a high cavity gain and a large loop delay [21]. Compared with the chaotic source based on a semiconductor laser, the nonlinear 47 48 49 50 51 52 53 54 55 56 57 dynamic characteristics of the OEO-based chaotic source depend on the loop structure and the devices outside of the laser source. Hence, it is insensitive to the complex laser properties, which is more stable and controllable. These advantages make the OEO-based chaotic source a promising candidate for high-precision radar and broadband secure communication applications. In this paper, a high-resolution radar ranging scheme is proposed and demonstrated based on using an OEO to generate a broadband chaotic signal with a flat spectrum and a low timedelayed signature (TDS). Through optimizing the OEO, a chaotic signal with a flat spectrum in the frequency range of 2 GHz to 16 GHz and a permutation entropy of 0.9754 is generated. In the radar ranging experiment, multiple target detection with a ranging resolution of 1.4 cm is achieved by using this chaotic signal. 58 2. Operation principle 59 60 61 62 63 64 65 66 67 68 69 70 71 72 Figure 1 shows the schematic diagram of the proposed chaotic radar ranging system. Highdimensional chaotic signals are generated by a broadband OEO as shown in the upper part of Fig. 1. In the OEO loop, there is no bandpass filter. Hence, the bandwidth of the OEO cavity is determined by the operation bandwidth of the employed microwave and optoelectronic devices. A variable optical attenuator (VOA) is used to tune the OEO loop gain, which guarantees that the broadband OEO works in chaotic signal generation state. The generated chaotic signals are divided into two parts by using an electrical splitter, i.e., ES2 in Fig. 1, where one part is used as the reference signal, and the other part is sent to the transmitting antenna. The echo signals received by the receiving antenna are amplified by an electrical amplifier, and are then sent to a high-speed oscilloscope together with the reference signals for digitization. After computing the cross-correlation between the echo signals and the reference signals, the round-trip times between the antenna and the targets can be precisely measured. Then, the distance of the target from the antenna can be calculated by using the formula D=c/(2TR), where D is the distance, c is the speed of light in vacuum, and TR is the round-trip time. 73 74 75 76 Fig. 1. Schematic diagram of the proposed chaotic radar ranging system. LD: laser diode; MZM: Mach-Zehnder modulator; SMF: single-mode fiber; VOA: variable optical attenuator; PD: photodetector; EA: electrical amplifier; ES: electrical splitter. 77 78 79 The kernel of the proposed scheme is the generation of high-dimensional chaotic signals by using a broadband OEO. Although there is no electrical bandpass filter in the cavity, the OEO still has a wide bandpass characteristic due to the low-frequency cut-off characteristic of the 80 81 82 83 84 85 86 87 88 89 90 91 92 93 94 electrical amplifier. Hence, the dynamic process in the OEO cavity can be mathematically described by Ikeda equation as 1 dV t 1 t V t dt GRP0 cos 2 V t TD Vbias V t dt t0 2 V 2 V 0 where Vπ and Vπ0 are the half-wave voltages of the radio-frequency (RF) input port and the direct-current bias port of the MZM, respectively. V(t) and Vbias are the signal voltage and the direct-current (DC) bias voltage applied to the MZM, respectively. τ and θ are the characteristic response times, which are inversely proportional to the high cut-off frequency fH and the low cut-off frequency fL of the OEO cavity, respectively. G is the controllable voltage net gain in the cavity. P0 is the input optical power of the MZM. R and γ are the matching resistance and the responsivity of the photodetector (PD), respectively. TD is the loop delay. In Eq. (1), the three terms on the left-hand side of the equal sign describe a 2nd-order bandpass filtering process. The term on the right-hand side of the equal sign contains the system gain, the loop delay and the nonlinearity. Thereinto, the cosine-squared nonlinearity is induced by the transfer function of the MZM. For simplicity, Eq. (1) can be rewritten as dx t dt 95 dy t dt 96 97 98 99 100 1 1 1 x t y t cos2 x t T (2) 1 xt where x(t)=πV(t)/(2Vπ) represents the dimensionless microwave signal. β=πγGRP0/(2Vπ) and φ=πVbias/(2Vπ0) are the Ikeda gain and the phase shift, respectively. y(t) is defined as 1 (3) x t ' dt ' t By normalizing the time-related parameters through τ, Eq. (2) can be written in a more convenient way as y t dx T 101 (1) dT dy T dT t 0 1 x T y T cos 2 x T T , T T , (4) x T 102 103 104 105 106 where T and T’ are normalized parameters of t and TD, respectively. α=τ/θ is the ratio of the low cut-off frequency to the high cut-off frequency. ξ(t) is the additive noise in the OEO cavity. Eq. (4) can be solved by using 4th-order Runge-Kutta method to study the dynamic behavior in the broadband OEO, where the feedback term can be added through 3rd-order Hermite interpolation. 107 3. Chaotic signal generation optimization 108 109 110 111 112 113 114 115 116 Numerical simulation is implemented to optimize the chaotic signal generation in the OEO. In the simulation, the loop delay τ is set to be 1.15 μs, which corresponds to a spool of SMF with a length of 300 m. The output optical power of the laser diode (LD) at 1550 nm is 16 dBm. The responsivity and the output matching resistance of the PD are 0.8 A/W and 50 Ω, respectively. In addition, the low cut-off frequency and the high cut-off frequency of the 2nd-order bandpass filter are set to be 200 MHz and 10 GHz, respectively. Hence, the ratio of the low cut-off frequency to the high cut-off frequency is calculated to be α=0.02. The two half-wave voltages of the MZM are set to be Vπ=6 V and Vπ0=6 V. Moreover, an initial Gaussian white noise with a power spectral density of -160 dBm/Hz is added after a single-loop transmission. 117 118 119 120 121 122 123 124 125 126 127 128 129 The bias voltage of the MZM has a great influence on the dynamic characteristics of the broadband OEO. Figure 2(a) and (c) show the bifurcation diagrams and the 0-1 test diagrams under different Ikeda gain β when the MZM is biased at its linear transmission point (LTP), i.e., Vbias=Vπ0/2, respectively. For comparison, Fig. 2(b) and (d) exhibit the bifurcation diagrams and the 0-1 test diagrams under different Ikeda gain β when the MZM is biased near its minimum transmission point (MITP), i.e., Vbias=21Vπ0/20, respectively. It can be seen from Fig. 2(a) that, when the MZM is biased at its LTP, the broadband OEO exhibits obvious period doubling process as the Ikeda gain β increases. This dynamic process is similar to that in the optical feedback chaotic lasers. Nevertheless, when the MZM is biased near its MITP, the period doubling process with the increasing Ikeda gain β vanishes. This irregular dynamic process is favorable for generating high-dimensional chaotic signals. In addition, it should be pointed out that the dynamic process for the MZM biased near its maximum transmission point (MATP) is similar to that in Fig. 2(b) and (d). 130 131 132 133 Fig. 2. Simulation results of the generated chaotic signals when the broadband OEO is biased at its LTP (left column) and near its MITP (right column). (a)-(b) Bifurcation diagrams. (c)-(d) 01 test diagrams. 134 135 136 137 138 139 140 141 142 143 144 145 146 For a nonlinear feedback system, there is an inevitable TDS in the autocorrelation diagram, since the feedback signal is a delayed replica of the output. The TDS not only leads to ranging ambiguity for inducing false side-lobes in the cross-correlation between the reference signals and echo signals [1], but also reduces the confidentiality of the chaotic radar system. Apart from the TDS, the bandwidth of the generated chaotic signal also plays a significant role in radar ranging since it directly determines the ranging resolution. Therefore, it is of great importance to optimize these characteristics for radar ranging. Figure 3(a) and (b) show the autocorrelation diagram and the spectrum when the MZM is biased at its LTP, i.e., Vbias=Vπ0/2, respectively. Figure 3(c) and (d) present the autocorrelation diagram and the spectrum when the MZM is biased near its MITP, i.e., Vbias=21Vπ0/20, respectively. For both cases, the Ikeda gain β is set to be 5.5. It can be seen from Fig. 3 that the generated chaotic signal for the MZM biased near its MITP has a flatter spectrum and a lower TDS, which is more favorable for radar ranging. 147 148 149 150 Fig. 3. Simulation results of the generated chaotic signals when the broadband OEO is biased at its LTP (upper row, blue line) and near its MITP (bottom row, red line). (a)-(b) Autocorrelation diagrams (The insets are autocorrelation peaks). (c)-(d) spectra. 151 4. Experimental results and analysis 152 153 154 155 156 157 158 159 160 161 162 163 164 165 166 167 168 169 170 A proof-of-concept experiment is carried out to demonstrate the proposed scheme for highresolution radar ranging. In the broadband OEO, continuous-wave (CW) light from a distributed feedback laser diode (DFB-LD) with a power of 16.33 dBm and a center wavelength of 1561.1 nm propagates through a 25 Gb/s electro-optic MZM (FUJITSU 7938EZ). The MZM is biased near its MITP, where the bias voltage for the MITP and the applied DC bias voltage are 8.50 V and 8.65 V, respectively. After propagating through a spool of SMF with a length of 300 m and a VOA, the modulated optical signals are detected by a PD whose bandwidth is 20 GHz. An electrical amplifier (GT-HLNA-0022G) with an operation bandwidth from 34.25 MHz to 22 GHz and a small-signal gain of 28 dB is employed to amplify the electrical signal from the PD. Besides, an electrical power divider (GTPD-COMB50G) with an operation bandwidth from DC to 50 GHz is used to extract the chaotic signal out of the OEO. Another electrical power divider (MARKI PD-0030) with an operation bandwidth from DC to 30 GHz divides the extracted chaotic signals into two parts. One part is transmitted by the transmitting antenna (HD-10200DRHA10S, 1-20 GHz), and the other part is recorded as the reference signal by a high-speed real-time oscilloscope (Tektronix DPO75002SX) with a sampling rate is 50 GSa/s. The echo signal from the receiving antenna (HD-10200DRHA10S, 1-20 GHz) is amplified by an electrical amplifier (TLPA50K20G-28-20) with an operation bandwidth from 698 MHz to 25 GHz and a small-signal gain of 31 dB, and then recorded by the high-speed real-time oscilloscope. Figure 4 shows the experimental setup for multiple target ranging. 171 172 Fig. 4. Experimental setup for multiple target ranging. 173 174 175 176 177 178 179 180 181 182 183 184 Figure 5 shows the experimental results of the OEO-based chaotic source. In Fig. 5(a), the temporal sequences of the generated chaotic signal within 5 µs and 5 ns are exhibited. In order to quantify the complexity of the chaotic signal, the temporal sequences with a length of 30000 are adopted for evaluating the permutation entropy (PE). The PE is calculated to be 0.9754 with an embedding dimension of 5 and an embedding delay of 1, indicating that a high-dimensional chaotic signal is generated. Figure 5(b) exhibits the spectrum of the generated chaotic signal. It can be seen that the spectrum is with an excellent flatness in the frequency range of 2 GHz to 16 GHz. The effective bandwidth of the chaotic signal is about 10 GHz, which fits in with the full-width at half-maximum (FWHM) of the autocorrelation peak shown in the inset of Fig. 5(c). In addition, as shown in Fig. 3(c), the maximum TDS in the autocorrelation diagram is 0.18. Although this value is larger than that in Fig. 3(b), it is much smaller than the TDS for the MZM biased at its LTP as shown in Fig. 3(a). 185 186 187 188 Fig. 5. Experimental results of the OEO-based chaotic source. (a) Temporal sequences within 5 µs (Left) and 5 ns (Right), (b) spectrum, and (c) autocorrelation diagram (The inset is the autocorrelation peak). 189 190 191 192 193 194 Figure 6 shows the experimental results of chaotic radar ranging. Thereinto, Fig. 6(a) presents the results for detecting target A at different distance. As target A moves away from the antenna, the strength of the echo signal is gradually attenuated, which makes the strength of the clutter relatively increase. It can be seen from the inset in Fig. 6(a) that the ranging resolution is about 1.4 cm. This value fits in with the theoretical resolution ∆r=c/(2B)=1.5 cm, where ∆r is the ranging resolution, c is the speed of light in vacuum, and B is the bandwidth of 195 196 197 198 199 the chaotic signal. Figure 6(b) exhibits the experimental results of chaotic radar ranging for target B and target C with different intervals. Since target B and target C are with different sizes and are made of different materials, they have different electromagnetic wave absorption characteristics. Hence, the cross-correlation peak corresponding to target B is lower and wider than that corresponding to target C. 200 201 202 Fig. 6. Experimental results of chaotic radar ranging. (a) Ranging results of target A (The inset is the FWHM of the cross-correlation peak). (b) Ranging results of target B and target C. 203 5. Conclusion 204 205 206 207 208 209 210 211 In summary, we have proposed and demonstrated a high-resolution radar ranging scheme based on ultra-wideband chaotic OEO. Numerical simulation is implemented to optimize the chaotic signal. The results indicate that high-dimensional chaotic signals with flat spectra and low TDSs can be easily generated when the MZM in the OEO loop is biased near its MITP or MATP. In the experiment, chaotic signal with a flat spectrum in the frequency range of 2 GHz to 16 GHz and a PE of 0.9754 is generated by biasing the MZM near its MITP. This chaotic signal is used to achieve multiple target ranging, where a ranging resolution of 1.4 cm is realized. 212 213 214 215 216 217 218 219 220 221 222 223 224 225 226 Funding. National Key Research and Development Program of China (2019YFB2203800); National Natural Science Foundation of China (NSFC) (61927821); Fundamental Research Funds for the Central Universities (ZYGX2020ZB012). Disclosures. The authors declare no conflicts of interest. Data availability. Data underlying the results presented in this paper are not publicly available at this time but may be obtained from the authors upon reasonable request. References 1. 2. 3. W. Z. Feng, N. Jiang, Y. Q. Zhang, J. Y. Jin, A. K. Zhao, S. Q. Liu, and K. 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