High-Resolution Radar Ranging with Chaotic OEO

1High-Resolution Radar Ranging Based on
2Ultra-Wideband Chaotic Optoelectronic
3Oscillator
4ZIWEI XU,1 HUAN TIAN, 1 LINGJIE ZHANG,1,2,* QINGBO ZHAO,1 ZHIYAO
5ZHANG1,2 SHANGJIAN ZHANG,1,2 HEPING LI1,2 , AND YONG LIU,1,2
61State Key Laboratory of Electronic Thin Films and Integrated Devices, University of Electronic
7Science and Technology of China, Chengdu 610054, P. R. China
82Advanced Research Center for Microwave Photonics (ARC-MWP), School of Optoelectronic Science
9and Engineering, University of Electronic Science and Technology of China, Chengdu 610054, P. R.
10 China
11 *[email protected]
12 Abstract: A high-resolution radar ranging scheme is proposed and demonstrated based on
13 ultra-wideband chaotic optoelectronic oscillator (OEO). Through biasing the electro-optic
14 intensity modulator near its minimum transmission point, high-dimensional chaotic signals
15 with flat spectra and low time-delayed signatures can be generated in the OEO, which are
16 favorable for increasing the ranging resolution and the confidentiality. In the experiment, the
17 optimized broadband OEO generates a high-dimensional chaotic signal with a flat spectrum in
18 the frequency range of 2 GHz to 16 GHz and a high permutation entropy of 0.9754. This chaotic
19 signal is used to achieve multiple target ranging, where a ranging resolution of 1.4 cm is
20 realized.
21 © 2023 Optica Publishing Group under the terms of the Optica Publishing Group Open Access Publishing
22 Agreement
23 1. Introduction
24 Chaotic signals, which are characterized by noise-like waveform, wide spectrum and low power
25 spectral density, are promising for radar and communication applications due to their benefits
26 for security, anti-interference and suppression of range-Doppler coupling effect [1]. The
27 common methods for generating chaotic signals are using electrical circuits [2-4] or function
28 iterations [5-7]. Nevertheless, due to the limited cut-off frequency of the triode, the bandwidth
29 of the generated chaotic signal is generally below a few gigahertz, which cannot meet the ever-
30 increasing requirement of high-resolution radars and broadband secure communications.
31 Nonlinear feedback systems based on semiconductor lasers or optoelectronic oscillators
32 (OEOs) are powerful candidates to solve the bandwidth limitation problem of chaotic signal
33 generation [8]. Broadband chaotic signals can be generated through disturbing the active layer
34 of a semiconductor laser via the delayed optical signals [9]. The main problem of this scheme
35 lies in that the spectrum flatness is poor, which is attributed to the relaxation oscillation effect
36 in the laser resonant cavity [10,11]. Continuous-wave (CW) optical injection is an effective
37 method to enhance the spectrum flatness, which has been widely researched in past years
38 [12,13]. However, the chaotic source based on a semiconductor laser is sensitive to external
39 disturbance [14], where a slight perturbation of working temperature or injected light intensity
40 will result in the instability of the chaotic state. Nonlinear feedback systems based on broadband
41 OEOs exhibit rich dynamic behaviors due to the nonlinearity induced by the optoelectronic
42 devices in the cavity, which can be used to generate various broadband and complex signals
43 such as periodic signals, pulse packages, chaotic breathers and hyper-chaos [15-20]. For
44 example, a hyperchaotic signal with a Lyapunov dimension of about 3700 and a bandwidth
45 over 10 GHz has been generated in a broadband OEO with a high cavity gain and a large loop
46 delay [21]. Compared with the chaotic source based on a semiconductor laser, the nonlinear

47 dynamic characteristics of the OEO-based chaotic source depend on the loop structure and the
48 devices outside of the laser source. Hence, it is insensitive to the complex laser properties,
49 which is more stable and controllable. These advantages make the OEO-based chaotic source
50 a promising candidate for high-precision radar and broadband secure communication
51 applications.
52 In this paper, a high-resolution radar ranging scheme is proposed and demonstrated based
53 on using an OEO to generate a broadband chaotic signal with a flat spectrum and a low time-
54 delayed signature (TDS). Through optimizing the OEO, a chaotic signal with a flat spectrum
55 in the frequency range of 2 GHz to 16 GHz and a permutation entropy of 0.9754 is generated.
56 In the radar ranging experiment, multiple target detection with a ranging resolution of 1.4 cm
57 is achieved by using this chaotic signal.
58 2. Operation principle
59 Figure 1 shows the schematic diagram of the proposed chaotic radar ranging system. High-
60 dimensional chaotic signals are generated by a broadband OEO as shown in the upper part of
61 Fig. 1. In the OEO loop, there is no bandpass filter. Hence, the bandwidth of the OEO cavity is
62 determined by the operation bandwidth of the employed microwave and optoelectronic devices.
63 A variable optical attenuator (VOA) is used to tune the OEO loop gain, which guarantees that
64 the broadband OEO works in chaotic signal generation state. The generated chaotic signals are
65 divided into two parts by using an electrical splitter, i.e., ES2 in Fig. 1, where one part is used
66 as the reference signal, and the other part is sent to the transmitting antenna. The echo signals
67 received by the receiving antenna are amplified by an electrical amplifier, and are then sent to
68 a high-speed oscilloscope together with the reference signals for digitization. After computing
69 the cross-correlation between the echo signals and the reference signals, the round-trip times
70 between the antenna and the targets can be precisely measured. Then, the distance of the target
71 from the antenna can be calculated by using the formula D=c/(2TR), where D is the distance, c
72 is the speed of light in vacuum, and TR is the round-trip time.
73
74 Fig. 1. Schematic diagram of the proposed chaotic radar ranging system. LD: laser diode; MZM:
75 Mach-Zehnder modulator; SMF: single-mode fiber; VOA: variable optical attenuator; PD:
76 photodetector; EA: electrical amplifier; ES: electrical splitter.
77 The kernel of the proposed scheme is the generation of high-dimensional chaotic signals by
78 using a broadband OEO. Although there is no electrical bandpass filter in the cavity, the OEO
79 still has a wide bandpass characteristic due to the low-frequency cut-off characteristic of the

80 electrical amplifier. Hence, the dynamic process in the OEO cavity can be mathematically
81 described by Ikeda equation as
82
0
2
0
0
1
1 cos 2 2
t
D bias
t
dV t
V t V t dt GRP V t T V
dt V V
(1)
83 where Vπ and Vπ0 are the half-wave voltages of the radio-frequency (RF) input port and the
84 direct-current bias port of the MZM, respectively. V(t) and Vbias are the signal voltage and the
85 direct-current (DC) bias voltage applied to the MZM, respectively. τ and θ are the characteristic
86 response times, which are inversely proportional to the high cut-off frequency fH and the low
87 cut-off frequency fL of the OEO cavity, respectively. G is the controllable voltage net gain in
88 the cavity. P0 is the input optical power of the MZM. R and γ are the matching resistance and
89 the responsivity of the photodetector (PD), respectively. TD is the loop delay. In Eq. (1), the
90 three terms on the left-hand side of the equal sign describe a 2nd-order bandpass filtering process.
91 The term on the right-hand side of the equal sign contains the system gain, the loop delay and
92 the nonlinearity. Thereinto, the cosine-squared nonlinearity is induced by the transfer function
93 of the MZM.
94 For simplicity, Eq. (1) can be rewritten as
95
2
1 1 1 cos
1
dx t x t y t x t T
dt
dy t x t
dt
(2)
96 where x(t)=πV(t)/(2Vπ) represents the dimensionless microwave signal. β=πγGRP0/(2Vπ) and
97 φ=πVbias/(2Vπ0) are the Ikeda gain and the phase shift, respectively. y(t) is defined as
98
0
' '
1
t
t
y t x t dt
(3)
99 By normalizing the time-related parameters through τ , Eq. (2) can be written in a more
100 convenient way as
101
2 , ,
1 cos
dx T x T y T x T T T T
dT
dy T x T
dT
(4)
102 where T and T’ are normalized parameters of t and TD, respectively. α= τ /θ is the ratio of the
103 low cut-off frequency to the high cut-off frequency. ξ(t) is the additive noise in the OEO cavity.
104 Eq. (4) can be solved by using 4th-order Runge-Kutta method to study the dynamic behavior in
105 the broadband OEO, where the feedback term can be added through 3rd-order Hermite
106 interpolation.
107 3. Chaotic signal generation optimization
108 Numerical simulation is implemented to optimize the chaotic signal generation in the OEO. In
109 the simulation, the loop delay τ is set to be 1.15 μs, which corresponds to a spool of SMF with
110 a length of 300 m. The output optical power of the laser diode (LD) at 1550 nm is 16 dBm. The
111 responsivity and the output matching resistance of the PD are 0.8 A/W and 50 Ω, respectively.
112 In addition, the low cut-off frequency and the high cut-off frequency of the 2nd-order bandpass
113 filter are set to be 200 MHz and 10 GHz, respectively. Hence, the ratio of the low cut-off
114 frequency to the high cut-off frequency is calculated to be α=0.02. The two half-wave voltages
115 of the MZM are set to be Vπ=6 V and Vπ0=6 V. Moreover, an initial Gaussian white noise with
116 a power spectral density of -160 dBm/Hz is added after a single-loop transmission.

117 The bias voltage of the MZM has a great influence on the dynamic characteristics of the
118 broadband OEO. Figure 2(a) and (c) show the bifurcation diagrams and the 0-1 test diagrams
119 under different Ikeda gain β when the MZM is biased at its linear transmission point (LTP),
120 i.e., Vbias=Vπ0/2, respectively. For comparison, Fig. 2(b) and (d) exhibit the bifurcation diagrams
121 and the 0-1 test diagrams under different Ikeda gain β when the MZM is biased near its
122 minimum transmission point (MITP), i.e., Vbias=21Vπ0/20, respectively. It can be seen from Fig.
123 2(a) that, when the MZM is biased at its LTP, the broadband OEO exhibits obvious period
124 doubling process as the Ikeda gain β increases. This dynamic process is similar to that in the
125 optical feedback chaotic lasers. Nevertheless, when the MZM is biased near its MITP, the
126 period doubling process with the increasing Ikeda gain β vanishes. This irregular dynamic
127 process is favorable for generating high-dimensional chaotic signals. In addition, it should be
128 pointed out that the dynamic process for the MZM biased near its maximum transmission point
129 (MATP) is similar to that in Fig. 2(b) and (d).
130
131 Fig. 2. Simulation results of the generated chaotic signals when the broadband OEO is biased at
132 its LTP (left column) and near its MITP (right column). (a)-(b) Bifurcation diagrams. (c)-(d) 0-
133 1 test diagrams.
134 For a nonlinear feedback system, there is an inevitable TDS in the autocorrelation diagram,
135 since the feedback signal is a delayed replica of the output. The TDS not only leads to ranging
136 ambiguity for inducing false side-lobes in the cross-correlation between the reference signals
137 and echo signals [1], but also reduces the confidentiality of the chaotic radar system. Apart
138 from the TDS, the bandwidth of the generated chaotic signal also plays a significant role in
139 radar ranging since it directly determines the ranging resolution. Therefore, it is of great
140 importance to optimize these characteristics for radar ranging. Figure 3(a) and (b) show the
141 autocorrelation diagram and the spectrum when the MZM is biased at its LTP, i.e., Vbias=Vπ0/2,
142 respectively. Figure 3(c) and (d) present the autocorrelation diagram and the spectrum when
143 the MZM is biased near its MITP, i.e., Vbias=21Vπ0/20, respectively. For both cases, the Ikeda
144 gain β is set to be 5.5. It can be seen from Fig. 3 that the generated chaotic signal for the MZM
145 biased near its MITP has a flatter spectrum and a lower TDS, which is more favorable for radar
146 ranging.

147
148 Fig. 3. Simulation results of the generated chaotic signals when the broadband OEO is biased at
149 its LTP (upper row, blue line) and near its MITP (bottom row, red line). (a)-(b) Autocorrelation
150 diagrams (The insets are autocorrelation peaks). (c)-(d) spectra.
151 4. Experimental results and analysis
152 A proof-of-concept experiment is carried out to demonstrate the proposed scheme for high-
153 resolution radar ranging. In the broadband OEO, continuous-wave (CW) light from a
154 distributed feedback laser diode (DFB-LD) with a power of 16.33 dBm and a center wavelength
155 of 1561.1 nm propagates through a 25 Gb/s electro-optic MZM (FUJITSU 7938EZ). The MZM
156 is biased near its MITP, where the bias voltage for the MITP and the applied DC bias voltage
157 are 8.50 V and 8.65 V, respectively. After propagating through a spool of SMF with a length
158 of 300 m and a VOA, the modulated optical signals are detected by a PD whose bandwidth is
159 20 GHz. An electrical amplifier (GT-HLNA-0022G) with an operation bandwidth from 34.25
160 MHz to 22 GHz and a small-signal gain of 28 dB is employed to amplify the electrical signal
161 from the PD. Besides, an electrical power divider (GTPD-COMB50G) with an operation
162 bandwidth from DC to 50 GHz is used to extract the chaotic signal out of the OEO. Another
163 electrical power divider (MARKI PD-0030) with an operation bandwidth from DC to 30 GHz
164 divides the extracted chaotic signals into two parts. One part is transmitted by the transmitting
165 antenna (HD-10200DRHA10S, 1-20 GHz), and the other part is recorded as the reference signal
166 by a high-speed real-time oscilloscope (Tektronix DPO75002SX) with a sampling rate is 50
167 GSa/s. The echo signal from the receiving antenna (HD-10200DRHA10S, 1-20 GHz) is
168 amplified by an electrical amplifier (TLPA50K20G-28-20) with an operation bandwidth from
169 698 MHz to 25 GHz and a small-signal gain of 31 dB, and then recorded by the high-speed
170 real-time oscilloscope. Figure 4 shows the experimental setup for multiple target ranging.