Microwave photonic radar with a fiber-distributed antenna array for three-dimensional imaging

Jingwen Dong; Fubo Zhang; Zekun Jiao; Qiang Sun; Qiang Sun; Wangzhe Li; Wangzhe Li

doi:10.1364/OE.393502

1. Introduction

Radar imaging has been widely used in target scattering diagnosis and identification, military surveillance, space resource surveys, etc. Compared with the 2D radar image, which is a projection of the 3D model, 3D image can provide energy distribution of scatterers and more details of the target, making great contribution to target identification and diagnostic analysis [1]. In the last few years, 3D imaging radar has attracted considerable interest worldwide. A general method is introducing interferometry into the conventional 2D imaging. More than one antenna forms an interferometric baseline perpendicular to the original 2D projected plane to obtain the scattering features in the third dimension. In this way, the firstly investigated radar for 3D imaging is the interferometric inverse synthetic aperture radar (InISAR) [2], which however, only has very limited applications to date due to two aspects: 1) it has difficulty to distinguish multiple dominant scatterers from a synthesis scatterer; 2) there is a trade-off that long interferometric baseline brings high accuracy while reducing the phase coherence [3]. To address the problems, many technologies adopting antenna array are proposed and effectively verified for 3D imaging, such as the linear array radar [4,5] or the multiple-input multiple-output (MIMO) radar [6–8]. The concomitant problems are: 1) the increased number of the transmitters and receivers is generally accompanied by the increased cost and system complexity; 2) on the other hand, the extended baseline brings challenges to electronic technology in signal coherent processing [9].

In recent years, benefiting from unique advantages such as the inherent wide bandwidth, low transmission loss and immunity to electromagnetic interference, photonics provides promising solutions to the electronic bottlenecks encountered by the conventional radars and is considered to illuminate the future of radar [10,11]. With the successful demonstration of the MWP radar in 2D imaging [12–16], the application of photonic technologies begins extending to 3D imaging radars [17,18]. An X-band photonics-based InISAR is established and the dynamic 3D reconstruction of moving targets is achieved, demonstrating the feasibility of MWP radar for 3D imaging [17]. Nevertheless, the synthesis scatterer problem and the trade-off between high accuracy and high coherence mentioned above in the InISAR are still inevitable. In addition, photonic technologies are applied in array radars, such as MIMO radar and distributed coherent radar, for 2D positioning and imaging, demonstrating its advantages over electronics in broadband signal transmission and multi-channel coherent processing [19–23]. The above results show the great potential of photonic technologies to overcome the existing problems in conventional distributed array radars, being favorable to high-resolution 3D imaging.

In this paper, an MWP radar with a fiber-distributed antenna array for 3D imaging is proposed and demonstrated for the first time. Employing wavelength-division multiplexing and radio-over-fiber techniques, a novel method based on the delay-dependent beat frequency division for multi-channel de-chirp processing is proposed, leading to multi-channel 2D ISAR imaging and further 3D reconstruction. In addition, the influence of the fiber transmission delay is discussed and the phase noise caused thereby is compensated in 3D imaging algorithm, improving the coherence between channels. In this way, the proposed system achieves large-scale distribution capability with a simple structure. Firstly, employing external modulation based photonic frequency doubling, a photonic radar signal is obtained, which is then replicated over different wavelengths in the CO and distributed to a Tx and multiple Rxs through fibers. Each replica being sent to the Rx as the photonic reference signal, is modulated by the echo signals and then returns to the CO for de-chirp processing. Due to the different fiber delays induced into the reference signals, the beat frequencies of the echoes and the reference signals from different Rxs are divided, thereby achieving parallel photonic de-chirp processing. By digitizing and processing the de-chirped results, multi-channel 2D ISAR imaging and 3D reconstruction are accomplished. A proof-of-concept experiment for 3D imaging of moving targets is carried out. A uniform linear array (ULA) radar with 16 equivalent antenna phase centers (APCs) is established, operating in Ku band with a bandwidth of 2 GHz. The results show that accurate 3D imaging of three trihedral corner reflectors (TCRs) is achieved with resolutions of 7.3 cm in range direction, 5.6 cm in cross-range direction, and 0.85° in height direction, verifying the ability of microwave photonic radar in high-resolution 3D imaging.

2. Principle

2.1 Architecture of the proposed MWP radar system

Figure 1(a) shows the architecture of the proposed MWP radar with a CO, a remote Tx and N remote Rxs, connected via fibers. In the CO, a radar signal is produced in optical domain via photonics-based frequency doubling and replicated over different optical wavelengths via WDM technique. The obtained replicas are then transferred to a Tx and N Rxs through fibers respectively for radar signal transmission and echo signal receiving. In the Rxs, the replicas, used as the photonic reference signals, are modulated by the echo signals and transmitted back to the CO for parallel photonic de-chirp processing. After digitalization, N de-chirped signals are extracted for 2D ISAR imaging and coherently processed for 3D reconstruction. The principles are described in more detail below. For clarity, the subscript i (i=1, 2, … N) indicates the ith of the N different optical carriers. The corresponding ith of N Rxs and the two-way fiber transmission delays between WDM2 and WDM3, i.e. the ith optical carrier with an angular frequency of ${\omega _i}$ is transmitted to Rx_i with a fiber delay of ${\tau _{Ti}}$ and back to the CO with a fiber delay of ${\tau _{Ri}}$.

Fig. 1. (a) Architecture of the proposed MWP radar system. (b) The instantaneous frequency-time diagram of the reference signals, the echo signal and the de-chirped signals. WDM: wavelength-division multiplexer; MZM: Mach-Zehnder modulator; EDFA: erbium-doped fiber amplifier; PD: photodetector; LNA: low-noise amplifier; PA: power amplifier; OBPF: optical band-pass filter; ELPF: electrical low-pass filter; ADC: analog-to-digital converter; DSP: digital signal processor.

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In the CO, N optical carriers generated by a laser array are multiplexed through a wavelength-division multiplexer (WDM1) and fed into a Mach-Zehnder modulator (MZM) for photonic radar signal generation and replication. The MZM is driven by an intermediate frequency (IF) signal generated by an electrical signal generator, which is a linear frequency modulated continuous wave (LFM-CW), and biased at the null point to suppress the optical carrier and even order sidebands. The obtained N replicas of the photonic radar signal are expressed as

(1)$$\begin{array}{c} {E_{Ti}}(t )\propto rect\left( {\frac{t}{{{T_p}}}} \right)j{J_1}({{\beta_{IF}}} )\{{\exp [{j({{\omega_i}t + {\omega_{IF}}t + \pi {k_{IF}}{t^2}} )} ]+ \exp [{j({{\omega_i}t - {\omega_{IF}}t - \pi {k_{IF}}{t^2}} )} ]} \},\\ rect\left( {\frac{t}{{{T_p}}}} \right) = {\left\{ {\begin{array}{c} {1{,_{}}|t |\le {{{T_p}} \mathord{\left/ {\vphantom {{{T_p}} 2}} \right.} 2}}\\ {0{,_{}}|t |\ge {{{T_p}} \mathord{\left/ {\vphantom {{{T_p}} 2}} \right.} 2}} \end{array}} \right._{}}, \end{array}$$

where ${\omega _{IF}}$, ${k_{IF}}$, and ${T_p}$ are the angular frequency, chirp rate, and duration of the IF LFM signal respectively, ${J_n}$ denotes the nth-order Bessel function of the first kind, ${\beta _{IF}} = {{\pi {V_{IF}}} \mathord{\left/ {\vphantom {{\pi {V_{IF}}} {\sqrt 2 {V_\pi }}}} \right. } {\sqrt 2 {V_\pi }}}$ is the modulation index of the MZM, ${V_{IF}}$ is the amplitude of the IF LFM signal and ${V_\pi }$ is the half-wave voltage. Here, small-signal modulation is assumed to only generate ±1st order sidebands. After being amplified by an erbium-doped fiber amplifier (EDFA1), N replicas are split by WDM2 to N branches. Through an optical splitter, part of the first replica is transmitted to the Tx via fiber with a time delay of ${\tau _0}$. The other part and the other (N -1) replicas are used as the photonic reference signals for de-chirp processing and transmitted to the corresponding Rxs. According to the radar range window, the transmission delays from CO to Rxs (${\tau _{Ti}}$) are set to satisfy ${\tau _{Ti + 1}} > {\tau _{Ti}}$ and ${\tau _{Ti}} \ge {\tau _0} + {\tau _{echo\_i}}$, where ${\tau _{echo\_i}}$ is the traveling time from Tx via target to Rx_i.

In the Tx, after heterodyning ±1st order sidebands of the replica at PD1, the frequency-doubled LFM signal is generated, which is amplified by a low noise amplifier (LNA) and a power amplifier (PA) for transmission, written as

(2)$${S_T}(t )\propto rect\left( {\frac{{t - {\tau_0}}}{{{T_p}}}} \right)\cos [{2{\omega_{IF}}({t - {\tau_0}} )+ 2\pi {k_{IF}}{{({t - {\tau_0}} )}^2}} ].$$

In Rx_i, the echo signal that is collected by the receiving antenna and amplified by LNAi is fed into MZMi that is biased at the quadrature point, to modulate the photonic reference signal. The output signal from MZMi is given by

(3)$$\begin{aligned} {E_{R\textrm{i}}}(t )&\propto {E_{Ti}}({t - {\tau_{Ti}}} )\times rect\left( {\frac{{t - {\tau_0} - {\tau_{echo\_i}}}}{{{T_p}}}} \right)\\ & \quad \times \{{{J_0}({{\beta_{Ri}}} )+ 2{J_1}({{\beta_{Ri}}} )\cos [{2{\omega_{IF}}({t - {\tau_0} - {\tau_{echo\_i}}} )+ 2\pi {k_{IF}}{{({t - {\tau_0} - {\tau_{echo\_i}}} )}^2}} ]} \}\\ & = rect\left[ {\frac{{t - {\tau_{Ti}} + {{({{\tau_{ref\_i}} - {\tau_{echo\_i}}} )} \mathord{\left/ {\vphantom {{({{\tau_{ref\_i}} - {\tau_{echo\_i}}} )} 2}} \right.} 2}}}{{{T_p} - ({{\tau_{ref\_i}} - {\tau_{echo\_i}}} )}}} \right]j{J_1}({{\beta_{IF}}} )\\ & \quad \times [{{J_0}({{\beta_{Ri}}} )({{E_1} + {E_2}} )+ {J_1}({{\beta_{Ri}}} )({E_3} + {E_4} + {E_5} + {E_6})} ], \end{aligned}$$

where ${\tau _{ref\_i}} = {\tau _{Ti}} - {\tau _0}$. ${\beta _{Ri}} = {{\pi {V_i}} \mathord{\left/ {\vphantom {{\pi {V_i}} {\sqrt 2 {V_\pi }}}} \right. } {\sqrt 2 {V_\pi }}}$ is the modulation index of MZMi and ${V_i}$ is the amplitude of the echo signal received by Rx_i. The spectrum components of E₁, E₂, E₃, E₄, E₅ and E₆ are illustrated in the inset B of Fig. 1(a), expressed as

(4)$$\begin{aligned} {E_h} &= \exp [{j{\omega_i}({t - {\tau_{Ti}}} )} ]\cdot \exp \{{j{{({ - 1} )}^h}[{{\omega_{IF}}({t - {\tau_{Ti}}} )+ \pi {k_{IF}}{{({t - {\tau_{Ti}}} )}^2}} ]} \},\\ {E_l} &= \exp [{j{\omega_i}({t - {\tau_{Ti}}} )} ]\cdot \exp \left\{ {j{{({ - 1} )}^l}\left[ {\begin{array}{c} {{\omega_{IF}}({t - {\tau_{Ti}}} )+ \pi {k_{IF}}{{({t - {\tau_{Ti}}} )}^2}}\\ { - 2{\omega_{IF}}({t - {\tau_{Ti}} + {\tau_{ref\_i}} - {\tau_{echo\_i}}} )}\\ { - 2\pi {k_{IF}}{{({t - {\tau_{Ti}} + {\tau_{ref\_i}} - {\tau_{echo\_i}}} )}^2}} \end{array}} \right]} \right\},\\ {E_m} &= \exp [{j{\omega_i}({t - {\tau_{Ti}}} )} ]\cdot \exp \left\{ {j{{({ - 1} )}^m}\left[ {\begin{array}{c} {{\omega_{IF}}({t - {\tau_{Ti}}} )+ \pi {k_{IF}}{{({t - {\tau_{Ti}}} )}^2}}\\ { + 2{\omega_{IF}}({t - {\tau_{Ti}} + {\tau_{ref\_i}} - {\tau_{echo\_i}}} )}\\ { + 2\pi {k_{IF}}{{({t - {\tau_{Ti}} + {\tau_{ref\_i}} - {\tau_{echo\_i}}} )}^2}} \end{array}} \right]} \right\}, \end{aligned}$$

where h=1, 2; l=3, 4; m=5, 6. Then, E₁, E₂, E₃ and E₄ are selected by an optical band-pass filter (OBPFi) for further de-chirp processing and transmitted to the CO with a fiber-induced delay of ${\tau _{Ri}}$.

In the CO, all the echo-modulated reference signals are combined by WDM3 and sent to a low-speed PD (PD2) after being amplified by EDFA2. Due to the different wavelengths of the optical carries from different Rxs, parallel de-chirp processing for all echo signals is implemented in PD2. The output de-chirped signal is written as

(5)$${S_R}\left( t \right) = \sum\limits_{i = 1}^N {{S_{Ri}}\left( t \right) = \sum\limits_{i = 1}^N {\left\{ {\begin{array}{l} {{V_{Ri}} \times rect\left[ {\frac{{t - {\tau _i} + {{\Delta {\tau _i}} \mathord{\left/ {\vphantom {{\Delta {\tau _i}} 2}} \right. } 2}}}{{{T_p} - \Delta {\tau _i}}}} \right]}\\ { \times \cos \left[ {2\pi {k_{RF}}\Delta {\tau _i}\left( {t - {\tau _i}} \right) + 2\pi {f_{RF}}\Delta {\tau _i} - \pi {k_{RF}}\Delta {\tau _i}^2} \right]} \end{array}} \right\}} } ,$$

where ${\tau _i} = {\tau _{Ti}} + {\tau _{Ri}}$, $\Delta {\tau _i} = {\tau _{ref\_i}} - {\tau _{echo\_i}} = {\tau _{Ti}} - {\tau _0} - {\tau _{echo\_i}}$. Here, ${f_{RF}} = 2{f_{IF}}$ and ${k_{RF}} = 2{k_{IF}}$ are the frequency and the chirp rate of the transmission radar signal, respectively. ${V_{Ri}}$ is the amplitude of the de-chirped signal of Rx_i. The frequency components higher than ${f_{RF}}$ are filtered out by an electrical low-pass filter (ELPF). From Eq. (5), each de-chirped signal ${S_{Ri}}(t )$ has a different frequency of ${k_{RF}}\Delta {\tau _i}$ as shown in Fig. 1(b), which is negatively related to ${\tau _{echo\_i}}$ (corresponding to the target range) and positively related to ${\tau _{Ti}}$, thus it can be distinguished and extracted from the spectrum of the de-chirped signal ${S_R}(t )$. In this way, N-channel parallel ISAR imaging processing can be implemented. After parallel de-chirp processing in PD2, the detected signal is digitized by an analog-to-digital converter (ADC) for offline 3D imaging processing with a digital signal processor (DSP). Here, two points should be noted: (1) the fiber delays should satisfy ${\tau _{Ti}} - {\tau _0} \ge {\tau _{echo\_i}}$; (2) from Eq. (5), the frequency spacings between the adjacent de-chirped signals are ${k_{RF}}[{({{\tau_{Ti + 1}} - {\tau_{Ti}}} )- ({{\tau_{echo\_i + 1}} - {\tau_{echo\_i}}} )} ]$, mainly depending on the transfer delay differences (${\tau _{Ti\textrm{ + }1}} - {\tau _{Ti}}$). In order to avoid the spectrum overlapping of the de-chirped signals of different channels, the width of the range window is limited to less than $c \times \min ({{\tau_{Ti + 1}} - {\tau_{Ti}}} )/2$. In other words, for the target range window from ${R_{\min }}$ to ${R_{\max }}$, the fiber delays should satisfy $c({{\tau_{Ti}} - {\tau_0}} )/2 \ge {R_{\max }}$ and $c({{\tau_{Ti + 1}} - {\tau_{Ti}}} )/2 \ge {R_{\max }} - {R_{\min }}$. Consequently, the range window of the target should be rapidly estimated via some UHF radars before imaging, according which the range window width and maximum imaging range of the system could be reconfigured employing tunable fiber delay lines to change ${\tau _0}$ and ${\tau _{Ti}}$. Besides, for sufficient effective bandwidth, the increment of the number of receivers would limit the width of the range window to some extent.

2.2 Array ISAR 3D imaging method based on the proposed MWP radar system

The 3D imaging geometry of the system is depicted in Fig. 2. For convenience, a 3D Cartesian coordinate system is established. The range, cross-range and height directions are along Y-axis, X-axis and Z-axis respectively. The antenna array is composed of a transmitting antenna and N receiving antennas. Under the far-field imaging condition ($R > 2{L^2}{f_{RF}}/c$, R is the distance between the antenna and the target, L is the distance between each pair of transmitting and receiving antennas), there are N APCs forming a ULA in the height direction. With the system described above, each APC operates as an independent channel and multi-channel ISAR imaging can be conducted using the de-chirped signal ${S_R}(t )$, finally obtaining N 2D ISAR images and completing 3D reconstruction. The flowchart of the 3D imaging method is depicted in Fig. 3.

Fig. 2. The 3D imaging geometry of the system.

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Fig. 3. Flowchart of the 3D imaging method based on the proposed MWP radar system.

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The range fast Fourier transform (FFT) of the digitized de-chirped signal ${S_R}(t )$ is carried out to reconstruct the range profile of the target, obtaining

(6)$${I_R}(f )= \sum\limits_{i = 1}^N {{A_{Ri}}{\mathop{\rm sinc}\nolimits} [{{T_p}^{\prime}({f - {k_{RF}}\Delta {\tau_i}} )} ]} \exp \left\{ j\left( {\begin{array}{l} {2\pi {f_{RF}}\Delta {\tau_i} - 2\pi {k_{RF}}\Delta {\tau_i}{\tau_i} - 2\pi f{\tau_i}}\\ { + 2\pi f\Delta {\tau_i} - \pi {k_{RF}}\Delta {\tau_i}^2} \end{array}} \right) \right\},$$

where ${T_p}^{\prime} = {T_p} - \Delta {\tau _i}$ and f is the fast-time frequency. In the phase of ${I_R}(f )$, the second term $- 2\pi {k_{RF}}\Delta {\tau _i}{\tau _i}$ and the third term $- 2\pi f{\tau _i}$ are both induced by the fiber transmission delay, which can cause the location of a target to be displaced in cross-range and deteriorate the coherence between channels for 3D reconstruction. The fourth term $2\pi f\Delta {\tau _i}$ and the last term $- \pi {k_{RF}}\Delta {\tau _i}^2$ are both induced by the de-chirp processing (the former is induced by the rectangular envelope delay and the latter is the residual video phase), which can smear the cross-range point scatterer response and defocus the image [24]. Considering the echo is range-compressed to a narrow pulse at the frequency of ${k_{RF}}\Delta {\tau _i}$, only the phase at $f = {k_{RF}}\Delta {\tau _i}$ need to be compensated. The above four terms are rewritten as

(7)$$\Delta {\phi _1}(f )= 2\pi f\Delta {\tau _i} - \pi {k_{RF}}\Delta {\tau _i}^2 = \pi {f^2}/{k_{RF}}.$$

(8)$$\Delta {\phi _2}({f,i} )={-} 2\pi {k_{RF}}\Delta {\tau _i}{\tau _i} - 2\pi f{\tau _i} ={-} 4\pi f{\tau _i}.$$

The compensation of $\Delta {\phi _1}$ can be achieved through multiplying ${I_R}(f )$ by the function [25]

(9)$${S_{c1}}(f )= \exp ({ - j\Delta {\phi_1}} )= \exp ({ - j\pi {f^2}/{k_{RF}}} ).$$

The phase error $\Delta {\phi _2}$ should be compensated according to the spectrum ranges of the de-chirped signals of each Rx via multiplying the range-compressed signals of each channel in Eq. (6) by the function

(10)$${S_{c2}}({f,i} )= \exp ({ - j\Delta {\phi_2}} )= \exp ({j4\pi f{\tau_i}} ).$$

Here, ${\tau _i}$ is determined by the corresponding fiber lengths, which can be obtained before imaging processing. Two points should be noted; (1) The error of ${\tau _i}$(expressed as ${\tau _{i\Delta }}$) can reduce the compensation accuracy, leading to a relative cross-range error of $2{k_{RF}}{\tau _{i\Delta }}/{f_{RF}}$. For a system working at a center frequency of 16 GHz with a bandwidth of 2 GHz and a duration of 200 µs, when the cross-range width of target is smaller than 1 km, a cross-range error less than 0.1 m requires ${\tau _{i\Delta }}$< 0.8 µs, corresponding to a fiber length error of 16 m which is achievable. (2) The fluctuation of ${\tau _i}$ during the echo signal collection (expressed as ${\tau _{i\delta }}$), can deteriorate the coherence between channels for 3D reconstruction, leading to defocusing. Generally, the variation of $\Delta {\phi _2}$ is required to be less than 5° for good coherence and the coherent integration time is far less than 1 min. The temperature dependence of fiber delay is less than 1×10⁻⁵ /°C. Under the circumstances that the frequency of the de-chirped signal is less than 1 GHz and the longest distance between the transmitting and receiving antennas is 1 km, the required ${\tau _{i\delta }}$ within the coherent integration time is less than 0.07 °C, corresponding to the temperature change rate of 4 °C/h which is usually attainable. For longer fiber transmission or a higher frequency of the de-chirped signal, the phase noise should be carefully analyzed to determine whether further compensation is necessary. The range profile of the target after phase compensation is

(11)$$\begin{aligned} {I_R}(f )&= \sum\limits_{i = 1}^N {{A_{Ri}}{\mathop{\rm sinc}\nolimits} [{{T_p}^{\prime}({f - {k_{RF}}\Delta \tau } )} ]} \exp ({j2\pi {f_{RF}}\Delta \tau } )\\ & = \sum\limits_{i = 1}^N {{A_{Ri}}{\mathop{\rm sinc}\nolimits} \left\{ {{T_p}^{\prime}\left[ {f + \frac{{{k_{RF}}}}{c}({{R_T} + {R_{Ri}} - 2{R_{ref\_i}}} )} \right]} \right\}} \\ & \times \exp \left[ { - j\frac{{2\pi {f_{RF}}}}{c}({{R_T} + {R_{Ri}} - 2{R_{ref\_i}}} )} \right], \end{aligned}$$

where ${R_{ref\_i}} = {{c{\tau _{ref\_i}}} \mathord{\left/ {\vphantom {{c{\tau_{ref\_i}}} 2}} \right.} 2} = {{c({{\tau_{Ti}} - {\tau_0}} )} \mathord{\left/ {\vphantom {{c({{\tau_{Ti}} - {\tau_0}} )} 2}} \right.} 2}$, ${R_T}$ and ${R_{Ri}}$ are the distances from the target to Tx and Rx_i respectively. By cross-range pulse compression, N complex 2D ISAR images are obtained

(12)$$\begin{aligned} {I_i}({f,{f_m}} )&= {A_i}{\mathop{\rm sinc}\nolimits} \left\{ {{T_p}^{\prime}\left[ {f + \frac{{{k_{RF}}}}{c}({{R_T} + {R_{Ri}} - 2{R_{ref\_i}}} )} \right]} \right\}{\mathop{\rm sinc}\nolimits} \left\{ {{T_A}\left[ {{f_m} + \frac{{({{V_T} + {V_{Ri}}} )}}{\lambda }} \right]} \right\}\\ & \times \exp \left[ { - j\frac{{2\pi {f_{RF}}}}{c}({{R_T} + {R_{Ri}} - 2{R_{ref\_i}}} )} \right], \end{aligned}$$

where ${f_m}$ is the Doppler frequency, ${V_T}$ and ${V_{Ri}}$ are the relative radial velocities of the target with respect to Tx and Rx_i respectively, $\lambda$ is the central wavelength of the transmitted radar signal. The first two Sinc functions represent the target’s range and Doppler information. Taking ${I_1}$ as the master image, through image registration, scatterers with the same range and Doppler frequency fall into the same pixel in the ISAR images but with different phases. Taking the height of a dominant scatterer as the reference, the amplitude and phase inconsistencies between the channels are corrected, obtaining

(13)$$\begin{aligned} {I_{i,j}}({f,{f_m}} )&= A{\mathop{\rm sinc}\nolimits} \left\{ {{T_p}^{\prime}\left[ {f + \frac{{{k_{RF}}}}{c}({{R_T} + {R_{R1}}} )} \right]} \right\}{\mathop{\rm sinc}\nolimits} \left\{ {{T_A}\left[ {{f_m} + \frac{{({{V_T} + {V_{R1}}} )}}{\lambda }} \right]} \right\}\\ & \times \exp \left[ { - j\frac{{2\pi {f_{RF}}}}{c}({{R_T} + {R_{R1}}} )} \right] \times \exp \left[ { - j\frac{{8\pi {f_{RF}}b{h_j}}}{{c({{R_T} + {R_{R1}}} )}}({i - 1} )} \right]. \end{aligned}$$

Here, b is the distance between two adjacent APCs, h_j is the relative height of the jth scatterer with respect to the first APC. Employing classical Fourier beamforming methods [26], the height information of scatterers is extracted and 3D reconstruction is completed.

3. Experiment and results

A proof-of-concept experiment is carried out. An MWP radar with fiber-distributed antenna array for 3D imaging is established and composed of a CO, a Tx and two Rxs shown in Fig. 4. Since the target is not too far from antennas, to achieve 3D imaging under the far-field conditions, the antennas do not have to be too far apart. Only the fibers transmitting replicas from CO to Rx₁ and Rx₂ are set as 150 m and 400 m long in order to avoid spectrum overlapping of the de-chirped signals, while the other fibers connecting the CO, Tx, Rx₁ and Rx₂ are just a few meters long.

Fig. 4. Experimental setup of the proposed MWP radar.

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In the CO, two optical carriers generated by two lasers (RIO orion and TeraXion PS-TNL) at 1549.32 nm and 1550.12 nm with powers of 13 dBm and 10 dBm are multiplexed by WDM1 and fed into an MZM (EO-space). An LFM CW that is generated by an arbitrary waveform generator (AWG) (Tektronix, AWG70001A) with a 7.5-GHz central frequency, a 1-GHz bandwidth and 200-µs time duration is amplified to 18 dBm and drives the MZM which is biased at the null point for photonic frequency doubling. The optical spectrum of the photonic radar signal generated by MZM is shown in Fig. 5(a), which is measured by an optical spectrum analyzer (Yokogawa, AQ6370D). It can be seen the photonic radar signal is replicated with two different optical carriers. After amplified by EDFA1, two replicas are split by WDM2. The first replica split into two parts in a power ratio of 90:10. The first part (10%) is transferred to the Tx and detected by PD1 with an input light power of 2 dBm to fulfill frequency doubling, generating a Ku-band radar signal with a bandwidth of 2 GHz. Figure 5(b) shows the electrical spectrum of the radar signal measured by a spectrum analyzer (Keysight, N9030A). The radar signal is amplified to 10 dBm and transmitted by an antenna with a gain of 22 dBi. The second part (90%) of the first replica and the second replica, as the photonic reference signals, are transmitted to Rx₁ and Rx₂ respectively. In each Rx, the echo signal is received by an antenna with the same gain of 22 dBi and amplified by an LNA and fed into an MZM biased at the quadrature point to modulate the respective photonic reference signal. The output modulated signals from MZM1 and MZM2 are filtered by OBPF1 (Yenista, XTM-50) and OBPF2 (Finisar, WaveShaper 4000s) respectively to select the desired sidebands, i.e. E₁, E₂, E₃ and E₄ mentioned above, and travel back to the CO. After combined by WDM3 and amplified by EDFA2, the echo-modulated reference signals are sent to PD2 for parallel de-chirp processing with an input light power of 3 dBm. Both the transition spectra of OBPF1, OBPF2 and the optical spectra of the echo-modulated reference signals before and after optical filtering are shown in Fig. 6, measured by the same optical spectrum analyzer (Yokogawa, AQ6370D). The de-chirped signal obtained from PD2 is digitized by an oscilloscope (Keysight, DSO-X 92004A) with a sample rate of 200 MSa/s for offline 3D imaging processing.

Fig. 5. (a) The optical spectrum of the replicated photonic radar signal output by MZM. (b) The electrical spectrum of the transmitted radar signal.

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Fig. 6. The transition spectra of OBPFs and the optical spectra of the echo-modulated reference signals before and after optical filtering.

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To evaluate the 3D reconstruction capability of the proposed radar system, demonstration of turntable 3D imaging of three TCRs is conducted. Figure 7 illustrates the relative positions of the antenna array and the TCRs accompanied with the photos of the antenna array’s back view and TCRs’ front view. Three TCRs are placed on a wooden stand fixed on a turntable 9 m away from the antennas in Y direction. The distances between every two adjacent TCRs in both Y and Z directions are 25 cm. In X direction, TCR1 and TCR3 are in the same position while TCR2 is 50 cm away from them. In order to form a ULA on the Z-axis, the emitting antenna is fixed, and two receiving antennas are 64 cm apart in Z direction and simultaneously move downward 8 cm once and for 7 times. In addition, the TCRs repeat rotation around Z direction and meanwhile two receiving antennas collect echo signals in each pair of positions for parallel 2D ISAR imaging, equivalent to 16 Rxs receiving echoes simultaneously and thereby forming a ULA of 16 APCs on the Z-axis. The equivalent aperture is 0.6 m long with a 4 cm spacing between adjacent APCs. In this way, the range, cross-range and height directions are along Y-axis, X-axis and Z-axis respectively. Although the far-field condition is not satisfied due to the limited space, the phase error caused thereby can be compensated via the phase inconsistence correction steps described above. In addition, for the time-space synchronization requirements of 3D reconstruction, a photoelectric switch composed of a laser and a PD is used to ensure the consistency of the target position in the 2D ISAR imaging of each channel. The laser rotates with the TCRs, and the PD is stationary nearby. When the TCRs rotate to a certain position, the PD will detect the laser light and output a trigger signal for de-chirped signal collection.

Fig. 7. The relative positions of the array antennas and the TCRs.

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First, a measurement of the static TCRs is performed. The spectrum of the recorded de-chirped signal is shown in Fig. 8. There are obviously two range windows around 7.45 MHz and 20.15 MHz with respect to Rx₁ and Rx₂. Three peaks in each window can be found corresponding to the three TCRs. The frequency differences between each two adjacent peaks in both two windows are 18.3 kHz and 25.3 kHz, corresponding to the ranges of 27.4 cm and 37.9 cm. The center frequency difference between two windows is about 12.7 MHz, which is equivalent to a time delay of 1.27 µs and well consistent with the length difference of the fibers connecting Tx to Rx₁ and Rx₂. In addition, the clutter in the second window are higher than that in the first window, which is caused by the difference between Rx₁ and Rx₂ in the gain and the intensity of the received clutter.

Fig. 8. The spectrum of the recorded de-chirped signal.

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Afterwards, 3D imaging experiment of the rotating TCRs is carried out. The wooden stand supporting TCRs repeats rotation at a speed of 15.6 degrees/s, while Rx₁ and Rx₂ move downward simultaneously for 7 times and in each pair of positions ISAR imaging with a coherent integration time of 0.6 s is implemented. In this way, 16 complex 2D images are obtained and then image registration is completed preparing for 3D reconstruction. Figure 9 shows two images obtained simultaneously by Rx₁ and Rx₂ in a pair of positions. The results indicate that the positions of the three TCRs both in range and cross-range directions are the same, and the relative positions of the three TCRs are also consistent with the actual positions. Taking TCR2 as the reference, the amplitude and phase inconsistency between APCs are corrected and the 3D reconstruction is realized by FFT along height dimension. The reconstructed 3D model of targets is in Fig. 10 and the orthographic projections of the reconstructed results on three planes are also presented in gray dots. To further analyze the 3D reconstruction quality, the power slices in range, cross-range and height of the imaged TCRs are shown in Fig. 11. The calculated 3D resolutions (3 dB width) are 7.3 cm in range direction, 5.6 cm in cross-range direction, and 13.3 cm in height direction (corresponding to an elevation resolution of 0.85° at the range of 9 m), which are close to the theoretical values, i.e. 6.6 cm (range) × 5.4 cm (cross-range) × 0.85° (elevation). The relative positions of the three TCRs are consistent with the actual positions. The distances between each two TCRs are calculated and compared with the actual values, shown in Table 1.

Fig. 9. 2D ISAR images obtained by (a) Rx₁ and (b) Rx₂ at one time.

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Fig. 10. 3D reconstruction results of the imaged TCRs.

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Fig. 11. Slices in range, cross-range and height directions of the imaged TCRs.

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Table 1. Comparison of measured and actual distances between the TCRs

View Table

4. Conclusion

An MWP radar with a fiber-distributed antenna array for 3D imaging is proposed based on the photonics-assisted signal generation, RoF transmission, and photonic parallel de-chirp processing. With a single Tx and multiple Rxs, a ULA radar with 16 equivalent APCs is established experimentally, working in Ku band with 2 GHz bandwidth. Accurate 3D reconstruction of the three moving TCRs is accomplished, achieving a range resolution of 7.3 cm, a cross-range resolution of 5.6 cm, and an elevation resolution of 0.85°. The proposed system provides a promising solution for large-scale distributed radar with a simple structure. The imaging results verify the feasibility of MWP radar in high-resolution 3D reconstruction.

Funding

National Key Research and Development Program of China (2018YFA0701900, 2018YFA0701901); National Natural Science Foundation of China (61690191, 61701476).

Disclosures

The authors declare no conflicts of interest.

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Microwave photonic radar with a fiber-distributed antenna array for three-dimensional imaging

Abstract

1. Introduction

2. Principle

2.1 Architecture of the proposed MWP radar system

2.2 Array ISAR 3D imaging method based on the proposed MWP radar system

3. Experiment and results

4. Conclusion

Funding

Disclosures

References

Cited By

Figures (11)

Tables (1)

Equations (13)

Optics Express