High-resolution W-band ISAR imaging system utilizing a logic-operation-based photonic digital-to-analog converter

Shaowen Peng; Shangyuan Li; Xiaoxiao Xue; Xuedi Xiao; Dexin Wu; Xiaoping Zheng; Bingkun Zhou

doi:10.1364/OE.26.001978

1. Introduction

Nowadays, W-band radar has been widely used in cloud observation, security check, autonomous cruise control systems, foreign objects debris (FOD) detection on runways and so on [1–5]. There are mainly three driving impetuses for the demand on W-band radars. Firstly, W-band wave can provide high reflection to dangerous metallic weapons and living tissues, as well as high penetration to certain materials such as paper, clothes, fog, smoke, clouds, etc [6, 7]. Besides, the W-band antenna is small, which can significantly reduce the bulk and weight of the radar system. Moreover, compared with the existing radars operating at low frequency [8–11], W-band radars can get more detail information of the target of interest with a higher spatial resolution thanks to its short wavelength and available bandwidth. Lots of W-band radars with different functions have been proposed recently [12–14]. In [12], a 3.9 mm range resolution was achieved in a W-band ranging radar. In [13], a two-dimensional inverse synthetic aperture radar (ISAR) imaging system was proposed and the results showed the effective range resolution is better than 3.1 cm. In [14], a 3-dimensional imaging radar system was presented with a longitudinal range resolution of 1.2 cm. In these radar systems, ISAR is one of the most important systems for automatic target recognition (ATR) and classification [15].

In order to realize high range resolution and fast imaging speed in an ISAR imaging system, broadband linear frequency modulated wave (LFMW) is always applied because the de-chirping process can significantly reduce the sampling rate and improve the speed of data processing [16]. Nevertheless, the frequency of the radio frequency (RF) signal generated by direct digital synthesizers (DDSs) is limited to a few gigahertz [17]. Nearly all of the W-band LFMWs in traditional electronic ISAR systems are generated by frequency up-conversion with cascaded multipliers and mixers. It not only seriously worsens phase noise of the generated signal [18], but also restricts the detecting resolution and influences imaging quality. In order to overcome these defects, photonic radio-frequency waveform generator is proposed and gets a rapid development in recent years [19]. Lots of methods to generate broadband LFMW have been presented, such as optical pulse shaping followed by frequency-to-time mapping (FTM) [12, 20, 21] and photonic digital-to-analog converter (PDAC) [22, 23]. The time aperture of the LFMW generated by FTM is limited to only several tens of nanoseconds, which seriously restricts the detecting range in radars. Though the time aperture of the LFMW generated by PDAC can be as large as several milliseconds, the bandwidth is usually limited by the rate of the driving digital signal. Therefore, generation of a broadband LFMW with large time-bandwidth product (TBWP) is a big challenge for W-band ISAR imaging system.

In this paper, we propose and demonstrate a photonic-based W-band ISAR imaging system utilizing a novel logic-operation-based photonic digital-to-analog converter (LOPDAC). Compared to conventional electrical digital-to-analog converter, the PDAC has the advantages of small time jitter, large bandwidth and immunity to electromagnetic interferences [24]. Because the equivalent sampling rate of the LOPDAC is twice as large as the rate of the digital driving signal, the LOPDAC can realize a broader bandwidth than the normal PDAC reported before, which significantly improves the range resolution of the W-band ISAR imaging system. At the transmitter, a broadband LFMW with a large time-bandwidth product (TBWP) is generated from the LOPDAC, then up-converted to W-band based on an optical frequency comb (OFC). At the receiver, the photonic-assisted de-chirping processing is applied to the down-converted echo. A high-resolution two-dimension image can be realized in the system thanks to the high frequency and large bandwidth of the transmitted signal. In the experiments, a photonic-based W-band ISAR with a TBWP as large as 79200 (bandwidth 8 GHz; temporal duration 9.9 us) is established. The radar system is evaluated through one-dimension range imaging of two metallic mirrors and two-dimension ISAR imaging of a pair of trihedral corner reflectors (TCRs). A two-dimension (range and cross-range) imaging resolution of ~1.9 cm × ~1.6 cm is achieved.

2. Principle

2.1 System configuration

Figure 1(a) shows the schematic diagram of the proposed W-band radar system. In the transmitter, an OFC is generated with the method presented in [25], which consists of a laser diode (LD1), an intensity modulator (IM), a phase modulator (PM), an amplifier (Amp1), a phase shifter, a power splitter (PS), and a signal generator (SG). Then two comb teeth spacing at $f_{R F} = n \cdot Δ f$ of the OFC are selected by the waveshaper and amplified by an erbium-doped fiber amplifier (EDFA), where $Δ f$ is the frequency interval of the comb teeth and $n$ is the interval number. An optical band-pass filter (OBPF) is utilized to reduce the amplified spontaneous emission (ASE) noise. After the OBPF, the selected two comb teeth is injected into a Mach-Zehnder modulator (MZM), which is biased at the quadrature point and driven by the IF-band LFMW generated by the LOPDAC. The instantaneous frequency of the IF-band LFMW can be expressed as $f_{I F} = f_{0} + k t$ , where $f_{0}$ is the initial frequency and $k$ is the chirp rate. When the amplitude of the driving signal is small, we just consider the two optical carriers and their first-order sidebands. Thus, after square-law detection at a photodetector (PD1), the up-converted LFMW is produced utilizing a band-pass filter (BPF1). By adjusting the frequency interval of the comb teeth and the number of the interval, a W-band LFMW can be obtained. The instantaneous frequency of the W-band LFMW can be expressed as $f_{W} = f_{0} + n \cdot Δ f + k t$ . Finally, the generated W-band LFMW is amplified by a power amplifier (PA1) and emitted to the free space through a horn antenna (HA1).

Fig. 1 (a) Schematic diagram of the proposed W-band radar system. (b) Schematic configuration of the LOPDAC. (c) Illustration showing a rate-doubled signal ( $i_{m}$ ) generated by logical operation of two lower-rate digital signals ( $s_{11}$ , $s_{12}$ ). LOPDAC: logic-operation-based photonic digital-to-analog converter; LD: laser diode; IM: intensity modulator; PM: phase modulator, Amp: amplifier; EDFA: erbium-doped fiber amplifier; OBPF: optical band-pass filter; MZM: Mach-Zehnder modulator; PD: photodetector; BPF: band-pass filter; PA: power amplifier; HA: horn antenna; SG: signal generator; PDAC: photonic digital-to-analog converter; PS: power splitter; DPMZM: dual-parallel MZM; LPF: low-pass filter; ADC: analog-to-digital converter; DSP: digital signal processing; LNA: low noise amplifier; OC: optical coupler; DMZM: dual-drive MZM.

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In the receiver, the echoes reflected from the targets are received by another horn antenna (HA2), amplified by a low noise amplifier (LNA) and down-converted to an IF-band LFMW by mixing with a frequency-multiplied signal of a sinusoidal source that is split from the SG. The multiplication order of the multiplier is the same as the interval number of the selected two teeth of the OFC, ensuring that the frequency of the down-converted IF-band LFMW is the same as the LFMW generated by the LOPDAC. A light wave from another laser diode (LD2) is fed into a dual-parallel MZM (DPMZM) to enable de-chirping processing, whose two sub-MZMs are modulated by two RF signals, separately. One is the reference LFMW split from the LOPDAC and the other is the down-converted LFMW, as mentioned before. Two sub-MZMs of the DPMZM are all biased at null transmission point (NTP), and the phase introduced by the main MZM is tuned to be zero. Thanks to the small modulation index and carrier suppression, we only consider the first-order sidebands. Using the Jacobi-Anger expansion, the output optical fields of the DPMZM can be expressed as

E_{o u t} (t) = - \frac{E_{i n} (t)}{2} {\begin{cases} r e c t (\frac{t}{T_{p}}) J_{1} (m_{1}) \cos [2 π * (f_{0} (t) + \frac{1}{2} k t^{2})] \\ + r e c t (\frac{t - τ}{T_{p}}) J_{1} (m_{2}) * \cos [2 π * (f_{0} (t - τ) + \frac{1}{2} k {(t - τ)}^{2})] \end{cases}}

where

E_{i n} (t)

is the input optical fields of LD2,

T_{P}

is the pulse width of the IF-band LFMW,

m_{1}

and

m_{2}

are the modulation indexes of the two sub-MZMs, separately, and

τ

is the time delay of the echo wave. Then the optical signal is sent to another photodetector (PD2) to perform an optical-to-electrical conversion. The desired signal, which has a low frequency at

f_{d e - c h i r p i n g} = k τ

, can be obtained after de-chirping processing with some high-frequency signal filtered by a low pass filter (LPF). According to [15], the theoretical range resolution of the radar is

δ_{r} = \frac{c}{2 B}

where

c

is the velocity of light and

B

is the bandwidth of the signal. The theoretical cross-range resolution is

δ_{a} = \frac{c}{2 ω T_{i} f_{c}} = \frac{c}{2 θ f_{c}}

where

ω

is the rotational velocity of the target,

T_{i}

is the coherent accumulation time,

f_{c}

is the center frequency of the LFMW, and

θ

is total viewing angle of the target rotating. From Eq. (3), it can be seen that there are two ways to improve the cross-range resolution. One is to increase the coherent accumulation time, but it influences the imaging speed and brings the phenomenon of hauling tail and moving blur [15], which will deteriorate the image quality. The other way is to transmit higher frequency signal, which is an efficient method. Therefore, the proposed W-band radar offers the advantage for high resolution of two-dimension ISAR imaging.

2.2 Principle of the LOPDAC

The schematic configuration of the proposed N-bit LOPDAC is shown in Fig. 1(b). In the configuration, N channels of incoherent continuous wave (CW) laser with different wavelengths are poured into N dual-drive MZM (DMZMs), respectively. The input optical powers of N branches are at the ratio of 1, 2, 4, 8… $2^{N - 1}$ , and the smallest/largest optical power corresponds to the least/most significant bit (LSB/MSB), respectively. The digital driving signal for each of the MZM is either ‘0’ or ‘1’, depending on the sampled and quantified data. By square-law detection in the photodetector (PD0), the N-channel data will superimpose incoherently. After being filtered by the band-pass filter (BPF0) and amplified by an amplifier (Amp0), the analog RF waveform can be obtained. Different from the traditional PDAC [22, 23], the sampling rate can be doubled by using the DMZM, which would enhance the bandwidth of the generated signal at a certain bit rate of the digital driving signal. To simplify the analysis, we just take channel 1 as an example. Two arms of the DMZM are driven by two non-return-zero (NRZ) digital driving signals $D_{11} (t) = v_{11} s_{11} (t)$ and $D_{12} (t) = v_{12} s_{12} (t - T / 2)$ , respectively, where $v_{11}$ and $v_{12}$ are the amplitudes of the two driving signals, $s_{11} (t)$ and $s_{12} (t - T / 2)$ are the binary codes designed according to the sampled and quantified data of the target waveform, and $T$ is the code width of the NRZ code. By adding the output of the two arms in the DMZM, we get the optical field at the output of the DMZM as

E_{o u t} (t) = E_{i n} (t) * \cos [\frac{β_{1} s_{11} (t) - β_{2} s_{12} (t - T / 2) - θ}{2}] \exp [j \frac{β_{1} s_{11} (t) + β_{2} s_{12} (t - T / 2) + θ}{2}]

where

β_{1} = π v_{11} / v_{π}

and

β_{2} = π v_{12} / v_{π}

are the modulation indices on the two arms of the DMZM, respectively,

v_{π}

is the half-wave voltage of the DMZM, and

θ

is the phase difference between the two arms. By turning the bias voltage to get

θ = π

and tuning the amplitude of the two driving signal to let

β_{1} = β_{2} = \frac{π}{2}

for bipolar code or let

β_{1} = β_{2} = π

for unipolar codes, the output current of the PD can be expressed as

\begin{matrix} i (t) \propto E_{o u t} (t) \cdot E_{o u t}^{*} (t) \\ = {\begin{matrix} 0 f o r s_{11} (t) = s_{12} (t - T / 2) \\ 1 f o r s_{11} (t) \neq s_{12} (t - T / 2) \end{matrix} \end{matrix}

Ignoring the amplitude of the output current, Eq. (5) can be rewritten as

{\begin{matrix} i (2 m) = s_{11} (m) \oplus s_{12} (m) \\ i (2 m - 1) = s_{11} (m) \oplus s_{12} (m - 1) \end{matrix}

where

m

is the ordinal number of the driving digital signal. Equation (6) shows that the output digital signal is directly determined by the two digital driving signals through XOR logic operation. For example, two low-rate digital signals 0100 and 0110 can be calculated to acquire a higher rate digital signal 00101110 according to Eq. (6), as shown in Fig. 1(c). Thus, the equivalent sampling rate of the LOPDAC is twice as large as the rate of the digital driving signal. Radio-frequency arbitrary waveforms, including FLMW, with large TBWP can be generated by the LOPDAC.

3. Experiment results and discussion

Experimental setup of the designed fully photonics-based W-band ISAR system is shown in Fig. 1. A 2-bit LOPDAC is implemented with two DMZMs (Fujitsu FTM7937EZ200). 4 channels of the designed 12 Gbit/s NRZ digital signal are generated from a pulse pattern generator (Anritsu MP1758A), and injected into the DMZMs to modulate two incoherent CW lasers after their relative delays being controlled and amplified by a digital signal amplifier (OA4SMM4). The two modulated optical signals are coupled together to PD0 (Discovery Semiconductors, Inc.) and transformed into a photocurrent. Filtered by BPF0 and amplified by Amp0, the electrical LFMW with a bandwidth of 8 GHz (2-10 GHz), a pulse width of 9.9 us and a period of 10 us is generated. Figure 2 shows the waveform and the instantaneous frequency of the LFMW acquired by the short-time Fourier transform (STFT) analysis. The signal-to-noise ratio (SNR) of the LFMW is 5.2 dB due to the quantization error related with the low bit number of the LOPDAC and the performance of the electronic devices, such as Amp0. The SNR would be greatly improved if more bits can be implemented and the performance of the electronic devices can be optimized. Then it is split into two parts with a 50:50 power splitter (PS). One is sent to an MZM (Eospace AZ-DV5-40-PFA-LV-SLB60) in the transmitter as an IF-band LFMW, and another is sent to a DPMZM (Fujitsu FTM7961EX) in the receiver as a reference LFMW, separately.

Fig. 2 Generation of the LFMW with a bandwidth of 8 GHz (2-10GHz), a pulse width of 9.9us and a period of 10us. (a)The waveform and (b) the instantaneous frequency of the generated LFMW.

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In the transmitter, the driving signal of the OFC is a sinusoidal signal at 14.5 GHz generated by an SG (Agilent E8403A). By adjusting the phase shifter and the bias voltage of the IM, an OFC can be generated. A waveshaper (Finisar WaveShaper 4000S) is used to select the $\pm 3$ side teeth of the OFC. Then it is fed into an MZM with a 3-dB bandwidth of 40 GHz and a half-wave voltage of 2.8 V, which is biased at the quadrature point and modulated by the IF-band LFMW generated by the LOPDAC. At the output of the MZM, a 100-GHz PD (Finisar XPDV4121R) is used to transform the light wave into a photocurrent, which is filtered by a BPF1 with a center frequency of 94 GHz and a bandwidth of 10 GHz and amplified by Amp1 with a gain of 22 dB, subsequently. To this point, the IF-band LFMW is up-converted to a W-band LFMW, which is emitted to the free space through HA1 with a gain of 25 dBi. The spectrum of the W-band signal with a bandwidth of 8 GHz (89-97 GHz) is shown in Fig. 3, which is measured by a spectrum analyzer (Agilent E8403A) with a Millimeter-Wave Frequency Extension Modules.

Fig. 3 The spectrum of the W-band LFMW with a bandwidth of 8 GHz (89-97 GHz)

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In the receiver, the echo received by HA2 is amplified by an LNA with a gain of 20 dB. Then it is down-converted to an IF-band LFMW through a mixer with a six multiplier signal of a 14.5 GHz-sinusoidal signal split from the SG. A light wave at 1550.116 nm with a power of 16 dBm from LD2 (Keysight N7714A) is sent to a DPMZM, which is modulated by the reference LFMW and the down-converted LFMW amplified by Amp2 with a gain of 26 dB. The output optical wave from the DPMZM is sent to PD2 to perform the optical-to-electrical conversion. The de-chirped signal can be obtained after the high-frequency interference signal is filtered by an LPF with a 3-dB bandwidth of 100 MHz and amplified by Amp3 with a gain of 30 dB.

To check the range resolution of the radar system, two static metallic mirrors are placed at a distance of ~0.80 m away from the antenna pair, as shown in Fig. 4. Firstly, we adjust the static metallic mirrors and make them separated by 2.7cm. The de-chirped signal is sampled and recorded utilizing the real-time oscilloscope (Agilent DSO81204B) working at a sampling rate of 100 MSa/s. By zero-padding, 9900-point discrete Fourier transform (DFT) is performed and the spectrum of the signal can be obtained, as shown in Fig. 5(a). The minimum spectral spacing is 10.1 KHz, in other words, the minimum range spacing is 0.187cm in range imaging. From Fig. 5(a), It can be clearly seen that the two tones are separated 0.14MHz away, meaning that the range distance between the two mirrors is 2.6 cm by calculating, which matches well with the relative position of the two mirrors. Then we move one mirror close to another mirror little by little, and we can still distinguish this two mirrors when they are separated by 1.9 cm. Figure 5(b) shows the spectrum of the sampled signal. It shows that the two tones are separated 0.1 MHz away, meaning that the range distance between the two mirrors is 1.9 cm, which also matches well with the relative position of the two mirrors. Thus, the results show that the range resolution of this system is close to the theoretical value of 1.875 cm according to Eq. (2).

Fig. 4 Configuration for detecting two metallic mirrors placed at a distance of ~0.80 m away from the antenna pair.

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Fig. 5 (a) spectrum of the de-chirped echo from two metallic mirrors separated by 2.7 cm; (b) spectrum of the de-chirped echo from two metallic mirrors separated by 1.9 cm.

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Then a two-dimension imaging experiment is performed to evaluate the imaging performance of the proposed W-band ISAR system. Two TCRs are placed on a rotating platform with a rotation speed of 100 r/min, as shown in Fig. 6(a). The two TCRs are separated approximately by 7.4 cm in both the range direction and the cross-range direction. The distance between the rotating platform and the antennas pairs is about 0.85 m. The de-chirped signal is still sampled and recorded utilizing the real-time oscilloscope working at a sampling rate of 100 MSa/s. For the sake of cross-range resolution and imaging quality, the signal is sampled for 10 ms for every imaging picture, which includes 1000 pulses. During that time, the rotating angle of the TCRs is $6^{°}$ . Figure 6(b) shows the obtained ISAR image. As can be seen, two TCRs can be clearly distinguished in the image, and both the distances of range direction and cross-range direction between the TCRs are 7.4 cm, corresponding to the real distances. According to Eq. (3), the cross-range resolution is 1.54 cm in this experiment. Thus, a 2-D (range and cross-range) imaging resolution of ~1.9 cm × ~1.6 cm is obtained. Compared to the ISAR proposed in [9–11], this W-band radar can realize a higher cross-range resolution with the same accumulated time when the target is same. In other words, this W-band radar needs a shorter accumulation time to obtain a same cross-range resolution for ISAR imaging. Moreover, real-time digital signal processing at 100 MSa/s sampling rate is not a problem in modern digital radar receivers for constructing an ISAR image [11]. Therefore, our W-band radar system has the potential to provide high-resolution and real-time imaging with an ultra-high frame rate.

Fig. 6 (a) Configuration of detecting two rotating TCRs; (b) ISAR image of two rotating TCRs.

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4. Conclusion

We have presented and experimentally demonstrated a high-resolution W-band ISAR imaging system utilizing an LOPDAC. The equivalent sampling rate of the LOPDAC is twice as large as the rate of the digital driving signal. Compared with the normal PDAC reported before, this LOPDAC can generate a signal with larger bandwidth, which ensures a high imaging resolution. In the experiment, a photonics-based W-band radar with a TBWP as large as 79200 (bandwidth 8 GHz; temporal duration 9.9 μs) is established. And a two-dimension resolution of ~1.9 cm × ~1.6 cm with a sampling rate of 100 MSa/s is verified.

Funding

National Nature Science Foundation of China (NSFC) under grant No. 61690191, 61690192, 61420106003, 61621064; Chuanxin Funding; Beijing Natural Science Foundation under grant 4172029.

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High-resolution W-band ISAR imaging system utilizing a logic-operation-based photonic digital-to-analog converter

Abstract

1. Introduction

2. Principle

2.1 System configuration

2.2 Principle of the LOPDAC

3. Experiment results and discussion

4. Conclusion

Funding

References and links

Cited By

Figures (6)

Equations (6)

Optics Express