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Abstract
A photonic generation scheme of a programmable coherent linear frequency modulated (LFM) signal is proposed and experimentally demonstrated. By heterodyne beating an agile optical frequency comb (OFC) with a fixed OFC, LFM signals in different bands can be obtained. The two OFCs are generated independently from two arms of a single dual-drive Mach-Zehnder modulator (DDMZM) and are then propagated through the same optical path, thus naturally ensuring the coherence of the LFM pulses at the minimum cost. The generation of the agile OFC only requires a sweeping intermediate frequency (IF) signal with the far lower center frequency and smaller bandwidth than the generated LFM signal. And by precisely controlling this IF signal, parameters of the LFM signal can be flexibly adjusted such as the center frequency, bandwidth, time duty, and sweeping pattern. In addition, envelope-tailorable LFM pulsed signals are further realized by pre-distorting the IF signal, supporting future multifunctional radar applications. We then establish a complete X-band radar system. The pulse-to-pulse phase coherent integration of the generated LFM signal enhances the signal-to-noise ratio of echo signals by ∼24 dB. A 5.8 cm range resolution is finally achieved, which is comparable to more complex photonic radar systems. This compact DDMZM based scheme not only improves the radar performance by realizing coherence pulses but also provides full control of these pulses, evidently benefiting the system integration and multifunctionality in future advanced radar applications.
© 2019 Optical Society of America under the terms of the OSA Open Access Publishing Agreement
1. Introduction
The linear frequency modulated (LFM) pulsed signal is one of the most common radar signals which maintains both high-power and high-resolution advantages because of its large time-bandwidth product (TBWP) characteristic [1]. To further meet the multifunctional demands of advanced radar systems, it requires more flexible adjustment of LFM signal parameters [2,3]. Meanwhile, the increasing needs for LFM signals with higher center frequencies and wider bandwidths also bring great pressure on traditional electrical schemes [4,5]. Thus, the photonics-based microwave signal generation technique shows a promising prospect thanks to its inherent advantages such as the large bandwidth, low loss, high agility and etc. [4–6].
In the past decades, many photonics-based LFM signal generation schemes have been proposed which can be mainly classified into two types. One is the frequency-to-time mapping method [7,8]. Although programmable high-frequency broadband LFM signals are achievable, the time durations of pulses are usually limited to a dozen nanoseconds due to the small time-delay provided by dispersive elements. The other type is based on the heterodyne beating of well-controlled optical spectral lines most commonly from different tones of agile optical frequency combs (OFCs) [9,10]. The OFC can be produced by a mode-locked laser [11,12] or electro-optic modulators driven by intermediate-frequency (IF) signals [13–15]. Compared with the mode-locked laser approach, the electro-optic modulator leads to wider bandwidths, larger TBWPs as well as superior reconfigurability benefiting from direct frequency multiplications [16–18]. Furthermore, dual OFCs with different repetition rates can be generated simultaneously by specially-designed electro-optic modulator schemes, which have higher flexibility such as obtaining multiband radar signals. In [19], two OFCs are first generated and propagated through two sets of cascaded modulators and then combined with each other. Because the two optical paths are separated, phase fluctuations may be induced by temperature variations and mechanical vibrations so that the pulse-to-pulse phase coherence is destroyed. To solve this problem, we used the optical phase-locked loop between two optical paths in [20] to accomplish phase coherence but the system complexity increased accordingly. Besides frequency and bandwidth characteristics, the fine controlling of LFM pulse shapes is also crucial for optimizing pulse peak-to-average ratio and for advanced radar applications. However, the frequency response of a radar transmitter is always uneven within broadband. Therefore, the envelope of the LFM pulsed signal is hard to control.
In this paper, we propose a simple and compact photonics-based scheme to generate programmable coherent LFM signals. Two OFCs with agile and fixed repetition rates are produced synchronously from two arms of a single dual-drive Mach-Zehnder modulator (DDMZM) ensuring the coherence of the LFM pulses. By using a programmable multi-channel waveshaper, multi-band LFM signals are obtained from independent channels. The frequency multiplication of the low-frequency narrowband IF signal is easily realized by selecting high-order optical lines and then implementing heterodyne beating procedures. Thus, LFM signals with high-frequencies, broadbands, and multiband characteristics are generated. Furthermore, through the programmable control of the IF signal, both time and spectral domain parameters of the LFM signal can be flexibly adjusted. Diverse shapes such as rectangular, sinusoidal, triangular, and sawtooth LFM pulses can be acquired, showing the envelope-tailorable ability. Then we establish a complete coherent X-band radar system, and a ∼9 dB signal-to-noise ratio (SNR) gain of echo signals is achieved with every tenfold time of coherent pulse integrations. When applying the radar to a dual-target detection experiment, the range resolution is measured to be ∼5.8 cm which is comparable to more complex photonics-based radar systems.
2. Principle
2.1 LFM signal generation
The core of generating highly reconfigurable LFM signals is first to generate an agile OFC and a fixed OFC with a single DDMZM and second to beat their specific spectral lines. The schematic diagram of the LFM signal generation scheme is shown in Fig. 1. A narrowband LFM signal is first obtained by selecting the lower sideband of a mixing signal of an IF signal and a radio frequency signal (shown as RF1). The IF signal can be described as
Then two arms of a single DDMZM are driven by this narrowband LFM signal and another single-tone RF2 signal, respectively. After the electro-optic modulation, two OFCs with agile and fixed repetition rates are generated synchronously with the expressions as follows
This compact scheme uses only a low-frequency narrowband IF signal to generate the high-frequency broadband LFM signal by virtue of direct frequency multiplication brought by the high-order optical carriers. In this way, the ingenious photonics-based method greatly eases the requirement for the large-bandwidth waveform generator thus reducing the system cost. Furthermore, this system has the ability to generate multiband LFM signals by properly filtering different-order pairs of optical lines simultaneously. Then multiband radars with the enhanced range resolution can be established which have both searching and tracking functions and better detection probability of small targets. Thanks to the symmetrical structure of two arms and the same propagation path of two OFCs, the systematic coherence is naturally assured which is essential in pulse doppler radars. Compared with our previous work [20], this compact design greatly reduces the system complexity and is very suitable for cost-sensitive, integrated applications.
2.2 Precise adjustment of LFM signals
The various parameters of the generated LFM signals can be precisely adjusted by controlling the IF signal. In the time domain, the pulse width and time duty of IF pulses are directly transferred to LFM pulses. While in the frequency domain, the center frequencies, bandwidths, as well as sweeping patterns of LFM signals, are multiple of those parameters of IF signals, depending on the frequency of the two beaten signals. Hence, through accurately selecting the desired optical-line order and setting IF signal parameters, the flexible reconfigurability of LFM signals can be realized.
Besides the aforesaid adjusting capabilities, we propose a pre-distortion method for controlling the shape of LFM pulses, which is of great use in the radar system. For example, the ideal rectangular LFM pulses can ensure the radar works at its maximum power and increase the radar detection distance. The procedures are as follows:
- • Firstly, design the amplitude of the desired LFM signal for each frequency in the time domain and import the corresponding waveform file of the IF signal into the arbitrary waveform generator (AWG);
- • Secondly, obtain the actual LFM signal measured by the real-time oscilloscope and transfer it to the Fourier domain;
- • Thirdly, calculate the theoretical values of the desired LFM pulse envelope in the Fourier domain and then record the ratios between the theoretical and measured envelope amplitude of each frequency point. According to the time-frequency linear mapping characteristic of LFM signals, the amplitude ratios of specific frequency points can directly represent the amplitude ratios of corresponding time-domain sections;
- • Finally, update the IF signal based on the ratios acquired in the previous step as a predistortion factor using Eq. (8):$${A_{\textrm{IF}\_\textrm{N}}}(f) = {A_{{\textrm{IF}\_\textrm{O}}}}(f)^{\ast} {P_{factor}} = {A_{{\textrm{IF}\_\textrm{O}}}}(f)^{\ast} (F({A_{\textrm{LFM}\_\textrm{T}}})/F({A_{\textrm{LFM}\_\textrm{M}}})).$$where ${A_{{\textrm{IF}\_\textrm{N}}}}(f)$ and ${A_{{\textrm{IF}\_\textrm{O}}}}(f)$ denote the amplitudes of newer and original IF waveforms at frequency f. $F({A_{\textrm{LFM}\_\textrm{T}}})$ and $F({A_{{\textrm{LFM}\_\textrm{M}}}})$ denote theoretical and measured LFM envelope amplitude transferred to the Fourier domain, respectively.
The above-mentioned pre-distortion method can be repeated several times to further improve the fidelity of the envelope shape. Note that the calculation and correction are done in the frequency domain for higher precision. In fact, LFM pulsed signals with rectangular, sinusoidal, triangular, sawtooth or any other shapes can all be obtained and optimized with this method. Diverse LFM pulses may find its versatile applications in next-generation multifunctional radars.
3. Experimental demonstration of programmable LFM signals
Figure 2 shows the schematic diagram of the photonics-based LFM signal generation system. A programmable IF signal within the S-band (2-3 GHz) is generated by an AWG (Keysight M8195A, 65 GSa/s), and a local oscillator (LO) signal of 27 GHz is generated by a signal generator (SG, R&S SMF100A). The AWG and the SG are synchronized by an external 10 MHz low noise frequency reference. The LO signal is equally divided into two paths by a power splitter. One branch is directly used as a modulation signal driving the lower arm of a DDMZM (Fujitsu, FTM7937EZ, ${V_\pi }\textrm{ = 1}\textrm{.8V}$, bias voltage = 0V, optical bandwidth (-3 dB): $\ge 25\textrm{GHz}$), and the other branch is mixed with the IF signal. The mixing signal is amplified by a power amplifier (PA) and only its lower sideband passes through the following bandpass filter. This narrowband LFM signal with the expression of Eq. (2) is then fed into the upper arm of the DDMZM. The power levels of two drive signals are both adjusted to ∼24 dBm. A 12-dBm continuous light-wave at 1550.26 nm is emitted from a fiber laser and is sent into the DDMZM. In this way, two OFCs with agile and fixed repetition rates are generated synchronously. After amplified by an erbium-doped fiber amplifier, the OFCs are then transferred into a programmable multi-channel waveshaper (Finisar, WaveShaper 4000s, minimum frequency selectivity: 1 GHz, minimum bandwidth: 10 GHz, insertion loss: 6.5 dB, optical isolation: 35 dB). Here the parameters of three waveshaper channels are appropriately set to select the + 1st, +2nd and + 4th-order pairs of optical lines respectively while other lines are filtered out. Each channel is followed by a photodetector (PD) to implement the optical-to-electrical conversion. The generated LFM signals are measured by a real-time oscilloscope (LeCroy, SDA845Zi-A, 120 GS/s).
Fig. 2. Schematic diagram of the experimental setup. AWG: arbitrary waveform generator; SG: signal generator; PS: power splitter; PA: power amplifier; BPF: electrical bandpass filter; DDMZM: dual-drive Mach-Zehnder modulator; EDFA: erbium-doped fiber amplifier; PD: photodetector; LFM: linear frequency modulated;
Dual OFCs are observed by an optical spectrum analyzer (APEX, AP2081A). The fixed OFC and agile OFC are shown in Figs. 3(a) and 3(b) respectively. Both OFCs have 9 comb lines whose optical power is more than -30 dBm. It is clear that the repetition rates of dual OFCs are 27 GHz and 24-25 GHz. Furthermore, direct frequency multiplications are demonstrated according to the width of high-order agile OFC tones. After setting the waveshaper to work as a multi-channel optical bandpass filter and carefully adjusting the center-frequency and bandwidth parameters of each channel, the + 1st, +2nd and + 4th-order pairs of optical lines are successfully obtained. The filtering result of the + 4th-order pair is displayed in Fig. 3(c). The optical power difference between + 4th-order optical lines and the adjacent + 3rd/+5th lines reaches ∼30 dBm.
Fig. 3. Optical spectrum graphs. (a) fixed OFC, (b) agile OFC, and (c) +4th-order pair of optical lines.
The tri-band LFM signal generation results are shown in Fig. 4. Figures 4(a), 4(b) and 4(c) illustrate the short-time Fourier transform (STFT) of S-band (2-3 GHz), C-band (4-6 GHz), and X-band (8-12 GHz) radar signals, respectively. The results verify the systematic ability to generate high-frequency broadband multiband LFM signals with only one low-frequency narrowband IF signal chirped from 2-3 GHz. Note that the LFM signal can even be extended to higher bands by selecting higher orders of optical lines. Thanks to the fusion technique of multiband data flows [12], this scheme has the potential to apply to complex situations such as long-distance and high-resolution target tracking.
Fig. 4. Tri-band LFM signals of (a) S-band (2-3 GHz), (b) C-band (4-6 GHz), and (c) X-band (8-12 GHz).
Taking the X-band radar signal as an example, Fig. 5 shows the precise adjustment of the generated LFM signals via the programmable control of the IF signals. The initial signal centered at 10 GHz with a 4-GHz bandwidth is demonstrated in Fig. 5(a). The time duration of this pulsed signal is 50 µs with a 50% duty cycle. By setting a longer time duration of 150 µs and a larger duty cycle of 75% to the IF signal, LFM pulses with a larger TBWP of 600000 are obtained in Fig. 5(b). Besides, modifying the center frequency and bandwidth of the IF signals will cause the proportional change of the LFM signals which are displayed in Fig. 5(c) and Fig. 5(d). In addition, the frequency sweeping pattern of the IF signals can be reset as decreasing, V-shaped or frequency-stepped modes. The corresponding results of the LFM signal are shown in Figs. 5(d)–5(f). By properly controlling fundamental parameters of the IF signal, the center frequency, bandwidth, sweeping pattern, and duty cycle of the generated LFM signal can be flexibly adjusted. Thus, the reconfigurability of the LFM generation system is fully realized.
Fig. 5. Programmable X-band LFM signals with different center frequencies, bandwidths, time duties, and sweeping patterns.
In Fig. 4 and Fig. 5, it is evident that the power values vary with different frequencies. This issue is introduced by the uneven frequency response of filters, PAs and the AWG. Thus, a pre-distortion method is used to improve the flatness of the rectangular pulse envelope of the LFM signal. Firstly, the original envelope shape (pulse width: 5 µs, duty ratio value: 50%) without any pre-distortion is directly collected by the oscilloscope and illustrated in Fig. 6(a). The overall trend of the rectangular edge is distinctly undulating. Then we operate pre-distortion procedures as described in the principle part on the IF waveforms. The flatness of the rectangular edge has been greatly improved as shown in Fig. 6(b). The STFT analysis associated with the time-domain signal is shown in Fig. 6(c). The power values are maintained at -85 dB/Hz and the sweeping linearity is well kept. This method is very concise which needs only two-round pre-distortion procedures to get the significant improvement of the rectangular envelope flatness. In this way, transmitting the compensated LFM signals with the constant amplitude value will guarantee radar operating at the peak power during the fulltime. The similar pre-distortion method can be applied to diverse envelope shapes. After only one round of pre-distortion, envelope-tailorable LFM pulses are obtained as shown in Figs. 6(d)–6(l), including sinusoidal, triangular, and sawtooth envelopes. All three kinds of envelope shapes are much closer to standard shapes using the pre-distorted IF waveforms. The results show the advantage of the pre-distortion method and the potential of generating multifunctional waveforms for future advanced radars.
Fig. 6. Envelope-tailorable pulsed LFM signal generation results. Rectangular, sinusoidal, triangular and sawtooth shapes are operated pre-distortion procedures. The first, second and third rows show the original envelope shapes without any pre-distortion, the optimized envelope shapes after pre-distortion and the associated STFT analyses, respectively.
4. Coherent X-band radar system and dual-target detection
We further build a complete X-band radar system to validate the quality and the coherence of the generated LFM signals as shown in Fig. 7(a). The photonics-based generation front end is followed by a power amplifier and then is sent to a transmitting antenna (Tx). The echo signal is collected by a receiving antenna (Rx). Two horn antennas are placed parallelly with a center-to-center space of ∼20cm in order to reduce the mutual-coupling interaction [21–25]. The half-power lobe widths of antennas are from 24° to 27°. The E-plane antenna pattern of 10 GHz is demonstrated in Fig. 7(b). After amplified by a low noise amplifier, the LFM signal is finally measured by the oscilloscope. Thanks to the proposed single DDMZM based scheme, the radar structure is very compact while remaining high coherence, which is practical for cost and volume sensitive applications.
Fig. 7. (a) Structure of the X-band radar. PA: power amplifier; LNA: low noise amplifier; Tx: transmitting antenna; Rx: receiving antenna, Fig. 7(b) E-plane antenna pattern of 10 GHz.
In coherent radar systems, pulse integrations can be implemented to achieve the SNR enhancement of echo signals. If n pulses with the same SNR were perfectly integrated by an ideal lossless pre-detection integrator, the integrated SNR would be increased by exactly n times [26]. Based on this theory, a single-target detection experiment is established. The pre-distorted rectangular LFM pulsed signal chirped at 9-11 GHz (pulse width: 5 µs, duty ratio value: 50%) is directly reflected from one target (a metal plate with a dimension of ∼20cm*10cm), and the echo signal is received by the Rx. Actually, when we use the AWG to generate IF signals, a synchronized trigger signal from another AWG output channel is generated at the same time. This trigger signal is a series of ultrashort pulses which mark the beginning of each IF signal pulse. We set the oscilloscope to be triggered at the rising edge of this trigger signal. Once a new echo signal pulse arrives, the “Average” function of the oscilloscope will add this new pulse to the former pulses and derive a new average value. Only if the pulse trains maintain coherence, the signal amplitude remains stable while the phase-disordered noise declines with the averaging process. Here we regard the ratio of the average signal level and the average noise level as the SNR. The SNRs of echo signals with 1-, 10-, 100-, 500- and 1000-time pulse integrations in the spectral domain are shown in Fig. 8. The amplitude peak values are all normalized to 0 dB. An approximate 9-dB SNR gain is acquired with every ten-fold integration time in Figs. 8(a)–8(d), which is close to the 10-dB theoretical value, verifying remarkable pulse-to-pulse phase coherence of this X-band radar system. When the integration times reaches more than 500, the analog-to-digital converters of the oscilloscope approach the quantization noise limit, and the SNR is no longer increased. It is a unique advantage of our coherent radar system that we don’t need to consider the minimum SNR. As long as the number of integrated pulses is large enough, the noise will decrease observably and the signal will become visible. Note that the amplitude fluctuations of the echo signal are due to the uneven frequency response of the receiver and the reflection characteristics of targets. Although other pairs of optical lines are removed by the optical bandpass filter, the cross-modulation of the two driving signals of the DDMZM still generates harmonics around 8 GHz, which falls in the filter passband. The power is 20 dB lower than the desired pulse, which might hinder the broadening of the X-band pulse signal if high pulse fidelity is required. This harmonic component can be eliminated by using a DDMZM whose two driving signals are strictly isolated or by using an electrical bandpass/bandstop filter to precisely remove the unwanted frequency component.
Fig. 8. Coherent pulse integration of the LFM echo signals. The spectral-domain SNRs of echo signals with (a) 1-time pulse integration, (b) 10-time pulse integrations, (c) 100-time pulse integrations, (d) 500-time pulse integrations, and (e) 1000-time pulse integrations.
Finally, a dual-target detection experiment is constructed to measure the range resolution of this system as shown in Fig. 9(a). The 8-12 GHz X-band LFM signal (pulse width: 5 µs, duty ratio value: 50%) is generated to detect dual targets (two metal plates with the same dimension of ∼20cm*10cm) which are placed side by side in the horizontal direction while separated by a distance along the ranging direction. Here we just measure the range resolution and don’t consider the aperture angle. The targets are ∼1.5 m distant from antennas. Foam pyramid microwave absorbers are used to reduce clutter echoes. While carefully shortening the horizontal distance between dual targets, a series of echo signals with different distances are collected after pulse compression processing. This time we don’t use the “Average” function and the SNR is ∼15 dB level. Here the transmitting LFM signal is used as the reference signal for matched filtering. The pulse compression results of different distances are shown in Figs. 9(b) and 9(c). The amplitude values are all normalized between 0 and 1. As can be seen, when dual targets are far apart from each other (∼40 cm), dual reflection peaks are clearly distinguished. When the distance continuously reduces, dual peaks gradually fuse with each other. When dual targets are at a distance of ∼5.8 cm, the fusion point of dual peaks is around the half maximum of the amplitude. This value can be regarded as the range resolution, which is similar to the ∼5.7 cm results measured in [7] and the theoretical value of 3.75 cm (${S_\textrm{r}}\textrm{ = }\frac{c}{{2{B_{\textrm{Tx}}}}}\textrm{ = 3.75} \thinspace \textrm{cm}$, where c is the velocity of light and ${B_{\textrm{Tx}}}$ is the pulse bandwidth). The slight resolution degradation is mainly due to the nonlinear frequency error and sidelobe influences [27], which can be improved by the real-time linearity correction method and adding windows to the frequency response of the matched filter.
Fig. 9. The dual-target detection with the proposed X-band radar. (a) Experimental configuration of the dual-target detection. Pulse compression results when the distance between dual targets is (b) ∼40 cm and (c) ∼5.8 cm.
In order to show the superior characteristics of our system, we list a comparison table of different photonics-based LFM radar systems as Table 1 indicates. We evaluate multiple crucial indicators including frequency bands, pulse widths, key techniques, envelope-tailorable characteristics, and range resolutions. As can be seen from the table, the proposed DDMZM based method has the highest reconfigurable capability in pulse width, envelope shape, bandwidth, and center frequency. Moreover, while keeping a similar range resolution, it has the lowest system complexity, which is very suitable for cost- and volume-sensitive radar applications.
Table 1. Comparison of different photonics-based LFM radar systems
5. Conclusion
In this paper, a photonics-based programmable coherent LFM signal generation scheme is proposed and the systematic reconfigurability is well demonstrated. Only low-frequency narrowband IF signals are needed to generate high-frequency broadband LFM signals by heterodyne beating high-order optical carriers. Thanks to the programmable control of the IF signal and waveshaper, the flexible adjustment of LFM signal parameters such as center frequencies, bandwidths, sweeping patterns, and multiband characteristics are achieved. By using the pre-distortion method for one or two rounds, envelope-tailorable pulsed LFM signals are also obtained. A complete X-band radar system is established based on this generation front end. Owing to the inherent pulse-to-pulse phase coherence brought by the DDMZM based LFM generation method, pulse integrations are implemented to enhance the SNR of echo signals by ∼24 dB. The ∼5.8 cm range resolution measurement result indicates the detection capability of our system. Compared with traditional electrical schemes, the photonics-based approach holds advantages such as the high precision and multifunctional control of LFM signals and low loss properties. This compact and cost-effective scheme will evidently benefit the system integration in future advanced radar applications.
Funding
National Natural Science Foundation of China (61690193, 61827807, 61901039).
Disclosures
The authors declare no conflicts of interest.
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