Photonics-based multi-band linearly frequency modulated signal generation and anti-chromatic dispersion transmission

Kun Zhang; Shanghong Zhao; Aijun Wen; Weile Zhai; Tao Lin; Xuan Li; Guodong Wang; He Li

doi:10.1364/OE.388200

1. Introduction

With the increasing complexity of observation scenes, modern radar systems are evolved to perform multiple functionalities, such as small target detection, Doppler blind-speed elimination and multiband detection [1–3]. This challenge requires radar systems to operate at multiple bands. However, electronic bottlenecks bring the problems of limited bandwidth, low central frequency and poor frequency reconfigurability. To remedy this deficiency, photonic approaches are widely investigated to generate flexible microwave waveform, especially the linearly frequency modulated (LFM) signals, offering advantages of wide frequency tunability and electromagnetic interference immunity. One typical approach to LFM signal generation is based on space-to-time mapping [4] or frequency-to-time mapping [5], but the system has poor stability and bulky structure. Approach based on Fourier domain mode lacked optoelectronic oscillator (FDML-OEO) can also be employed to generate LFM signals with large time-bandwidth product (TBWP) [6]. However, the frequency tunability is limited by the reflection bandwidth of the phase-shifted fiber Bragg grating (PS-FBG). An improved method of FDML-OEO combined with stimulated Brillion scattering is employed to enhance the frequency tunability [7]. Besides, LFM signals can be generated by introducing parabolic signal to phase-coherent lightwaves, but the TBWP is always limited by the maximum power of the modulator [8]. To solve this problem, phase-encoding method [9] or electrically split parabolic waveform approach [10] is proposed to improve the time duration or bandwidth of the LFM signal, which, however, has complicated operation and deteriorated spectrum purity. Other approaches based on changing the input power of the external injection light [11] or photonic frequency up-converting the intermediate-frequency (IF) LFM signal [12] are also proposed to generate LFM signal with high carrier frequency. It should be noted that all the mentioned approaches are difficult to generate multi-band LFM signals simultaneously.

Multi-band radar systems can achieve multiple functionalities for the multi-carrier frequencies employed [13]. In [14], by using an integrated dual-polarization quadrature phase shift keying (DP-QPSK) modulator, dual-band LFM signals at different frequencies are generated. To expand the carrier frequency number, mode-locked laser (MLL) based approach is proposed [15], but bandwidths of the generated LFM signals are limited to the repeated rate of the MLL. In [16], two coherent optical frequency combs (OFCs) are used as multi-frequency optical LOs. By modulating one comb with IF-LFM signal, LFM signals with flexible central-frequency can be obtained, while separated optical paths lead to the LFM signal a large phase noise. Optical phase-locked loop can enhance the phase coherence, but photonic processors make the system complex and bulky [17]. To remedy this problem, an approach based on dual-driven Mach-Zehnder modulator (DDMZM) is employed to generate an agile OFC and a fixed OFC in the two arms [18]. By precisely controlling the IF signal, programmable LFM signals with high phase coherence are generated and demonstrated in X-band radar system. For the coherent multi-band LFM signals employed, the signal-to-noise ratio (SNR) increases exponentially. In the multistatic radar system, signal processing and generation are conducted in central station (CS). After fiber transmission, remote base stations (BSs) radiate the signal to free space and complete the target detection. However, for the double-sideband (DSB) modulation brought, the previous dual-OFC systems face the chromatic-dispersion-induced power fading (CDIPF) problem [19]. To remedy this deficiency, approach based on DP-QPSK modulator is proposed to generate and transmit dual-chirp signal with anti-chromatic dispersion ability, while the carrier frequency is limited [20].

In this paper, we propose and experimentally demonstrate a photonic-based system to generate multi-band LFM waveforms with anti-CDIPF ability. In the CS, the DP-QPSK modulator is respectively driven by an RF signal and an IF-LFM signal to generate flexible OFC and frequency shift lightwave. Benefiting from the multiple optical LO offered by the OFC, multi-band LFM signals with high carrier frequency can be generated simultaneously. Thanks to employ the frequency shift lightwave, CDIPF phenomenon in the fiber transmission is totally eliminated, and multi-band LFM signals with largest power can be obtained in every remote BS. The anti-chromatic dispersion processes are completed in the CS, which effectively reduces the costs and operational complexity of the BSs. The multi-band LFM signals are generated by modulating a single optical source, which endows low phase noise and high phase coherence. Besides, benefiting from frequency un-conversion processing, the system can generate LFM signals with high carrier frequency beyond the bound of the devices.

2. Theory and principle

Figure 1 shows the schematic of the proposed multi-band LFM signals generator. A linearly polarized lightwave is emitted from the laser diode (LD), and injected into the DP-QPSK modulator, which consists of two QPSKMs and a polarization beam combiner (PBC). In the upper QPSKM1, the sub-MZM1 is driven by an RF signal with angular frequency of ω_RF and amplitude V_RF, while the sub-MZM2 is not connected to the RF signal. Optical outputs from QPSKM1 can be given as:

(1)$$\begin{aligned}{E_{up}}(t) &= \frac{{{E_{in}}(t)}}{4}\left\{ \begin{array}{l} \exp \left( {j\frac{\pi }{{{V_\pi }}}{V_{\textrm{bias}1}}} \right)\exp \left[ {j\frac{\pi }{{2{V_\pi }}}{V_{RF}}\sin ({{\omega_{RF}}t} )} \right] + \exp \left[ { - j\frac{\pi }{{2{V_\pi }}}{V_{RF}}\sin ({{\omega_{RF}}t} )} \right]\\ + \exp \left[ {j\frac{\pi }{{{V_\pi }}}({{V_{\textrm{bias2}}} + {V_{\textrm{bias3}}}} )} \right] + \exp \left( {j\frac{\pi }{{{V_\pi }}}{V_{\textrm{bias3}}}} \right) \end{array}\right\}, \end{aligned}$$

where E_in(t)=E_cexp(jω_ct) represents the optical carrier from LD, E_c and ω_c are the amplitude and angular frequency of the optical carrier, m_RF=πV_RF/2V_π is the modulation index of sub-MZM1, V_π is the half-wave voltage of the MZMs, V_bias1, V_bias2 and V_bias3 are the three bias voltages respectively. Equation (1) can be simplified by the first Bessel function as:

(2)$${E_{up}}(t) = \frac{{{E_{in}}(t)}}{4}\left\{ {\sum\limits_{n ={-} \infty }^{ + \infty } {[{\exp ({j{\varphi_1}} )+ {{( - 1)}^n}} ]{J_n}({{m_{RF}}} )\exp ({jn{\omega_{RF}}t} )} + \exp j[{{\varphi_2} + {\varphi_3}} ]+ \exp ({j{\varphi_3}} )} \right\},$$

where Jn is the nth first-kind Bessel function, φ₁=πV_bias1/V_π, φ₂=πV_bias2/V_π and φ₃=πV_bias3/V_π are the three bias phases respectively. To obtained a OFC, amplitudes of the different order harmonics should be equal.

Fig. 1. Schematic diagrams of (a) the proposed multi-band LFM signal generator with anti-CDIPF transmission; (b) layout of the DP-QPSK mod; (c) structure of remote receiver. LD, laser diode; PC, polarization controller; DP-QPSK mod, dual-polarization quadrature phase shift keying modulator; PR, polarization rotator; PBC, polarization beam combiner; PBS, polarization beam split; SMF, single-mode fiber; EDFA, erbium-doped fiber amplifier; BPD, balanced photodetector.

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Intensities of the optical carrier and nth-order (n≠0) sidebands from QPSKM1 can be respectively expressed as:

(3a)$$\begin{aligned}{I_{up0}} \propto {|{{E_{up0}}} |^2} &= \frac{{{{|{{E_{in}}} |}^2}}}{8}\{{({1 + \cos {\varphi_1}} )J_0^2({m_{RF}}) + \cos ({\varphi_2}) + [{\cos ({{\varphi_1} - {\varphi_2} - {\varphi_3}} )} } \\ &\quad+ {\cos ({{\varphi_2} + {\varphi_3}} )+ \cos ({{\varphi_1} - {\varphi_3}} )+ \cos ({\varphi_3})} ]{J_0}({m_{RF}}) + 1 \}, \end{aligned}$$

(3b)$${I_{upn}} \propto {|{{E_{up{\kern 1pt} n}}} |^2} = \frac{{{{|{{E_{in}}} |}^2}}}{8}[{1 + {{( - 1)}^n}\cos ({\varphi_1})} ]J_n^2({m_{RF}}).$$

Solving the equation I_up_±1=I_up_±2, we get:

(4)$$\cos ({{\varphi_1}} )= \frac{{J_1^2({{m_{RF}}} )- J_2^2({{m_{RF}}} )}}{{J_1^2({{m_{RF}}} )+ J_2^2({{m_{RF}}} )}}.$$

From Eq. (4) we can know, for any m_RF, there is always a proper φ₁ to make I_up_±1=I_up_±2. Then, equation I_up₀=I_up_±1 can also be obtained by adjusting φ₁ and φ₃:

(5)$${\sin ^2}(\frac{{{\varphi _1}}}{2})J_1^2({m_{RF}}) - {\cos ^2}(\frac{{{\varphi _2}}}{2}) - {\cos ^2}(\frac{{{\varphi _1}}}{2})J{}_0^2({m_{RF}}) = 2\cos ({\varphi _3} - \frac{{{\varphi _1} - {\varphi _2}}}{2})\cos (\frac{{{\varphi _2}}}{2})\cos (\frac{{{\varphi _1}}}{2}){J_0}({m_{RF}}).$$

From Eq. (4) and Eq. (5), we can know that flat 5-line OFC can be obtained by properly adjusting m_RF, φ₁, φ₂ and φ₃. For example, when m_RF=0.83, V_bias1=0.13V_π, V_bias2=-0.3V_π and V_bias3=-0.8V_π can be adjusted to generate 5-line OFC. Furthermore, adjusting m_RF to realize I_up±1=I_up±3 and combining the 5-line OFC generation, equation I_up0=I_up±1=I_up±2=I_up±3 is realized. Thence, flat 7-line OFC can also be obtained by properly adjusting m_RF and three bias voltages, i.e., m_RF=3.05, V_bias1=0.63V_π, V_bias2=0.92V_π and V_bias3= 0.73V_π.

Mathematically, optical field of the OFC from QPSKM1 can be expressed as:

(6)$${E_{up}}(t) = A\{{\exp (j{\omega_c}t) + \exp j({\omega_c} \pm {\omega_{RF}})t + \cdots + \exp j[{{\omega_c} \pm (n - 1)/2{\omega_{RF}}} ]t} \},$$

where A and n (n≤7) are the amplitude and comb number of the OFC.

In the bottom QPSKM2, the two sub-MZMs are driven by IF-LFM signals with 90° electrical hybrid. Then, optical outputs from QPSKM2 are given as:

(7)$${E_{bot}}(t) \propto {E_c}(t)\left\{ \begin{array}{l} [{\exp ({jm\cos ({\omega_{\textrm{IF}}}t + k{t^2}) + j{\theta_1}} )+ \exp ({ - jm\cos ({\omega_{\textrm{IF}}}t + k{t^2})} )} ]\exp ({j{\theta_3}} )\\ + [{\exp ({jm\sin ({\omega_{\textrm{IF}}}t + k{t^2}) + j{\theta_2}} )+ \exp ({ - jm\sin ({\omega_{\textrm{IF}}}t + k{t^2})} )} ]\end{array} \right\},$$

where m=πV_IF/2V_π is the modulation index of the QPSKM2, V_IF, ω_IF and k are the peak voltage, carrier frequency and chirp rate of the IF-LFM signal, θ₁, θ₂ and θ₃ are DC bias phases of the two sub-MZMs and the main-MZM, respectively. It is well known that frequency shift lightwave can be obtained by applying quadrature RF signals into QPSKM [21]. Here, the two sub-MZMs are set at minimum transmission point (MITP), and the main-MZM are set at quadrature transmission point (QTP), corresponding to θ₁, θ₂ and θ₃ of π, π and π/2. Under small signal condition and ignoring high-order sideband, the optical fields from QPSKM2 can be written as:

(8)$${E_{bot}}(t) \propto {E_c}(t){J_1}(m )\exp [{j({\omega_{\textrm{IF}}}t + k{t^2})} ].$$

The OFC from QPSKM1 and frequency shift lightwave from QPSKM2 are combined with orthogonal polarization directions via PBC, and can be given as:

(9)$${E_{PBC}}(t) = \hat{x}{E_{up}} + \hat{y}{E_{bot}},$$

where $\hat{x}$ and $\hat{y}$ donate the polarization directions of the PBC.

Then the two orthogonal-polarization lightwaves are multiplexed for single-mode fiber (SMF) transmission. The transfer function of the SMF can be expressed as [22]:

(10)$$H(j\omega ) = \exp \left[ {\frac{{ - \alpha L}}{2} + \frac{{j{\beta_2}L{{(\omega - {\omega_c})}^2}}}{2}} \right],$$

where L, α and β₂ are the length, fiber attenuation and dispersion coefficient of the SMF. The outputs of the SMF can be written as:

(11)$${E_{SMF}}(t) = \left[ \begin{array}{l} {E_{x1}}(t)\\ {E_{y1}}(t) \end{array} \right] = {E_c}\exp (j{\omega _c}t)\exp (\frac{{ - \alpha L}}{2})\left\{ \begin{array}{l} \frac{A}{{{E_c}}}\sum\limits_{p = 0}^{(n - 1)/2} {[{\exp ({\pm} jp{\omega_{RF}}t)\exp (j{\varphi_p})} ]} \\ {J_1}(m )\exp [{j({\omega_{\textrm{IF}}}t + k{t^2})} ]\exp (j{\varphi_{IF}}) \end{array} \right\},$$

where φ_IF=β₂L(ω_IF)²/2 and φ_p=β₂L(pω_RF)²/2 are the dispersion-induced phase shift of IF-LFM signal and p-order OFC as relative to the optical carrier, respectively.

Then the remote transmission lightwaves are split into two paths by the PBS, of which the polarization axes have angles of 45° and 135°. The two outputs from PBS can be expressed as:

(12a)$${E_{P1}}(t) = {E_{x1}}(t)\cos {45^ \circ } + {E_{y1}}(t)\sin {45^ \circ },$$

(12b)$${E_{P2}}(t) = {E_{x1}}(t)\cos {135^ \circ } + {E_{y1}}(t)\sin {135^ \circ }.$$

The separated optical signals are introduced into BPD for square-law detection. And the photocurrent of the PD1 can be given as:

(13)$$\begin{aligned}{i_1}(t) &= \eta E_{P1}^ \ast (t) \times {E_{P1}}(t)\\ &= \eta E_c^2\exp ( - \alpha L)\left\{ \begin{array}{l} J_1^2(m) + \frac{{2A{J_1}(m)}}{{{E_c}}}\sum\limits_{l = 0}^{(n - 1)/2} {\cos [{(l{\omega_{RF}} + {\omega_{\textrm{IF}}})t + k{t^2} + {\varphi_{IF}} - {\varphi_l}} ]} \\ + \frac{{2A{J_1}(m)}}{{{E_c}}}\sum\limits_{i = 1}^{(n - 1)/2} {\cos [{(i{\omega_{RF}} - {\omega_{\textrm{IF}}})t - k{t^2} - {\varphi_{IF}} + {\varphi_i}} ]} \\ + \sum\limits_{h = 0}^{(n - 1)} {{A_h}\cos (h{\omega_{RF}}t + {\varphi_h})} \end{array} \right\}, \end{aligned}$$

where η is the responsivity of the PD1, A_h and φ_h are the amplitude and phase of the generated harmonics microwave signals at frequency of hω_RF, which are related to the dispersion-induced phase shifts from the OFC. In Eq. (13), multi-band LFM signals at central frequencies of (lω_RF+ω_IF) (0≤l ≤ n/2-1/2) and (iω_RF-ω_IF) (1<i ≤ n/2-1/2) are generated, while DC and one-tone RF signals also appear in the photocurrent. To remedy this problem, BPD is employed to eliminate harmonic components. The generated photocurrent of BPD is given as:

(14)$$\begin{aligned}{i_{BPD}}(t) &= \eta E_{P1}^\ast (t) \times E_{P1}^\ast (t) - \eta E_{P2}^\ast (t) \times E_{P2}^\ast (t)\\ &= \textrm{4}\eta A{J_1}({m_2}){E_c}\exp ( - \alpha L)\left\{ \begin{array}{l} \sum\limits_{l = 0}^{(n - 1)/2} {\cos [{(l{\omega_{RF}} + {\omega_{\textrm{IF}}})t + k{t^2} + {\varphi_{IF}} - {\varphi_l}} ]} \\ + \sum\limits_{i = 1}^{(n - 1)/2} {\cos [{(i{\omega_{RF}} - {\omega_{\textrm{IF}}})t - k{t^2} - {\varphi_{IF}} + {\varphi_i}} ]} \end{array} \right\}. \end{aligned}$$

Comparing with Eq. (13), DC term and one-tone signal terms are eliminated for the balanced detection. Thence, background-free multi-band LFM signals with opposite chirp rates are generated. In central frequencies (lω_RF+ω_IF) (0≤l ≤ n/2-1/2), the generated LFM signals have positive chirp, while in central frequencies of (iω_RF-ω_IF) (1<i ≤ n/2-1/2), the generated LFM signals have negative chirp. LFM signals with opposite chirps can effectively eliminate range-Doppler coupling from single-chirp signal, which applies to distance and velocity measurements of maneuvering targets [23]. Besides, to avoid frequency overlap between adjacent channels, the constraint (ω_RF-2ω_IF>2πB) should be satisfied, where B = kT/π is the bandwidth of the IF-LFM signal.

From Eq. (14), we can know the fiber dispersion only has impact on the initial phases of the generated multi-band signals rather than the amplitudes. Thereby, the CDIPF effect in SMF transmission is eliminated, indicating that multi-band LFM signals can be transmitted to remote BSs with maximum power. The generation and processing of multi-band signals are conducted in CS, and transmitted to every remote BS by SMFs with anti-CDIPF, which can reduce the BSs cost and volume. Compared with Ref. [16], the generated multi-band LFM signals feature good phase coherent for a single integration modulator offered. Different from Refs. [17,18], the proposed approach can generate and transmit multi-band LFM signals to remote BS with the larger power for the anti-CDIPF ability featured.

3. Experiment demonstration

To verify the feasibility of the proposed multi-band LFM signals generator, experiments are demonstrated based on Fig. 1. In the experiment, LD (Emcore 1782) emits a linearly polarized lightwave with wavelength of 1552.25 nm and power of 14 dBm. Then, the lightwave is introduced into the DP-QPSK modulator (FTM7977EX), which is driven by an RF signal from microwave signal generator (MSG, R&S SMW200A) and an IF-LFM signal from arbitrary waveform generator (AWG, Tektonix AWG7082) respectively. The DP-QPSK modulator has an insertion loss of 15 dB and each sub-MZM has a half-wave voltage of 4 V and extension of 35 dB. The fiber (Corning SMF-28e) has an attenuation of 0.2 dB/km, chromatic dispersion of 18 ps/nm·km and polarization mode dispersion (PDM) of 0.06 ps/km^1/2. After SMF transmission, a BPD (Finisar XPDV 2150R) with responsivity of 0.6 A/W is employed to perform square-law detection. The optical spectra, electrical spectra and waveforms are respectively monitored by an optical spectrum analyzer (Advantest Q8384), an electrical spectrum analyzer (Rohde Schwarz FSV30) and a real-time oscilloscope (DSOV334).

In the upper QPSKM1, the sub-MZM1 is driven by an RF with carrier frequency of 7.5 GHz and modulation index of 0.83. After properly adjusting the V_bias1, V_bias2 and V_bias3, 5-line OFC can be generated from QSPK1, as shown in Fig. 2 with red line. The flatness is 0.36 dB, and the unwanted sideband suppression ratio is about 30 dB, demonstrating a quasi-rectangular spectral shape. In the bottom QPSKM2, we use AWG to generate two quadrature IF-LFM signals with temporal duration of 1 µs, central frequency of 1.7 GHz and bandwidth of 0.4 GHz. Modulation indices of the IL-LFM signals are set to 0.8. After adjusting the two sub-MZMs at MITP and the main-MZM at QTP, frequency shift lightwave is generated, as shown in Fig. 2 with blue line. Optical carrier is suppressed and the frequency shift is 1.7 GHz. For the polarization alignment error of the PBS, OFC signals also exist and the optical polarization suppression ration is 28.1 dB.

Fig. 2. Output spectra of the DP-QPSK modulator. OFC in red line and frequency shift lightwave in blue line.

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Then the two orthogonally polarized wavelengths are transmitted to remote BSs with 50 km SMF. In the BS, erbium doped fiber amplifiers (EDFA) compensates the power of the lightwaves to -6 dBm. After heterodyning detection in BPD, five-band LFM signals with bandwidth of 0.4 GHz are generated in BPD. The waveform and electrical spectrum are given in Fig. 3(a) and Fig. 3(b). It is noticed that carrier frequencies of the IF-LFM signals are respectively up-converted to L (1.7 GHz), C (5.8 GHz), X (9.2 GHz), and Ku (13.3 GHz, 16.7 GHz) bands. As compared with OFC in Fig. 2, flatness of the multi-band signals is reduced to 3.6 dB, which is mainly for the uneven responsivity of the BPD. Thus, the proposed approach is immune to CDIPF affect from SMF and can transmit multi-band LFM signals to remote BSs with the largest power. Besides, DC and one-tone RF signals at 7.5 GHz and 15 GHz appear in the electrical spectrum, which are mainly caused by the limited extinction ratio of DP-QPSK modulator and unbalanced detection of BPD. In practice application, radar systems can employ bandpass filters to suppress harmonic components.

Fig. 3. (a) Waveform, (b) electrical spectrum and (c) instantaneous frequency-time diagram of the five-band LFM signal with 50 km SMF transmission.

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Figure 3(c) shows the time-frequency diagram of the waveform, which is extracted by short-time Fourier transform (STFT). It is noticed that LFM signals at 1.7 GHz, 9.2 GHz and 16.7 GHz have positive chirp, while LFM signals at 5.8 GHz and 13.3 GHz have negative chirp. Temporal duration and bandwidth of the LFM signals are 1 µs and 0.4 GHz, corresponding to a TBWP of 400. Carrier frequency and bandwidth of the generated multi-band signals are mainly limited by the sampling rate of the AWG, which can be improved by photonic frequency multiplying operation [12]. Time-frequency curves of the five-band LFM signals are bright, indicating that the CDIPF effect in SMF transmission are suppressed.

The multi-band LFM signals are generated by modulating the single optical carrier, showing good phase coherence performance and low phase noise, which can be used in distributed coherent radar system. Every BS in the radar system operates at certain frequency. After date fusion in CS, an integrated recognition on detecting target will be achieved. In our experiment, to separate the five-band LFM signals, electrical filters with bandwidth of 3 GHz and central frequencies at 2 GHz, 5.5 GHz, 9.5 GHz, 13 GHz and 17 GHz are employed. Figure 4(i) and Fig. 4(ii) show the waveforms and exacted instantaneous frequencies in every BS. For the uneven responsivity of the BPD, LFM signal in 5th BS owns a little lower power and darker time-frequency curves. To investigate the detection performance, auto-correlations of the generated waveforms are conducted, as shown in Fig. 4(iii). The full width at half-maximums (FWHM) of the auto-correlation peaks are 2.97 ns, 2.78 ns, 2.85 ns, 2.75 ns and 3.01 ns, respectively, corresponding pulse compression ratios (PCR) of 337, 360, 251, 363 and 332. Therefore, thanks to the anti-chromatic dispersion processing, all BSs can receive LFM signals with largest power from CS.

Fig. 4. (i) Waveforms, (ii) instantaneous frequency-time diagrams and zoom-in view of the auto-correlation peaks of the generated LFM signals in the (a) BS1st to (e) BS5th, respectively.

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As contrasts, multi-band LFM waveforms generation and transmission with DSB modulation scheme are conducted. In this research, initial phases of the two driven IF-LFM signals are set to the same. The main-MZM of the QPSKM2 is set to bias at maximum transmission point (MATP). Thence, optical outputs of the QPSKM2 contain ±1st sidebands from IF-LFM signal. Then the sweeping DSB signal is polarization-coupled with OFC from QPSKM1 in PBC. After 50 km SMF transmission and amplified to -6 dBm by EDFA, the two orthogonally polarized wavelengths are introduced into BPD for heterodyne detection. Waveform and electrical spectrum of the photocurrent are shown in Fig. 5(a) and Fig. 5(b). For the low carrier frequency, power of the LFM signal at 1.7 GHz remains unchanged, while powers of the LFM signals at 5.8 GHz and 9.2 GHz are about 14.6 dB lower due to the CDIPF effect. Seriously, LFM signals at 13.3 GHz and 16.7 GHz are drowned in the noise. Thus, the DSB approach suffers from CDIPF problem, which may result in a lower power receive in remote BS. Electrical amplifier (EA) can enhance the LFM signals with faded power, but the SNR will be destroyed. Figure 5(c) shows the frequency-time diagram by STFT. It is noticed that chirp frequency curves at five central frequencies are obtained. But due to the CDIPF effect, time-frequency curves at 13.3 GHz and 16.7 GHz become faded.

Fig. 5. (a) Waveform, (b) electrical spectrum and (c) instantaneous frequency-time diagrams of the five-band LFM signal with 50 km SMF transmission under DSB condition.

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The generated multi-band LFM signals are separated by electrical filters in every BS. In the Fig. 6(a_i), LFM waveform at L band (1.75 GHz) is obtained. In the Fig. 6(a_ii), time-frequency diagram shows bright curve in the temporal duration of 1 µs, corresponding to a chirp rate of 0.4 GHz/µs. Auto-correlation of the generated waveform is conducted, as shown in Fig. 6(a_iii). FWHM of the auto-correlation peak is 3.05 ns, and the PCR is calculated to 332. PCR of the generated waveform after autocorrelation is approximately equal to the TBWP, indicating that CDIPF has little impact on the LFM signal at 1.7 GHz. In Fig. 6(b_ii), the time-frequency curve becomes darker. In the auto-correlation Fig. (b_iii), the FWHM is 1.56 ns, corresponding to a PCR of 641. Visibly, the PCR is not equal to TBWP due to the low SNR of the generated LFM signal. In the Fig. 6(c_ii), the time-frequency curve is very dim. In the Fig. 6(c_iii), FWHM of the generated waveform after auto-correlation is 1.225 ns, corresponding to a PCR of 725. Obviously, envelope of the auto-correlation peak is no longer a Sinc function, indicating that CDIPF has serious impact on the generated LFM waveform.

Fig. 6. (i) Waveforms, (ii) instantaneous frequency-time diagrams and (iii) autocorrelation functions of the generated LFM signals in (a) BS1, (b) BS3 and (b) BS5 under CS-DSB approach. The insets present the zoom-in view of the auto-correlation peaks.

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Furthermore, carrier frequencies of the RF signals are set at 5.3 GHz and 8.5 GHz, and the central frequency and bandwidth of the IF-LFM signal are set at 1.5 GHz and 0.2 GHz to evaluate the anti-CDIPF performance of the proposed approach, with the electrical spectra given in Fig. 7. In Fig. 7(a), multi-band LFM signals at L (1.5 GHz), S (3.8 GHz), C (6.8 GHz), X (9.1 GHz) and Ku (12.1 GHz) bands are obtained. The flatness is 2.0 dB. In Fig. 7(b), for the increased frequency of the driven RF signal, multi-band LFM signals at L (1.5 GHz), C (7 GHz), X (10 GHz), Ku (15.5 GHz) and K (18.5 GHz) band are obtained. The flatness become to 1.9 dB for the uneven responsivity of the BPD, while the CDIPF problem has no impact on the electrical spectra. Therefore, the proposed approach can transmit multi-band LFM signals to remote BSs with anti-CDIPF ability.

Fig. 7. Electrical spectra of the generated multi-band LFM signals under 50 km SMF with the driven RF signal at (a) 5.3 GHz and (b) 8.5 GHz, when the IF-LFM signal has the central frequency of 1.5 GHz and bandwidth of 0.2 GHz.

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In the experiments, DC and one-tone RF signals are observed in the spectra, which are mainly for the unbalanced responsivity of the BPD. This problem can be eliminated by properly adjusting an attenuator to one-port of the BPD. In practice radar applications, BPD with high balance should be employed to further enhance the output photocurrent. Besides, because the length of the SMF is 50 km and the PDM is small, the influence of the PDM on the fiber link is negligible as relative to the chromatic dispersion [24,25]. Considering the long-distance SMF transmission in the future, fibers with smaller PDM or signal generation scheme without polarization requirements should be employed [26]. Besides, OFC with more comb lines (largest to 13) can be obtained by using a QPSK modulator with high extinction ratio, which offers promising application for multi-band LFM signals generation with more carrier frequencies [27].

4. Discussion

According to electromagnetic propagation characteristics, radar system at certain central-frequency can collect different target information. After date fusions in CS, a complete cognitive on target will be achieved. In the proposed approach, LFM signals with up-chirp and down-chirp rates are simultaneously generated, which can effectively eliminate range-Doppler coupling from single-chirp signal [28]. Multi-band LFM signals are radioed to free space for detection. Then target echo signals are spilt for match-filter processing in every BS, as shown in Fig. 8. Here, we simulated the generation and compression of dual-frequency LFM signals for moving target detection. In the simulation, BS1 employs an up-chirp LFM signal at X-band (10 GHz), of which the temporal duration is set at 200 µs and the frequency chirp is from 9.5 GHz to 10.5 GHz; BS3 employs a down-chirp LFM signal at Ka-band (30 GHz), the temporal duration and frequency chirp are set at 200 µs and 30.5 GHz to 29.5 GHz. The radial velocity of the target is 1.2 km/s and the distance from the radar is 24 km.

Fig. 8. Multi-band radar system for moving target detection. C.P., compressed pulse; T.D., true delay.

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Match-filter results from the two BSs are introduced into CS for data fusion processing, as show in Fig. 9. It is noticed that two peaks exist in the date fusion results, corresponding to the match-filter results from BS1 with up-chirp signal and BS3 with down-chirp signal, respectively. The peak-to-sidelobe ratio is calculated to 6.34 dB. In the simulation, carrier frequency of the down-chirp LFM signal is three times to the up-chirp LFM signal, indicating that the threefold Doppler frequency shift (DFS) to the up-chirp signal. The DFS can also be evaluated by the formula of F_d=Δt·B/T, where Δt is the time shift from range-Doppler coupling effect, B and T are the bandwidth and temporal duration of the LFM signal. In Fig. 9, the two peaks have time distance of 32 ns. Thence, due to the DFS effect, the down-chirp peak and up-chirp peak deviated from true delay can be calculated to +24 ns and -8 ns, respectively. Therefore, the true delay of the detected target is 160 µs, corresponding to a distance of 24 km. Besides, match-filter peak of the up-chirp signal is left-shifted 8 ns to the true delay, indicating that target moves away from the radar, and the radial velocity is 1.2 km/s, which is consistent with the simulation parameter.

Fig. 9. Envelope of data fusion results in the CS.

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On the other hand, as the radar system adopts single-chirp LFM signal to detect the moving target, for the range-Doppler coupling, BS1 and BS3 will has range errors of 1.2 m and 3.6 m respectively. With the increase of signal carrier frequency and target velocity, the detection error will further increase, which has serious impact on radar accuracy for moving target detection. The proposed approach can generate and transmit multi-band LFM signals with anti-CDIPF ability. After data fusion, range-Doppler coupling will be effectively eliminated.

In the approach, by adjusting the RF amplitudes and DC voltages of the QPSKM1, OFC with tunable comb lines will be realized, enabling multi-band LFM signals generation with reconfigurable frequency, including central frequency and carrier-frequency number. Chirp rates of the LFM signal can also be adjusted by tuning the driven IF-LFM signal. Comparing with traditional radar system, the proposed multi-band LFM radar has the virtues of high detection performance for the pulse compression characteristics from LFM signal, and multiple functionalities performance for the multi-carrier frequencies. The generated multi-band LFM signals show good phase coherence for a single optical source employed, which can be used for distributed coherent radars and multiple-input-multiple-output (MIMO) radars system [29,30]. Besides, the approach can overcome CDIPD problem for multi-band LFM signals transmission. Thus, detection ranges of the distributed coherent radars and MIMO radars can be enlarged for the low-loss fiber offered. Moreover, amplitudes of the OFC spectra will fluctuate with time for the bias drift, which has impact on the power flatness of the generated multi-band signals. Therefore, bias feedback control technology should be employed to maintain long-time stability of the DP-QPSK modulator in real-world radar applications [31].

5. Conclusion

In conclusion, we proposed and experimentally demonstrated an anti-CDIPF system for multi-band LFM signals generation and transmission. By adjusting the RF signals and IF signals, the approach can flexibly configure the parameters of the LFM signals, including central frequency, bandwidth, multiband characteristics, chirp rate and chirp polarity. Experiment results show the multi-band LFM signals at carrier frequency of 1.5 GHz, 7 GHz, 10 GHz, 15.5 GHz and 18.5 GHz with flatness of 1.9 dB are simultaneously obtained after 50 km fiber transmission, while the normally DSB approach experiences a significant power fading for the fiber dispersion. The multi-band signals feature good phase coherence, and range-Doppler coupling is effectively suppressed by employing two LFM signals with opposite chirps. Therefore, the approach has promising applications in multistate radar system for multifunction detection.

Funding

National Natural Science Foundation of China (61231012, 61571461); Project of Science and Technology New Star of Shaanxi Province (2019KJXX-082); Natural Science Foundation of Shaanxi Province (2019JQ707).

Disclosures

The authors declare no conflicts of interest.

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Photonics-based multi-band linearly frequency modulated signal generation and anti-chromatic dispersion transmission

Abstract

1. Introduction

2. Theory and principle

3. Experiment demonstration

4. Discussion

5. Conclusion

Funding

Disclosures

References

Cited By

Figures (9)

Equations (16)

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