Photonic Generation of Multiband and Multi-Format Chirped Microwave Waveforms Based on an Optoelectronic Oscillator

Abstract

We propose and demonstrate a microwave photonic system to generate multiband and multi-format microwave waveforms based on an actively mode-locked optoelectronic oscillator (AML-OEO) using a dual-polarization dual-drive Mach–Zehnder modulator (DPol-DDMZM). In the proposed system, the upper DDMZM is injected by two baseband single-chirped signals, and the lower DDMZM is biased to realize single-sideband (SSB) modulation using a 90° hybrid coupler. The lower DDMZM is also used to construct an AML-OEO loop, which outputs microwave frequency comb signals. By setting the phase difference in the applied two single-chirped signals, multiband up-, down-, and dual-chirped microwave signals are successfully generated. Furthermore, the tunability of the system can be realized by adjusting the frequency and power of the injection signal in the AML-OEO loop, the passband of the electrical filter, and the chirp rate of the single-chirped signal. The proposed scheme is theoretically analyzed and experimentally verified.

1. Introduction

Linearly chirped microwave signals are extensively used in modern radars to improve the range and velocity resolution, benefiting from their excellent competence of pulse compression [1,2]. Thanks to the advantages of microwave photonics technology in terms of wide bandwidth, high carrier frequency, low transmission loss, and strong immunity to electromagnetic interference, it has the potential to overcome the electrical bottleneck. At present, a great number of photonic-assisted schemes have been reported for generating chirped microwave signals which can improve the range–Doppler resolution [3,4,5,6].

Nevertheless, for multi-function radars, multiband and multi-format chirped microwave waveforms are generally necessary to satisfy multi-scene application requirements. For example, the up-chirped signal has a strong echo signal to the approaching object in the radar system, while the down-chirped signal has a strong echo signal to the distant object [7]. The up- and down-chirped waveforms can improve the dynamic range of the radars. And the dual-chirped waveforms are proposed to solve the problem of large range–Doppler coupling caused by the knife-edge-type ambiguity function of single-chirped waveforms and increase the range-Doppler resolution [5,8]. Recently, a few photonic-assisted methods have been proposed to generate multi-format chirped signals using a dual-polarization dual-parallel Mach–Zehnder modulator (DPol-DPMZM) [9,10] and a dual-parallel Mach–Zehnder modulator (DPMZM) [11]. All the above photonic techniques can realize chirped signals at the single band. They mainly serve single-band radars.

Actually, it is noted that multiband radars have played an important role in modern wars because of their ability to meet complex war conditions. Several photonic schemes for multiband radar signal generation have been proposed [12,13,14,15,16]. For example, an electro-optic modulator driven by a microwave signal is used to generate an optical frequency comb (OFC), and the OFC is further used as an input optical source to generate multiband radar signals [12,13,14]. It is also reported that versatile multi-frequency radar signals can also be obtained by simply using microwave sources with multiple frequencies [15].

Recently, the actively mode-locked photoelectric oscillator (AML-OEO) was proposed as a potential candidate for multiband signal generation [17,18]. By actively mode-locking an OEO, the simultaneous oscillation of multiple modes within the passband of an electrical filter is realized. These oscillation modes act as local oscillator (LO) signals to up-convert a baseband signal to a multiband signal. In this way, microwave pulses, chirped, and phase-coded microwave signals have been generated with the assistance of AML-OEO. For practical radar systems, linearly chirped microwave signals with multi-format waveforms, e.g., up-, down-, or dual-chirped signals, are of great importance to satisfy multi-scene application requirements. For instance, in order to improve the capability of remote sensing and target recognition in the next-generation synthetic aperture radar (SAR) system, it is necessary to have the ability of multiband operation under high-frequency conditions and the increasing time-bandwidth product [19]. Therefore, multiband and multi-format chirped microwave waveforms have potential applications in SAR systems.

In this paper, we propose a microwave photonic approach that can generate chirped microwave signals with multi-formats based on AML-OEO. The proposed scheme is mainly based on a dual-polarization dual-drive Mach–Zehnder modulator (DPol-DDMZM). In the two orthogonal polarization states of the DPol-DDMZM, the sub-DDMZM in one polarization state is used to construct an AML-OEO loop, while the sub-DDMZM in the other polarization state is driven by a baseband single-chirped microwave waveform. By adjusting the phase difference between the two single-chirped microwave signals injected into the two ports of the latter sub-DDMZM, the up-, down-, and dual-chirped microwave signals can be generated. Consequently, the possibility of generating multiband and multi-format chirped signals is experimentally demonstrated, and the switchable capability of the system is also verified. In addition, the single-sideband (SSB) modulation of the generated microwave signals ensures the anti-dispersion transmission in long-distance fiber [20,21].

2. Principle and Methods

Figure 1a displays the configuration diagram of the proposed multiband and multi-format microwave signals generation system. A linearly polarized incident optical wave produced by a laser diode (LD) is coupled into a DPol-DDMZM, which consists of two sub-DDMZMs (x-DDMZM and y-DDMZM, respectively), as shown in Figure 1b. The two sub-DDMZMs are orthogonally coupled by a polarization beam combiner (PBC). The two electrical input ports of the upper x-DDMZM are injected by two baseband single-chirped microwave signals with a phase difference, while the lower y-DDMZM is devoted to constructing an AML-OEO loop. Afterwards, the output light from DPol-DDMZM is divided equally into two paths by an optical coupler (OC). In the AML-OEO path, a polarization controller (PC1) and a polarizer (Pol.1) are cascaded to select the optical signal from y-DDMZM. A roll of long single-mode fiber (SMF) acts as an energy storage element to reduce the phase noise. Furthermore, an electrical amplifier (EA) is used to compensate for the loss of the loop, ensuring the oscillation of the OEO. A photodetector (PD1) converts the optical signal into an electrical signal. A wideband electrical bandpass filter (EBPF) selects the oscillation frequency bandwidth of the OEO. In this way, lots of modes are allowed to oscillate due to the wide passband of the EBPF. Normally, the mode spacing is limited to the kHz level using a long optical fiber. To enlarge the mode spacing, a sinusoidal radio frequency (RF) signal is injected into the OEO loop to actively lock the oscillation modes. The AML-OEO can output multiband LO signals, which is the key to up-converting the baseband signal to LO bands.

An OEO loop without an external RF injection is in a free-running oscillator, and multi-mode oscillation can be achieved in the wide passband of EBPF. The principle of AML-OEO is analogous to that of an actively mode-locked laser. At the onset of oscillation, it is posited that the dominant mode of OEO in the frequency domain corresponds to f_m. When the injection signal f_inj with a frequency equal to an integer multiple of the free spectrum range (FSR) of the OEO cavity is applied into the OEO loop, the modes spaced at frequency f_inj in the EBPF bandwidth are enhanced, thus resulting in the actively mode-locking. And we have a microwave frequency comb (MFC), as shown in Figure 1c [22]. The frequencies of the MFC can be written as f_m ± nf_inj (n = 0, 1, 2, …). Here, we only consider one frequency component of the MFC; when it is driven into the DPol-DDMZM through a 90° hybrid coupler, the optical field at the output of the y-DDMZM can be expressed as follows:

(1)$E_{\mathrm{y}\text{-}\mathrm{MFC}}(t)={\displaystyle \frac{\sqrt{2}}{4}}{E}_0{e}^{j{\omega }_{0}t}\{e^{j{\beta }_{\mathrm{y}}\sin [({\omega }_{\mathrm{m}}\pm n{\omega }_{\mathrm{inj}})t]}+e^{j{\beta }_{\mathrm{y}}\sin [({\omega }_{\mathrm{m}}\pm n{\omega }_{\mathrm{inj}})t+\phi ]}{e}^{j\alpha }\},$

where E₀ and ω₀ are the amplitude and angular frequency of the linearly polarized incident optical carrier, respectively; β_y = πV_y/V_π is the modulation index of the y-DDMZM, V_y is the amplitude of the microwave signal applied to the y-DDMZM, V_π is the half-wave voltage of two sub-DDMZMs; α represents the phase shift induced by the direct current (DC) bias in y-DDMZM, which is set to π/2. Due to the use of a 90° hybrid coupler, the phase difference φ between the two oscillating microwave signals injected into the y-DDMZM is π/2. Applying the Jacobi–Anger expansion to Equation (1) with the condition of small signal modulation, we obtain the following:

(2)$E_{\mathrm{y}\text{-}\mathrm{MFC}}(t)={\displaystyle \frac{\sqrt{2}}{4}}{E}_0{e}^{j{\omega }_{0}t}[(1+j)J_0({\beta }_{\mathrm{y}})+2J_{-1}({\beta }_{\mathrm{y}})e^{-j({\omega }_{\mathrm{m}}\pm n{\omega }_{\mathrm{inj}})t}],$

where J₀(β) and J₋₁(β) are the zero and negative first-order Bessel functions of the first kind, respectively. It can be seen from Equation (2) that negative first-order optical sidebands with frequency f₀ − (f_m ± nf_inj) (f = ω/2π, n = 0, 1, 2, …) are generated, and the SSB modulation of each comb in MFC is realized. An optical frequency comb (OFC) centered at frequency f₀ − f_m and spaced at frequency f_inj is generated. At this point, the OFC can be shown as follows:

(3)$E_{\mathrm{y}\text{-}\mathrm{out}}(t)\propto {\displaystyle \sum _{n=0}^N{E}_0{e}^{j{\omega }_{0}t}[e^{-j({\omega }_{\mathrm{m}}\pm n{\omega }_{\mathrm{inj}})t}+}1],$

where N represents the number of comb lines on one side of the center frequency f₀ − f_m, satisfying the relationship 2N + 1 ≤ EBPF_bw/f_inj (EBPF_bw is the bandwidth of the EBPF).

To generate multi-format chirped microwave waveforms, two baseband single-chirped signals cos(kt²) with a certain phase difference θ are injected into the x-DDMZM. The bandwidth of the single-chirped signals is kT/π, where k and T are the chirp rate and duration of the baseband single-chirped signal, respectively. By adjusting the DC bias α’ of x-DDMZM to equal π/2, under small signal modulation conditions, the optical field at the output of the x-DDMZM can be given as follows:

(4)$\begin{array}{cc}{E}_{\mathrm{x}\text{-}\mathrm{out}}(t)\hfill & ={\displaystyle \frac{\sqrt{2}}{4}}{E}_0{e}^{j{\omega }_{0}t}\{e^{j{\beta }_{\mathrm{x}}\cos (k{t}^2)}+e^{j{\beta }_{\mathrm{x}}\cos (k{t}^2+\theta )}{e}^{j{\alpha }^{\prime }}\}\hfill \\ & ={\displaystyle \frac{\sqrt{2}}{4}}{E}_0{e}^{j{\omega }_{0}t}\{J_0({\beta }_{\mathrm{x}})+2j{J}_1({\beta }_{\mathrm{x}})\cos (k{t}^2)+[J_0({\beta }_{\mathrm{x}})+2j{J}_1({\beta }_{\mathrm{x}})\cos (k{t}^2+\theta )]e^{j{\displaystyle \frac{\pi }{2}}}\}\hfill \\ & ={\displaystyle \frac{\sqrt{2}}{4}}{E}_0{e}^{j{\omega }_{0}t}[(1+j)J_0({\beta }_{\mathrm{x}})+2(j-\cos \theta )J_1({\beta }_{\mathrm{x}})\cos (k{t}^2)+2J_1({\beta }_{\mathrm{x}})\sin \theta \sin (k{t}^2)],\hfill \end{array}$

where J₁(β) is the first-order Bessel function of the first kind and J₁(β) = −J₋₁(β), β_x = πV_x/V_π is the modulation index of the x-DDMZM, and V_x is the amplitude of the baseband single-chirped signal.

In the other path, a PC2 is used to control the polarization state of the optical signal from DPol-DDMZM such that the principal axis of Pol.2 is aligned with one of the principal axes of the polarization beam combiner (PBC) in DPol-DDMZM at γ. After PC2 and Pol.2, the optical signals in two orthogonal polarization states are combined into the same polarization state, and the optical field after Pol.2 can be written as follows:

(5)$\begin{array}{cc}{E}_{\mathrm{Pol}.2}(t)\hfill & =E_{\mathrm{x}\text{-}\mathrm{out}}(t)\cos \gamma +E_{\mathrm{y}\text{-}\mathrm{out}}(t)\sin \gamma \hfill \\ & \propto E_0{e}^{j{\omega }_{0}t}\{\cos \gamma [(1+j)J_0({\beta }_{\mathrm{x}})+2(j-\cos \theta )J_1({\beta }_{\mathrm{x}})\cos (k{t}^2)+2J_1({\beta }_{\mathrm{x}})\sin \theta \sin (k{t}^2)]+\hfill \\ & \hspace{1em}\hspace{1em}\hspace{1em}\hspace{1em}\sin \gamma [(1+j)J_0({\beta }_{\mathrm{y}})-2J_1({\beta }_{\mathrm{y}}){\displaystyle \sum _{n=0}^N{e}^{-j({\omega }_{\mathrm{m}}\pm n{\omega }_{\mathrm{inj}})t}}]\}.\hfill \end{array}$

If cosγJ₀(β_x) + sinγJ₀(β_y) = 0, the cancelation interference of the modulated optical carriers in x-DDMZM and y-DDMZM can be realized. Assuming that γ is equal to 3π/4, we simply need to adjust the amplitudes of the signals to V_x = V_y (that is, β_x = β_y = β) to achieve the cancelation interference. Consequently, Equation (5) can be reduced to the following:

(6)$E_{\mathrm{Pol}.2}(t)\propto E_0{e}^{j{\omega }_{0}t}{J}_1(\beta )[(j-\cos \theta )\cos (k{t}^2)+\sin \theta \sin (k{t}^2)+{\displaystyle \sum _{n=0}^N{e}^{-j({\omega }_{\mathrm{m}}\pm n{\omega }_{\mathrm{inj}})t}}].$

When θ is equal to π/2, 0, or −π/2, respectively, the optical field is detected by the PD2. The low-frequency categories, such as beat frequency between each sideband in OFC, are hardly radiated by the antennas and can be ignored. Therefore, the photocurrent can be shown as follows:

(7)$\begin{array}{cc}i(t)\hfill & =E_{\mathrm{Pol}.2}(t)\cdot E_{\mathrm{Pol}.2}(t{)}^{*}\hfill \\ & \propto \left\{\begin{array}{cc}{E_0}^2{J_1}^2(\beta )\cos [({\omega }_{\mathrm{m}}\pm n{\omega }_{\mathrm{inj}})t-k{t}^2+{\displaystyle \frac{\pi }{2}}],\hfill & (\theta ={\displaystyle \frac{\pi }{2}})\hfill \\ {E_0}^2{J_1}^2(\beta )\{\cos [({\omega }_{\mathrm{m}}\pm n{\omega }_{\mathrm{inj}})t+k{t}^2-{\displaystyle \frac{\pi }{4}}]+\cos [({\omega }_{\mathrm{m}}\pm n{\omega }_{\mathrm{inj}})t-k{t}^2-{\displaystyle \frac{\pi }{4}}]\},\hfill & (\theta =0)\hfill \\ {E_0}^2{J_1}^2(\beta )\cos [({\omega }_{\mathrm{m}}\pm n{\omega }_{\mathrm{inj}})t+k{t}^2+{\displaystyle \frac{\pi }{2}}],\hfill & (\theta =-{\displaystyle \frac{\pi }{2}})\hfill \end{array}\right.\hfill \end{array}$

We can see from Equation (7) that the microwave photonic link generates multiband up-, down- and dual-chirped microwave waveforms with center frequencies of ω_m ± nω_inj (n = 0, 1, 2, …), respectively. Therefore, the proposed scheme can realize the photonic generation of multiband and multi-format chirped microwave waveforms. Meanwhile, we have proved in Ref. [21] that SSB modulation can achieve the anti-dispersion transmission over the long-distance fiber of chirped microwave signals, so the proposed system can also be immune to the power fading caused by chromatic dispersion.

3. Experiments and Results

A proof-of-concept experiment was performed according to the setup diagram in Figure 1a. A linearly polarized optical carrier centered at 1550 nm from an LD was injected into the DPol-DDMZM. After an OC, on the one hand, the y-polarization state of the modulated optical carrier was selected by a PC1 and a Pol.1 in the OEO loop. And it was injected into a PD1 after a roll of 2 km SMF. An EA was used to compensate for the loss of the OEO loop and realize continuous and stable oscillation of the OEO. The EBPF has a passband from 16.5 to 19.5 GHz, which covers part of the Ku-band and part of the K-band. It was employed to select oscillation modes. The oscillating microwave signal generated by OEO and an external injection signal were fed to the two RF ports of y-DDMZM through a 90° hybrid coupler.

In the experiments, due to the uneven magnitude response of the microwave photonic link, the mode at the maximum gain within the EBPF bandwidth wins the mode of competition. This mode is regarded as the dominant mode. As shown in Figure 2a, the OEO loop produced a single-tone signal centered at 17.5016 GHz without external RF injection. It is noted that the frequency of the oscillated signal is not stable due to the wide bandwidth of the EBPF. Figure 2b shows the zoom-in view of Figure 2a. The FSR of the OEO cavity is about 93.92 kHz without external RF injection. In order to enlarge the mode spacing, an external RF signal with a frequency of 804.01 MHz and a power of 3.80 dBm was injected into the OEO loop. After RF injection locking, RF modes centered at 16.688, 17.492, 18.296, and 19.100 GHz oscillated, as shown in Figure 3a,b. Figure 3a shows the spectrum of signals from the AML-OEO within a frequency range of 0–30 GHz. Figure 3b illustrates the electrical spectrum of the signals within the passband of EBPF.

In order to show the tunability of the proposed system, we first adjusted the frequency and power of the injection signal to 536.10 MHz and 4.10 dBm, respectively. The measured electrical spectrum of the output signals is shown in Figure 3c. In this case, we obtained RF signals with frequencies of 16.619, 17.155, 17.691, 18.228, 18.764, and 19.300 GHz. In addition, the oscillated signals are also related to the bandwidth of the EBPF. When we replaced the EBPF with a passband from 22 to 26 GHz and injected an RF signal with a frequency of 943.96 MHz, oscillated signals are at frequencies of 22.540, 23.484, 24.428, and 25.373 GHz, as shown in Figure 3d. The passband is within the K-band, which is mainly used for tracking and guidance in radar systems. Therefore, by adjusting the frequency and power of the external injection signal and the passband of the EBPF, the oscillated signals generated by AML-OEO are tunable. The proposed system has the ability to generate LO signals in the normally used radar bands to adapt to different application scenarios. The phase noise of the oscillated signals is quite similar in our experiment. For example, it was measured to be −112.85 dBc/Hz at an offset frequency of 10 kHz for an RF signal at 17.492 GHz, as shown in Figure 4.

Outside the OEO loop, a PC2 and a Pol.2 were inserted to combine the two orthogonally polarized optical signals from the DPol-DDMZM to the same polarization state. For linearly chirped microwave signal generation, the x-DDMZM was driven by two baseband single-chirped microwave signals with a phase difference in θ. They are generated by a multi-channel arbitrary waveform generator (AWG). The linearly single-chirped microwave waveforms have a frequency ranging from 0 to 0.05 GHz and a time duration of 1 μs. By properly adjusting the PC2 as described in the Principle Section, the optical carriers in x-DDMZM and y-DDMZM were canceled for each other. In this way, the generation of undesired components can be well avoided, and only the desired, chirped microwave signals were generated after photodetection. When θ was set to π/2, −π/2, and 0, respectively, we could have down-, up-, and dual-chirped microwave signals with center frequencies of 16.688, 17.492, 18.296, and 19.100 GHz, as shown in Figure 5. Figure 5a,d,g are the measured electrical spectra of the generated down-, up-, and dual-chirped microwave signals, respectively. Figure 5b,e,h show the corresponding time-domain waveforms. Figure 5c,f,i show the corresponding instantaneous frequency–time diagrams of these signals.

We adjusted the baseband single-chirped microwave signals to 0.1 GHz/1 µs to prove the bandwidth tunability of the proposed scheme. The experimental results are shown in Figure 6. Figure 6a,d,g show the electrical spectra of the generated down-, up-, and dual-chirped microwave signals, respectively. Figure 6b,e,h show the corresponding time-domain waveforms, while Figure 6c,f,i show the corresponding instantaneous frequency–time diagrams. Due to the limitation of the polarization extinction ratio of Pol.2, the optical carriers in x-DDMZM and y-DDMZM could not cancel each other out completely. The residual optical carriers beat with the sidebands, resulting in the generation of undesired signals. Therefore, the experimental results show that the bandwidth of the generated multi-format chirped microwave signals can be tunable by adjusting the bandwidth of the baseband single-chirped signal.

4. Discussion

A photonic-assisted scheme based on a DPol-DDMZM and an AML-OEO for generating multiband multi-format chirped microwave waveforms is proposed. Compared with other multi-format chirped microwave signal generators [9,10,11], our system can generate multiband chirped microwave signals, which is applied to multiband multi-function radar systems. In addition, compared with our recently proposed multiband phase-coded and dual-chirped microwave signal generator [18], this scheme can generate switchable up-, down-, and dual-chirped microwave signals. It is worth noting that this system can be immune to the power-fading effect caused by chromatic dispersion benefiting from SSB modulation [20,21]. In Table 1, we mainly highlight the technical advantages of this work over some chirped microwave waveform generation methods, where “√” stands for achievable and “×” for unachievable. By adjusting the frequency and power of the external injection signal, the passband of the EBPF, and the bandwidth of the baseband single-chirped signals, the tunability of the generated multiband multi-format chirped microwave signals can be realized. Furthermore, the PCs used in our system are sensitive to environmental conditions, so a polarization control feed-back device might be required to reduce the impact of environmental changes in practical applications.

5. Conclusions

We proposed and experimentally demonstrated a microwave photonic system for generating multiband, multi-format, chirped microwave waveforms. The proposed scheme is mainly based on the sophisticated use of a DPol-DDMZM. This modulator is adopted to form an AML-OEO, on the one hand. It also acts as a frequency up-converter to generate multiband and multi-format, chirped signals on the other hand. We gave a theoretical analysis of the proposed method. Furthermore, the operation principle of the scheme has been proved by a series of experiments. The up-, down-, and dual-chirped microwave signals have been successfully obtained in our experiments. In addition, we have also shown the tunability of the system in terms of the center frequency and bandwidth of the chirped signals. These results show that the proposed scheme can provide multiband operation capability and multi-format chirped waveform generation, such as SAR systems, to adapt to different application scenarios and has potential application in multiband and multi-function radars.

Author Contributions

Conceptualization, J.D., F.L. and W.L.; methodology, J.D., F.L. and H.T.; software, J.D., F.L. and Z.K.; validation, J.D., F.L., H.T. and Z.K.; formal analysis, J.D.; investigation, J.D.; resources, M.L. and W.L.; data curation, J.D. and F.L.; writing—original draft preparation, J.D.; writing—review and editing, J.D. and W.L.; visualization, J.D.; supervision, W.L.; project administration, W.L.; funding acquisition, W.L. All authors have read and agreed to the published version of the manuscript.

Institutional Review Board Statement

Not applicable.

Informed Consent Statement

Not applicable.

Data Availability Statement

Data are contained within the article.

Conflicts of Interest

The authors declare no conflicts of interest.

Footnotes

Disclaimer/Publisher’s Note: The statements, opinions and data contained in all publications are solely those of the individual author(s) and contributor(s) and not of MDPI and/or the editor(s). MDPI and/or the editor(s) disclaim responsibility for any injury to people or property resulting from any ideas, methods, instructions or products referred to in the content.

Figures and Table

Figure 1. (a) The schematic diagram of the proposed multiband and multi-format chirped microwave waveforms generation system. LD, laser diode; DPol-DDMZM, dual-polarization dual-drive Mach-Zehnder modulator; OC, optical coupler; PC, polarization controller; Pol., polarizer; SMF, single-mode fiber; PD, photodetector; EA, electrical amplifier; EBPF, electrical bandpass filter. (b) The layout of the DPol-DDMZM. DDMZM, dual-drive Mach–Zehnder modulator; 90° PR, 90° polarization rotator; PBC, polarization beam combiner; RF, radio frequency. (c) The principle of the actively mode-locked OEO in the frequency domain.

Figure 2. Frequency spectra of the free-running OEO without an injection signal in different ranges: (a) 0–30 GHz; (b) 17.5010–17.5020 GHz.

Figure 3. Frequency spectra of the AML-OEO under different conditions of the injection signal: (a,b) the frequency of 804.01 MHz and the power of 3.80 dBm; (c) the frequency of 536.10 MHz and the power of 4.10 dBm; (d) the EBPF passband range of 22–26 GHz and the frequency of 943.96 MHz.

Figure 4. The measured phase noise result of the RF signal generated by the AML-OEO loop. The blue solid line is the raw data and the pink solid line is the smooth data (smoothing value: 1%).

Figure 5. Measured (a,d,g) electrical spectra; (b,e,h) time-domain waveforms; and (c,f,i) instantaneous frequency–time diagrams of the down-, up-, and dual-chirped microwave signals centered at 16.688, 17.492, 18.296, and 19.100 GHz with sweeping rates of 0.05 GHz/1 µs, respectively.

Figure 6. Measured (a,d,g) electrical spectra; (b,e,h) time-domain waveforms; and (c,f,i) instantaneous frequency–time diagrams of the down-, up-, and dual-chirped microwave signals centered at 16.688, 17.492, 18.296, and 19.100 GHz with sweeping rates of 0.1 GHz/1 µs, respectively.

Table 1

A comparison of chirped waveform generation using difference methods.

Methods for Chirped Waveform Generation	Multiband	Multi-Format Chirped Waveforms	Immune to the Power-Fading Effect
Based on DPol-DPMZM [9]	×	√	×
Based on DPol-DPMZM [10]	×	√	√
Based on DPMZM [11]	×	√	×
Based on DPol-MZM and AML-OEO [18]	√	×	×
Based on DPol-DDMZM and AML-OEO (This work).	√	√	√

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