Photonic Generation of Reconfigurable Ternary Modulated Microwave Signals with a Large Frequency Range

Abstract

A photonic scheme generating ternary modulated signals, which include amplitude, phase, and frequency modulated signals, has been proposed and demonstrated. This scheme is based on a dual-polarization dual-parallel Mach-Zehnder modulator (DP-DPMZM), where the X-DPMZM is used to generate an optical frequency comb (OFC), and the Y-DPMZM is utilized to accomplish ternary modulation. The key feature of this scheme is that ternary modulated signals with eight wavebands can be obtained by using only the DP-DPMZM in situations of different input signals. In the simulation, a 2.5 Gbit/s amplitude shift keying (ASK), phase shift keying signal (PSK), or an 8 GHz bandwidth linearly frequency modulated (LFM) signal are obtained. The generated signals have eight wavebands with a large frequency range from 10 GHz to 80 GHz. Moreover, the recovery and pulse compression performances of the generated signals are evaluated.

1. Introduction

In the communication field, basial modulation formats could be sorted into amplitude, phase, and frequency modulation [1], corresponding to the common ASK, PSK, and LFM signals. Many photonic schemes have been proposed to generate them in recent years [2]. Among the ternary modulated signals, the ASK signals are usually regarded as basic digital modulation format to composed advanced modulation signals [3]. The traditional generation approach based on frequency-to-time mapping attaches poor stability, therefore, an external modulator scheme was proposed to obtain stable ASK signals in [4], with a low frequency. The PSK signals, especially the multi-band PSK signals are widely used in multi-band radar systems for overcoming the problems encountered in a single frequency radar system and to realize different functions by different frequencies [5,6]. The generation of multi-band PSK signals has attracted much attention [7]; the literature [8,9] has generated two wavebands PSK signal, but the multi-wavelength light source makes the system costly. The LFM signals are significant in the synthetic aperture radar application [10,11], meanwhile, the multi-band LFM signals are also highly desirable and meaningful in the multi-band radar systems [12,13]. The scheme in [14] obtained seven wavebands LFM signals, while the frequency range was limited by the rigid modulation configuration. Although the ASK, PSK, and LFM signals play an important role in communication and radar systems, only one kind of them can be generated in most schemes.

In the case of some comprehensive communication or radar systems, more than one kind of modulated signal should be considered, such as the ASK and PSK signals used in optical label switching system for superior transmission performance [15] and high spectral efficiency [16]. ASK and LFM signals are employed in the integrated communication and radar system for joint data communication and radar sensing [17]. As for high-speed communication and high-resolution radar sensing application [18], the QAM-LFM signal has been designed, which is generated by superposition of ASK and LFM signals [19]. Moreover, a combined LFM and PSK signal can be applied in the Wuhan ionospheric oblique back-scattering sounding system to achieve higher range resolution and larger signal processing gain [20]. Nowadays few schemes may generate two kinds of modulated signals in the same structure. For example, ASK and PSK signals can be obtained by a dual-polarization quadrature phase-shift keying modulator [21], and PSK and LFM signals are generated through a dual-polarization dual-drive Mach–Zehnder modulator [22]. A structure of flexibly generating ternary modulated signals may meet more comprehensive scenarios. Sadly, such a scheme hasn’t been reported.

In this paper, we propose a photonic scheme to generate ternary modulated micro-wave signals, including ASK, PSK, and LFM signals. This signal generator is compact because the generation of ternary modulated signals is accomplished by using only a DP-DPMZM, and there is no costly multi wavelength light source. In simulation, this system finally generates an 8 GHz bandwidth LFM signal, and 2.5 Gbit/s ASK and PSK signals at eight wavebands. Benefiting from the independent modulation configuration of two DPMZMs, the large frequency range covers from 10 GHz to 80 GHz and the operation of switching ternary signal is flexible.

2. Principle

The schematic diagram of the proposed ternary modulated microwave signals generator is shown in Figure 1i. A linearly polarized optical wave from a laser diode (LD) gets through a polarization controller (PC) and is sent to DP-DPMZM, which consists of a polarization beam splitter (PBS), two dual-parallel Mach-Zehnder modulators (DPMZMs), and a polarization beam combiner (PBC). The radio frequency (RF) signal is loaded on the Mach–Zehnder modulator1 (MZM1) and MZM2 of the main X-DPMZM, while the Y-DPMZM is driven by an electrical binary coding or single-chirp waveform from an arbitrary waveform generator (AWG). Then, the output of DP-DPMZM is send to the erbium-doped fiber amplifier (EDFA); after amplification, the light wave is split by the PBS. The two split signals from PBS are injected into a balanced photodetector (BPD) to perform square law detection. The spectrum of optical signal and microwave signal has been displayed in Figure 1ii, and the modulation configurations of DP-DPMZM for generating ASK, PSK, and LFM signals are shown in Figure 1iii–v.

In the X-DPMZM, the direct current (DC) biases of MZM1, MZM2, and the main MZM are, respectively, set at maximum transmission point (MATP), minimum transmission point (MITP), and quadrature transmission point (QTP). Assuming that the optical wave from LD is $E_{\mathrm{in}}\left(t\right)=E_0\exp \left(j{\omega }_{0}t\right)$, the output of X-DPMZM can be expressed as:

$$\begin{array}{cc}{E}_x\left(t\right)& =\frac{\sqrt{2}}{2}{E}_0{e}^{j{\omega }_{0}t}\left[e^{j{\beta }_1\cos \left({\omega }_{s}t\right)}+e^{-j{\beta }_1\cos \left({\omega }_{s}t\right)}+e^{j{\beta }_2\cos \left({\omega }_{s}t\right)+j\pi /2}-e^{-j{\beta }_2\cos \left({\omega }_{s}t\right)+j\pi /2}\right]\hfill \\ & =\frac{\sqrt{2}}{2}{E}_0{e}^{j{\omega }_{0}t}\left[{\displaystyle \sum _{m=-\infty }^{+\infty }{J}_{2m}\left({\beta }_1\right)}{e}^{j2m {\omega }_{s}t}+{\displaystyle \sum _{n=-\infty }^{+\infty }{J}_{2n-1}\left({\beta }_2\right)}{e}^{j \left(2n-1\right) {\omega }_{s}t}\right]\hfill \end{array}$$

(1)

where $E_0, {\omega }_0$ denote the amplitude, angular frequency of optical carrier, and $J_{2m}, J_{2n-1}$ are the (2m)th-order and 2(n − 1)th-order first-kind Bessel function. ${\beta }_1=\pi V_{RF1}/V_{\pi },$ ${\beta }_2=\pi V_{RF2}/V_{\pi }$ indicate the modulation indexes of MZM1 and MZM2, where $V_{\pi }$ is the half wave voltage. $V_{RF}$ and ${\omega }_s$ are the amplitude and angular frequency of RF signal.

An OFC with 17 sidebands can be obtained by properly setting modulation indexes, such as ${\beta }_1=6.38, {\beta }_2=5.31,$ there is $\left|J_0\left({\beta }_1\right)\right|\approx \left|J_1\left({\beta }_2\right)\right|\approx \left|J_2\left({\beta }_1\right)\right|\approx \left|J_3\left({\beta }_2\right)\right|\approx \left|J_4\left({\beta }_1\right)\right|\approx \left|J_5\left({\beta }_2\right)\right|\approx \left|J_6\left({\beta }_1\right)\right|\approx A, and \left|J_7\left({\beta }_2\right)\right|\approx \left|J_8\left({\beta }_1\right)\right|\approx B.$ The higher-order components are too small to be considered, then Equation (1) can be simplified as:

$$\begin{array}{cc}\hfill E_x\left(t\right)& =\frac{\sqrt{2}}{2}{E}_0{e}^{j{\omega }_{0}t}\left[{\displaystyle \sum _{m=-4}^4{J}_{2m}\left({\beta }_1\right) }{e}^{j2m {\omega }_{s}t}+{\displaystyle \sum _{n=-3}^4{J}_{2n-1}\left({\beta }_2\right)} e^{j \left(2n-1\right) {\omega }_{s}t}\right]\hfill \\ & =\frac{\sqrt{2}}{2}{E}_0{e}^{j{\omega }_{0}t}\left[A{\displaystyle \sum _{m=0}^6\cos \left(m{\omega }_{s}t\right)+B{\displaystyle \sum _{n=7}^8\cos \left(n{\omega }_{s}t\right)}}\right]\hfill \end{array}$$

(2)

The output signal Ex(t) of the X-DPMZM and the modulated light wave Ey(t) from the Y-DPMZM are injected into the PBS after amplification. The polarization axes of PBS have angles of 45° and 135° [23], the output signal can be written as:

$$\left[\begin{array}{l}{E}_1\left(t\right)\\ E_2\left(t\right)\end{array}\right]=[\begin{array}{l}\cos 45°\\ \cos 135°\end{array}\begin{array}{r} \sin 45°\\ \sin 135°\end{array}]\cdot \left[\begin{array}{l}{E}_x\left(t\right)\\ E_y\left(t\right)\end{array}\right]$$

(3)

Finally, the output signals of PBS are introduced into BPD for photoelectric conversion. The photocurrent of the BPD can be given by:

$$\begin{array}{cc}{i}_{BPD}\left(t\right)\hfill & =\eta E_1\left(t\right)\cdot E_1{}^{\ast }\left(t\right)-\eta E_2\left(t\right)\cdot E_2{}^{\ast }\left(t\right)\hfill \\ & \propto \left[A{\displaystyle \sum _{m=0}^6\cos \left(m{\omega }_{s}t\right)+B{\displaystyle \sum _{n=7}^8\cos \left(n{\omega }_{s}t\right)}}\right]\left[e^{j{\omega }_{0}t}{E}_y^{\ast }\left(t\right)+e^{-j{\omega }_{0}t}{E}_y\left(t\right)\right]\hfill \end{array}$$

(4)

where the η is the responsibility of the BPD. As can be seen from Equation (4), the microwave signal with a large frequency range covering from ${\omega }_s$ to $8{\omega }_s$ has been generated. What is more, the generated signal is obviously affected by the modulated lightwave Ey(t) which is determined by the injected electrical baseband signal $s\left(t\right)$. The details are following as.

2.1. Generation of ASK Signal

A binary coding signal is sent to the Y-DPMZM, the DC biases of MZM3, MZM4, and the main MZM are set at MATP. Then, the output signal Ey(t) of the Y-DPMZM can be expressed as:

$$\begin{array}{cc}\hfill E_y\left(t\right)& =\frac{\sqrt{2}}{2}{E}_0{e}^{j{\omega }_{0}t}\left[e^{j{\beta }_3{s}_a\left(t\right)}+e^{-j{\beta }_3{s}_a\left(t\right)}+e^{j{\beta }_3{s}_a\left(t\right)}+e^{-j{\beta }_3{s}_a\left(t\right)}\right]\hfill \\ & =\sqrt{2} E_0{e}^{j{\omega }_{0}t}\cos \left({\beta }_3{s}_a\left(t\right)\right)\hfill \end{array}$$

(5)

where ${\beta }_3=\pi V_3/V_{\pi }$ is the modulation index of Y-DPMZM, and $V_3$ is the amplitude of electrical coding signal. As the coding signal $s_a\left(t\right)$ has the amplitude of $V_{\pi }/2$, the Equation (4) can be rewritten as following to express the ASK signal:

$$i_{\mathrm{ASK}}\left(t\right)\propto \{\begin{array}{l}A{\displaystyle \sum _{m=1}^6\cos \left(m{\omega }_{s}t\right)+B{\displaystyle \sum _{n=7}^8\cos \left(m{\omega }_{s}t\right)for bit ‘0’}}\\ 0for bit ‘1’ \end{array}$$

(6)

2.2. Generation of PSK Signal

Similarly, the phase coding modulation can be realized while the $s_a\left(t\right)$ has the amplitude of $V_{\pi }$. In this situation, the PSK signal can be expressed as:

$$i_{PSK}\left(t\right)\propto \{\begin{array}{l}A{\displaystyle \sum _{m=1}^6\cos \left(m{\omega }_{s}t\right)+B{\displaystyle \sum _{n=7}^8\cos \left(n{\omega }_{s}t\right)for bit ‘0’}}\\ -A{\displaystyle \sum _{m=1}^6\cos \left(m{\omega }_{s}t\right)-B{\displaystyle \sum _{n=7}^8\cos \left(n{\omega }_{s}t\right)for bit ‘1’}}\end{array}$$

(7)

The generated PSK signal has a phase difference of π rad when the coding signal varies from zero to one.

2.3. Generation of LFM Signal

While in the frequency modulation, an electrical single-chirped signal, $s_f\left(t\right)=\cos \left(k{t}^2\right)$ is split into two parts with a phase difference of 90 degrees and applied to drive the Y-DPMZM, the Ey(t) can be given by:

$$\begin{array}{cc}{E}_y\left(t\right)\hfill & =\frac{\sqrt{2}}{2}{E}_0{e}^{j{\omega }_{0}t}\left[e^{j{\beta }_4\cos \left(k{t}^2\right)}{+e}^{-j{\beta }_4\cos \left(k{t}^2\right)}{+e}^{j{\beta }_4\sin \left(k{t}^2\right)}+e^{-j{\beta }_4\sin \left(k{t}^2\right)}\right]\hfill \\ & =\frac{\sqrt{2}}{2}{E}_0{e}^{j{\omega }_{0}t}\left[2J_0\left({\beta }_4\right)+2{\displaystyle \sum _{p=1}^{\infty }{(-1)}^p{J}_{2p}\cos \left(2pk{t}^2\right)+2{\displaystyle \sum _{q=1}^{\infty }{J}_{2q}\cos \left(2qk{t}^2\right)}}\right]\hfill \\ & \approx \frac{\sqrt{2}}{2}{E}_0{e}^{j{\omega }_{0}t}\left[2J_0\left({\beta }_4\right)+2{\displaystyle \sum _{p=1}^2{(-1)}^p{J}_{2p}\cos \left(2pk{t}^2\right)+2{\displaystyle \sum _{q=1}^2{J}_{2q}\cos \left(2qk{t}^2\right)}}\right]\hfill \\ & =\frac{\sqrt{2}}{2}{E}_0{e}^{j{\omega }_{0}t}\left[2J_0\left({\beta }_4\right)+4J_4\left({\beta }_4\right)\cos \left(4k{t}^2\right)\right]\hfill \end{array}$$

(8)

where ${\beta }_4=\pi V_4/V_{\pi }$ is the modulation index of Y-DPMZM, and $V_4$ is the amplitude of $s_f\left(t\right)$. When ${\beta }_4$ is set to satisfy $J_0\left({\beta }_4\right)=0$, only the ±4 order sidebands are retained in Equation (8). Substituting the result of Equation (8) for the Ey(t) in Equation (4), then the Equation (4) could be expressed as following to show the LFM signal:

$$\begin{array}{c}{i}_{LFM}\left(t\right)=A\cos \left(4k{t}^2\right)+A{\displaystyle \sum _{m=1}^6\left[\cos \left(m{\omega }_{s}t+4k{t}^2\right)+\cos \left(m{\omega }_{s}t-4k{t}^2\right)\right]}\\ +B{\displaystyle \sum _{n=7}^8\left[\cos \left(n{\omega }_{s}t+4k{t}^2\right)+\cos \left(n{\omega }_{s}t-4k{t}^2\right)\right]}\end{array}$$

(9)

As can be seen from Equation (9), the bandwidth of eight chirped signals has been expanded to eight times, which highly increase the time-bandwidth product of the signal. The bandwidth of the LFM signals can be further increased by increasing the chirp rate k, or the duration time t.

3. Results and Analysis

For verifying the feasibility of the ternary modulated signals generator, a simulation based on Figure 1 is established and demonstrated. The carrier frequency, linewidth, and power of the light wave are 193.1 THz, 10 MHz, and 12 dBm, respectively. The BPD has a responsivity of 0.6 A/W, a dark current of 10 nA, and a thermal noise of $1\times {10}^{-22}$ W/Hz. The DP-DPMZM has a half wave-voltage of 4 V, and an extinction ratio of 20 dB. The X-DPMZM was driven by the RF signal with an angular frequency of 10 GHz.

3.1. Generation of ASK Signal

Regarding the generation of ASK signal, an electrical baseband coding signal $s_a\left(t\right)$ with a bit rate of 2.5 Gbit/s and a duration of 8 ns is sent to the Y-DPMZM. After the electro-optic modulation, the modulated optical signal is combined by a PBC. Then, the combined signal is amplified by the 20 dBm EDFA which introduces a noise of 4 dB. The following PBS is employed to split the optical signal at two orthogonal polarization directions. Through square law detection by the BPD, multiple wavebands ASK signal is obtained. The spectrum of the obtained signal is presented in Figure 2. It is obvious that the signal has eight wavebands at 10 GHz, 20 GHz, 30 GHz, 40 GHz, 50 GHz, 60 GHz, 70 GHz, and 80 GHz, and the simulation results are consistent with the derivation of Equation (6).

The waveform of $\cos \left[{\beta }_4{s}_a\left(t\right)\right]$ is shown in Figure 3a. As can be seen, the coding signal $\cos \left[{\beta }_4{s}_a\left(t\right)\right]$ is “00010010011011101000”. For investigating the performance of generated signal at a single frequency, Figure 3b displays the filtered ASK signal centered at 10 GHz. The envelope of signal has been extracted and shown in Figure 3c. It can be seen that the envelope matches well with the binary coding signal, which shows good performance of recovery. What is more, Figure 3d–f shows the $\cos \left[{\beta }_4{s}_a\left(t\right)\right]$ with bits of “11101011000101101111”, the signal at 80 GHz, and corresponding envelope. The result demonstrates the generated ASK signals present good performance.

3.2. Generation of PSK Signal

As for the generation of PSK signal, the amplitude of $s_p\left(t\right)$ is set to 0 V and 4 V, corresponding to bit ‘0’ and bit ‘1’. After optical-to-electrical conversion, the PSK signal with eight wavebands can be generated at the output of the BPD. The electrical spectrum is displayed in Figure 4, which show that the eight wavebands covering from 10 GHz to 80 GHz. The spectrum distribution accord well with Equation (7). Furthermore, no obvious spurs can be observed in spectrum diagram benefitting from the balance detection.

Two phase coding signals with frequency of 10 GHz and 80 GHz have been filtered to analyze and display in Figure 5; the waveforms are displayed in Figure 5a,d. Apparent phase difference between the coded waveform can be observed in the diagrams of waveform. In simulation, the coding signal $\cos \left[{\beta }_4{s}_P\left(t\right)\right]$ is “11110100100011010111” and the binary signal matches well with the recovered phase information; every phase difference is corresponding to a phase jump of $\pi$ rad, which are presented in Figure 5b,e. Figure 5c,f illustrate the autocorrelation of generated signals, and the key parameters of autocorrelation like pulse compression ratio (PCR), peak-to-sidelobe ratios (PSR), and full width at half-maximum (FWHM) has also been displayed. The PSR and FWHM of the 10 GHz signal is 8.1067 dB and 0.3896 ns, respectively, and the 80 GHz signal’s PSR and FWHM is 7.9732 dB and 0.4043 ns, respectively. After calculation, PCRs of two signals are 20.5312 and 19.7873, respectively, and the theoretical PCR of phase coding signal is 20 (duration time × bit rate). The results are very close to theoretical value, which shows good pulse compression performance.

3.3. Generation of LFM Signal

In order to generate LFM signal, the Y-DPMZM is driven by a base-band single-chirp signal $\cos \left(k{t}^2\right)$, which has a time duration of 256 ns and a bandwidth of 1 GHz. The eight wavebands LFM signal is shown in Figure 6a; its waveform has stable amplitude cause of flat power. A baseband signal with a bandwidth of 4 GHz, and eight signals with a bandwidth of 8 GHz can be observed in Figure 6b, which agree well with the result of Equation (9). Figure 6c exhibits the time-frequency diagram, which is obtained by short-time Fourier transform. The instantaneous frequency curves present a clear and highlighted track, since little interference is generated simultaneously.

Figure 7a,c show the recovered instantaneous frequency of the 10 GHz and 80 GHz LFM signals. It is noticed that every chirping signal is composed of two opposite linearly chirped microwave waveforms with a bandwidth of 4 GHz. The instantaneous frequency diagrams confirm that the two opposite chirped waveforms agree well with $\cos \left(m{\omega }_{s}t+4k{t}^2\right)+\cos \left(m{\omega }_{s}t-4k{t}^2\right)$ term of Equation (9). A LFM signal with two opposite chirped waveforms may increase the range-Doppler resolution of radar [24]. Autocorrelations have also been calculated to evaluate the pulse compression capability in Figure 7b,d. As illustrated in diagrams, the PSRs are 11.1349 dB and 11.2149 dB, and the FWHM of the autocorrelation peaks are 0.14844 ns and 0.15078 ns, corresponding to PCRs of 1724.6 and 1697.8, which is close to the theoretical PCR of 2048 (duration time × bandwidth). That is to say, the results reveal a good pulse compression capability. In addition, the PCR is mainly limited by the duration time and bandwidth of the injected chirped signal, which has been highly increased through the implementation of octuple bandwidth in this scheme, and it can also be further increased by extending the duration time.

Table 1. Performance comparison of proposed approach with other published work.

Reference	Signals	Wavebands	Frequency
Ref. [4]	ASK	1	1 GHz
Ref. [7]	PSK	2	11 GHz, 22 GHz
Refs. [8,9]	PSK	2	10~30 GHz
Ref. [10]	LFM	2/3/5	2~20 GHz
Ref. [11]	LFM	4	10~40 GHz
Ref. [12]	LFM	7	2~24 GHz
Ref. [19]	ASK/PSK	1	12 GHz
Ref. [20]	PSK/LFM	2	10 GHz, 15 GHz
Proposed approach	ASK/PSK/LFM	8	10~80 GHz

presents the performance comparison of proposed approach with other published work. The comparison result clearly shows that our proposed approach demonstrates an improvement in the generation of more wavebands and sorts of signals, as well as a frequency range.

4. Conclusions

In summary, a reconfigurable signals generator for obtaining ternary modulated microwave signals has been proposed and demonstrated based on the photonic method. The generator is capable of generating an 8 GHz bandwidth LFM signal, a 2.5 Gbit/s ASK, and PSK microwave signals at eight wavebands. Independent modulation of two DPMZMs, the operation of switching between ternary modulated signals, is flexible, as well as a large frequency range covering from 10 GHz to 80 GHz. The simulation results show good performance of recovery and pulse compression capacity. This scheme provides a way to obtain eight waveband signals, which may enable multi-band radar to realize different functions by different frequencies. In addition, the ternary modulated signal generator has a flexible application scenario in some comprehensive systems, such as optical label switching systems, integrated communication and radar systems, and so on.