1. Introduction

With the advent of the era of the fifth generation fixed networks (F5G), the features of full-fiber connection (FFC), enhanced fixed broadband (eFBB), and guaranteed reliable experience (GRE) make the optical networks turn into the most widely deployed and important communication infrastructure. The FFC optical networks in F5G will help to support the most demanding applications such as Ultra/Super High-Definition Video streaming (4K/8K video), Internet of Things (IoT), Virtual/Augmented Reality (VR/AR) gaming, and telemedicine [1,2]. Inevitably, more sensitive information such as financial transactions, confidential intellectual property, and medical records [3] will be transmitted on them. Although various security mechanisms are used to protect the confidentiality, integrity, and availability triad supported by some dedicated hardware above the network layer such as firewalls and intrusion detection systems, security enhancement in the optical layer has not been attracting much attention. However, the optical layer is also vulnerable to attack by in-band jamming and out-of-band crosstalk [4], resulting in some intrusion traffic or considerable illegal IP packets. Meanwhile, some optical security threats like the exposed 0-day vulnerability in a Netlink Gigabit-Capable Passive Optical Network (GPON) router [5] or other remote code execution vulnerability in the majority of GPON home routers [6] which may be attacked by some botnets are increasing. As a result, the two abovementioned reasons have facilitated more and more attention on optoelectronic firewall [7] for the security of the optical layer in modern optical infrastructure.

As a promising active method to guarantee security, the optoelectronic firewall technology can eliminate some classes of insidious and malicious traffic at a dramatic operating speed within manageable costs directly in the optical domain, only allowing wanted traffic to transmit. A best-known optoelectronic firewall example is the project named WIrespeed Security Domains using Optical Monitoring (WISDOM) in 2006 [8]. The project proves that an optoelectronic firewall can avoid the cost-consuming optical-to-electrical-to-optical conversion inside a communication node and accelerate the data rate up to 42.6Gps. Nevertheless, the optoelectronic firewall in WISDOM works with the on-off keying (OOK) or intensity modulation (IM) format [7], which is hard to satisfy the required feature of efficient eFFB in F5G. Some high-order modulation formats, e.g., quadrature phase shift keying (QPSK) or 16-quadrature amplitude modulation (16QAM), must be supported to achieve high-speed optoelectronic firewalls in the future. Intuitively, all-optical pattern recognition, identifying a specific target pattern sequence from the optical input signal, is the most significant and challenging component of a high-speed optoelectronic firewall [9]. The subsequent strategies for eliminating some traffic all rely on the results of pattern recognition. Therefore, the higher the modulation formats’ order and baud rate supported by pattern recognition, the higher the processing rate of optoelectronic firewalls can reach.

For higher-speed all-optical pattern recognition supporting higher-order modulation formats, researchers never stopped. The main way is constructed by all-optical logic gates and a recursive operation, which is the initial design of the pattern recognition component in an optoelectronic firewall [7]. Webb’s team and Huang’s team have both made contributions in this way. Webb et al. [10] began to design the structure, which includes an equivalence gate (XNOR), an AND gate, and a recirculating loop integrated with a regenerator, with the data rate at 42Gbps. As continuations of [10], Xu et al. [11], Liu et al. [12] and Li et al. [13] substituted the semiconductor optical amplifiers (SOA) with high non-linear fibers (HNLF) in [10] to further accelerate the data rate of up to 200Gbps. The structure can recognize symbols of arbitrary length from the input signals, nevertheless, the structure can only deal with the modulation formats of OOK/IM or BPSK, especially for the usage of the AND gate, which may be too ossified to satisfy the required feature of dynamic GRE in F5G. Our previous works [9,14,15] have preliminarily attempted to achieve the recognition system for the high-order modulation format of QPSK by employing the format conversion based on four-wave mixing (FWM) but it can only handle one modulation format as well. Therefore, a reconfigurable requirement should be supported as well for future all-optical pattern recognition systems, especially for the reconfigurable all-optical pattern recognition supporting different high-order modulation formats used in optoelectronic firewalls for the optical layer security of F5G.

In this work, a novel reconfigurable all-optical pattern recognition system for PSK and QAM signals with two implementation architectures is proposed and simulated. The proposed system consists of two cascaded parts: a generalized XNOR (GXNOR) and a recirculating loop. The GXNOR part dominates the system. The recirculating loop part stemming from [10] is easy to understand and implement. Therefore, we first define the specific meaning of the GXNOR as an expanded concept of XNOR and dramatically find that the GXNOR is equivalent to the conjugate multiplication. Then, according to the equivalence, we propose two architectures to implement the GXNOR by employing cascaded IQ Mach-Zehnder modulators (IQMZMs) and FWM over an HNLF, respectively. Different from our previous work in [9,14,15], the format conversion and logic gate based on multiple FWM processes are no longer employed. Instead, only one FWM process is employed here to achieve the conjugate multiplication. Detailed operating principles of the two architectures are theoretically derived. Finally, after applying the two architectures to complete the proposed system, the numerical simulation results demonstrate that the proposed system is reconfigurable for different high-order modulation formats such as QPSK, 8PSK, and 16QAM. The proposed system based on the two implementation architectures of the GXNOR can both achieve all-optical pattern recognition with a recorded baud rate of up to 260GBaud. The proposed system has incomparable advantages of reconfigurable high-order modulation formats and arbitrary target pattern recognition over all the existing ways, which can be applied to the high-speed optoelectronic firewalls in F5G.

The rest content of this paper is organized as follows. In section 2, elaborate theoretical derivations for the operating principles of two reconfigurable pattern recognition architectures supporting high-order modulation formats are analyzed. In section 3, the simulation setup and parameters are configured and some simulation results are discussed for the two architectures before concluding this paper in section 4.

2. Operating principle

In this section, we first introduce the general structure of our proposed system. Then an expansion of XNOR, named GXNOR, is defined. Its two implementation architectures including the cascaded IQMZMs-based GXNOR and the FWM-based GXNOR are designed and their theoretical derivations are given at the end.

Figure 1 illustrates the general structure of our proposed system. It consists of two cascaded parts: one is GXNOR of the repeated source signal and the slowed-down target pattern signal to be recognized, and the other is a recirculating loop with a one-symbol delay.

 

Fig. 1. The structure of the reconfigurable pattern recognition system

Download Full Size | PDF

2.1 Generalized XNOR definition

Before defining the GXNOR, let us start according to the truth table of the conventional XNOR displayed as Table 1. For simplicity, assume the source and target signals are both in BPSK modulation format, with the phase $\varphi _{BPSKs}$ and $\varphi _{BPSKt}$, respectively. $\varphi _{BPSKs}=\pi$ or $\varphi _{BPSKt}=\pi$ describes the information bit 0 while $\varphi _{BPSKs}=0$ or $\varphi _{BPSKt}=0$ describes the information bit 1. The XNOR result is also in BPSK modulation format and the phase describes the same information bit as the source and target. In terms of the BPSK phase, we define two types of phases that will be used multiple times in the following description. The first one is called the reference phase, described as $\varphi _{ref}$, which is a selected constant phase. The second one is named the rotated phase, described as $\varphi _{rot}$, which is the phase rotated from the source phase to $\varphi _{ref}$. Based on the definition of two types of phases and Table 1, we can reinterpret the logic XNOR as follows:

Table 1. XNOR truth table

View Table | View all tables in this article

After the reinterpretation, the concept of XNOR can be expanded similarly for the QPSK modulation format, only $\varphi _{ref}$ and $\varphi _{rot}$ may be a little different. For simplicity again, assume $\varphi _{QPSKs}$ or $\varphi _{QPSKt}$ is the source or target phase of the Gray-code QPSK modulation format signal, respectively. $\varphi _{QPSKs}=\pi /4$ or $\varphi _{QPSKt}=\pi /4$ describes the information bits 11, $\varphi _{QPSKs}=3\pi /4$ or $\varphi _{QPSKt}=3\pi /4$ describes the information bits 01, $\varphi _{QPSKs}=-3\pi /4$ or $\varphi _{QPSKt}=-3\pi /4$ describes the information bits 00, and $\varphi _{QPSKs}=-\pi /4$ or $\varphi _{QPSKt}=-\pi /4$ describes the information bits 10. The XNOR for the QPSK modulation format can be expanded as follows:

The analogous truth table of the above XNOR is displayed in Table 2. For a QPSK signal, although the different source phases from the target phase are rotated through the same rotated phase $\varphi _{rot}$, they are totally different from the reference phase $\varphi _{ref}$, which could be considered an expansion of the concept of XNOR, defined as GXNOR here. Similarly, the GXNOR can be applied to other $m$PSK modulation formats by merely changing $\varphi _{rot}$ to $2n\pi /m$, $n\in \left \{m, m-1, m-2, \ldots, 1\right \}$ when $\varphi _{ref}$ is selected to be $\pi /m$, $m\ge 4$.

Table 2. Analogous XNOR truth table

View Table | View all tables in this article

For the $m$PSK modulation, by further considering the target phase input $\varphi _{mPSKt}$ and $\varphi _{rot}$, we dramatically found that they are associated with a linear relationship expressed as

When operating the GXNOR, the $m$PSK source phase is rotated through the phase $\varphi _{rot}$ and obtained the GXNOR phase $\varphi _{GXNOR}$ given by

In Eq. (2), the amplitudes of both source and target $m$PSK signals are omitted due to their constant power. When the reference phase $\varphi _{ref}$ is selected, $\exp \left (j\varphi _{ref}\right )$ is a costant as well. Therefore, the GXNOR can be achieved by conjugately multiplying the source and target $m$PSK signals.

The GXNOR, equivalent to the conjugate multiplication, can be further applied to $m$QAM modulation formats beyond $m$PSK. Completely consider Fig. 1, an example is given here that a pattern $T_1T_2$ would be recognized from the source $S_1S_2S_3S_4$, according to Eq. (15) in [9], and applying the fact of conjugately multiplying for GXNOR, the results of each loop in Fig. 1 can be listed as

Then the highest level over a threshold in $\left \{S_4\overline {T_1}+S_1\overline {T_2},\ S_2\overline {T_1}+S_2\overline {T_2},\ S_2\overline {T_1}+S_3\overline {T_2},\ S_3\overline {T_1}+S_4\overline {T_2}\right \}$ should coincide with the last symbol of the pattern $T_1T_2$ in the source. Based on the example of Eq. (3), we can abstract the process in Eq. (3) to a more general formula. Assume that the source signal is $S_i$, $i=1,\ 2,\ \cdots,\ M$ and the target signal is $T_j$, $j=1,\ 2,\ \cdots,\ N$, where $M$ and $N$ is the number of the symbols of the source and target signal, respectively. The output $GXNOR$ after the GXNOR part in Fig. 1 can be obtained as the Hadamard product of $S_i$ and $T_j$ in the form of the matrix shown as Eq. (4).

In Eq. (4), each column of the matrix $GXNOR$ describes the conjugate multiplication result after each loop. Then, according to the example in Eq. (3) and corresponding Refs. [9,10], the first column of $GXNOR$ should represent the first loop result in the recirculating loop part. After the whole loop, it can be equivalent to being delayed ($N$-1)-symbol. Then, the second column of $GXNOR$ should be equivalent to being delayed ($N$-2)-symbol. We can deduce the rest column in the same manner until the last column should be equivalent to no delay. Next, the delayed columns are summarized along each row to obtain the final output $Output$. We formulate the abovementioned process and compact $Output$ in a summed form in Eq. (5).

The summed form in Eq. (5) is exactly the cross-correlation of $S_i$ and $T_j$ just with a time shift of $M-N$. Since the cross-correlation is defined to judge the similarity of the two inputs, this fact reveals that the conjugate multiplication description of GXNOR achieving $Output$ in Fig. 1 can be undoubtedly applied to $m$QAM modulation formats in a pattern recognition system.

According to the abovementioned definition, implementing the GXNOR will be the most challenging and innovative part of the pattern recognition system in Fig. 1. In the next two subsections, we design two implementation architectures of the GXNOR based on the fact that it is equivalent to conjugate multiplication.

2.2 Cascaded IQMZMs-based GXNOR theoretical derivation

The first implementation architecture employs two cascaded IQMZMs, as Fig. 2 illustrates. For a push-pull IQMZM, the field transfer function $h\left (t\right )$ to transform the input signal $E_{in}\left (t\right )$ can be defined as Eq. (6). In Eq. (6), $\alpha$ is the insertion loss of the IQMZM, $a$ and $b$ describe the split ratios of the two child MZMs (MZM-I and MZM-Q in Fig. 2) and the parent MZM, respectively, which are only associated with their extinction ratios, i.e., $a=\left (\sqrt {ER_c}+1\right )/\sqrt {2\left (ER_c+1\right )}$ and $b=\left (\sqrt {ER_p}+1\right )/\sqrt {2\left (ER_p+1\right )}$, $V_{\pi RF1}$ and $V_{\pi RF2}$ are the peak radio frequency (RF) voltages of the two child MZMs required for $\pi$ phase change, $V_{\pi DC1}$ and $V_{\pi DC2}$ are the direct current (DC) voltages of the two child MZMs required for $\pi$ phase change, $V_{\pi DCp}$ is the DC voltage of the parent MZM required for $\pi$ phase change, $v_1\left (t\right )$ and $v_2\left (t\right )$ describes the in-phase (I) and quadrature (Q) tributaries of the input sequence, respectively, $V_1$, $V_2$, and $V_p$ describes the DC bias of the two child MZMs and the parent MZMs.

An $m$PSK or $m$QAM modulation format signal is usually modulated by setting $V_1=(k-1/2)V_{\pi DC1}$, $V_2=(k-1/2)V_{\pi DC2}$, (null point) and $V_{p}=(k/2-1/4)V_{\pi DCp}$ (quadrature point), $k\in \mathcal {Z}$, where $\mathcal {Z}$ is the set of all integers. To simplify the analysis, we suppose an ideal linewidth, i.e. $\textrm {0Hz}$, of the output of the Laser Diode (LD), leading $E_{in}\left (t\right )=\sqrt {P_0}$, where $P_0$ is the output power of the LD, an ideal insertion loss, i.e., $\alpha =1$, and infinite extinction ratios, resulting in $a=b=\sqrt {2}/2$. As a result, the output of the first IQMZM $S\left (t\right )$ can be formulated as

 

Fig. 2. Implementating the GXNOR by two cascaded IQMZMs.

Download Full Size | PDF

Equation (7) describes a conventional modulation process of an $m$PSK or $m$QAM modulation format for the source sequence. The modulation process of the target sequence can be achieved by the same process, especially, when we substitute $k=1$ only for $V_p$, the output $T\left (t\right )$ is modified as

For Eq. (8), it is interesting to point out that we achieve the form of conjugation compared to Eq. (7) by only modifying the DC bias of the parent MZM $V_p$. If we cascade the IQMZMs modulating $S\left (t\right )$ and $T\left (t\right )$, i.e., substitute $E_{in}\left (t\right )=S\left (t\right )$ in Eq. (8), the output will be expressed as

Equation (9) is obviously the conjugate multiplication of the source and target sequence, which implements the GXNOR part.

2.3 FWM-based GXNOR theoretical derivation

Although the first implementation architecture has already achieved the conjugate multiplication, the second IQMZM must know the constellation mapping of the $m$PSK or $m$QAM signal so that the target pattern can be conjugately modulated, especially for the signals not modulated by IQMZMs, e.g., [16]. As a supplement to addressing this minor weakness, the second implementation architecture adopting Non-degenerate FWM (NFWM) to operate conjugate multiplication directly is proposed, as Fig. 3 illustrates.

 

Fig. 3. Implementating the GXNOR by FWM over HNLF.

Download Full Size | PDF

Before the derivation of the operation principle, it is necessary to give the following basic definitions, assumptions, and approximations. Firstly, for the signals’ forward propagation along the fiber, we take the beginning of the HNLF as the origin and establish a coordinate system along the propagation direction of the optical field using the coordinate $z$. Secondly, under the quasi-continuous-wave conditions, the time dependence of the signals is neglected so that the dispersion-related term in the fiber’s non-linear Schrodinger equation could be ignored. Thirdly, although FWM is a polarization-sensitive effect, we assume that all input signals at the beginning are aligned with the fast axis (X axis) linear part of the polarization to find the approximate solution analytically from the complex coupled amplitude equations (CAEs). Finally, since the peak powers of the incident pumps to stimulate FWM are usually high enough, stimulated inelastic scattering such as stimulated Raman scattering (SRS) and stimulated Brillouin scattering (SBS) could be generated. We take no account of their influence here [9].

As illustrated in Fig. 3, suppose the input source signal [definitely can be $S\left (t\right )$ in Eq. (7)] at $z=0$ is described as $S\left (0,t\right )=S\left (t\right )=A_s\exp \left [j\left (2\pi f_c t+\varphi _{s}\right )\right ]$, where $A_s$ is the amplitude, $f_c$ is the center frequency, $\varphi _{s}$ is the phase of the source signal while the target signal is described as $T\left (0,t\right )=T\left (t\right )=A_t\exp \left \{j\left [2\pi \left (f_c+\Delta f\right ) t+\varphi _{t}\right ]\right \}$. An NFWM process is stimulated by amplifying $T\left (0,t\right )$ through an erbium-doped fiber amplifier (EDFA) over an HNLF fed with an input pump $P\left (0,t\right )=P\left (t\right )=A_p\exp \left \{j\left [2\pi \left (f_c-2\Delta f\right ) t+\varphi _{p}\right ]\right \}$ by a multiplexer (MUX). A desired idle signal at frequency $f_c-2\Delta f+f_c+\Delta f-f_c=f_c-\Delta f$ described as $I\left (z,t\right )$ will be generated after the NFWM process as Fig. 4 illustrates. Then $S\left (z,t\right )$, $T\left (z,t\right )$, $P\left (z,t\right )$ and $I\left (z,t\right )$ should satisfy a CAEs given by

 

Fig. 4. The wavelength allocation of the NFWM.

Download Full Size | PDF

In Eq. (10), assume that the power of $P\left (z,t\right )$ and $T\left (z,t\right )$ are much larger than that of $S\left (z,t\right )$ or $I\left (z,t\right )$, i.e., $\left |P\right |^2, \left |T\right |^2 \gg \left |S\right |^2, \left |I\right |^2$ and the initial value of $I\left (z,t\right )$ is 0, i.e., $I\left (0,t\right )=0$. $\gamma$ is the nonlinear parameter of the HNLF, $\Delta k=\beta _{S}+\beta _{I}-\beta _{P}-\beta _{T}$ is the mismatch of the input signals’ mode-propagation constant $\beta _{P}$, $\beta _{T}$, $\beta _{S}$, and that of output signal $\beta _{I}$. According to the assumptions and parameters described above, the solution of Eq. (10) can be solved as

For $I\left (z,t\right )$ in Eq. (11), $\gamma$, $\kappa$, and $g$ are all only related to the HNLF. The pump $P\left (0,t\right )$ does not carry any information, which can be regarded as a constant. Therefore, the conjugate multiplication of $\overline {S\left (0,t\right )}T\left (0,t\right )$ can be achieved by filtering $I\left (z,t\right )$ as $I\left (t\right )$ through an optical filter (OF) when a certain length of the HNLF is decided. Obviously, the conjugately multiplying form $\overline {S\left (0,t\right )}T\left (0,t\right )$ in Eq. (11) will lead to the conjugation $\overline {GXNOR}$ of the matrix $GXNOR$ in Eq. (4). Then, $Output$ in Eq. (5) can be compacted in the summed form $\sum _{j=1}^{N}{\overline {S_{\left (j+M-N+i-1\right )\textrm { mod }M+1}}T_j}=\overline {\sum _{j=1}^{N}{S_{\left (j+M-N+i-1\right )\textrm { mod }M+1}\overline {T_j}}}$, which is right the conjugation of the cross correlation of $S_i$ and $T_j$. In section 3, only the I tributary of the demodulated result is needed, therefore, even the NFWM process in Eq. (11) achieves the different conjugately multiplying form $\overline {S\left (0,t\right )}T\left (0,t\right )$ from that in Eqs. (3–5), the recognition result should still be maintained.

In a word, two implementation architectures can both achieve the GXNOR. We can choose an appropriate architecture based on different scenarios and then execute the subsequent recirculating loop to obtain the pattern recognition results according to Eq. (5). In addition, the time shift $M-N$ of the cross-correlation result in Eq. (5) indicates that the recognized position in the recognition result is coincident with the last symbol of the target pattern.

3. Simulation setup and results analysis

Having defined and theoretically derived the two GXNOR implementation architectures, in this section, two simulation setups of the two implementation architectures in our proposed system are illustrated first. Then the configurations of their parameters are introduced one by one. Finally, their respective performance for reconfigurable modulation formats such as QPSK, 8PSK, and 16QAM are demonstrated based on some figures of the pattern recognition results.

We use VPITransmissionMaker 9.5 to simulate the performance of the proposed system at the recorded baud rate of 260GBaud, which is the highest record baud rate supported by current commercial electro-optic modulators [17] and photodetectors [18]. The complete schematics of the proposed two architectures are illustrated in Figs. 5 and 6, respectively.

 

Fig. 5. Setup of the cascaded IQMZMs-based GXNOR architecture.

Download Full Size | PDF

 

Fig. 6. Setup of the FWM-based GXNOR architecture.

Download Full Size | PDF

3.1 Performance of the cascaded IQMZMs-based GXNOR

In Fig. 5, according to the way in [10], the source sequence is repeated for the number of target symbols times at first and then its I and Q tributaries are fed into MZM-I and MZM-Q of the first IQMZM, respectively. With the optical source of LD input and the null and quadrature point configuration of the IQMZM, $S\left (t\right )$ will be generated. From [9], we know that the pattern recognition component in an optoelectronic firewall should usually process signals transmitted from a remote node. Thus, to simulate a real transmission scenario between the pattern recognition system in the local node and the remote source-signal-generating node, we add EDFAs (EDFA1 as a booster and EDFA2 as an in-line amplifier) and standard single-mode fiber (SSMF) and dispersion compensating fiber (DCF) between the first IQMZM and the second IQMZM. The dispersion of SSMF will distort $S\left (t\right )$ severely, which must be compensated before the second IQMZM for a perfect conjugate multiplication. For an all-optical system, we simply employ the DCF here, and other all-optical technologies such as fiber Bragg grating, Gires-Tournois filter, and optical phase conjugation can also be adopted. In the second IQMZMs, the target sequence is slowed down to $1/(\textrm {the number of target symbols})$ of the original baud rate at first and then is modulated in the IQMZM. At this time, the null point is maintained while the quadrature point should be configured differently from the first IQMZM as Eq. (8) shows. After the second IQMZM, $S\left (t\right )\overline {T\left (t\right )}$ is achieved and subsequently coupled into a recirculating loop constructed by a MUX with the output of a time delay line (TDL) feedback. The number of loops is equal to the number of target symbols. In the end, the output of the recirculating loop is demodulated by a coherent receiver with the local oscillator (LO) to obtain the pattern recognition results. Such a coherent receiver here is implemented by a Costas loop [19], and only I tributary of the demodulated result is needed.

3.1.1 Parameters configuration

For the I or Q tributaries of the source and target signals, a square-root raised cosine filter with the roll-off factor of $\textrm {0.2}$ and the truncated symbols of $\textrm {64}$ is applied as the shaping filter to limit the bandwidth and reduce the Inter Symbol Interference (ISI) during the transmission. We adopt the center frequency of $\textrm {193.4145THz}$ ($\textrm {1550nm}$), the linewidth of $\textrm {100kHz}$, and the output power of $\textrm {10mW}$ with the initial phase of $\pi /4$ (to compensate the phase rotation caused by $V_p$) for the LD. For the two IQMZMs, they are both push-pull IQMZMs with $\textrm {35dB}$ extinction ratio, i.e., $ER_c=ER_p=\textrm {35dB}$, $\textrm {3dB}$ insertion loss, $V_{\pi RF1}=V_{\pi DC1}=V_{\pi RF2}=V_{\pi DC2}=\textrm {1V}$ [20], and driver voltage of $\textrm {62.5mV}$ of I or Q tributary. Both EDFAs in Fig. 5 are set to power-controlled mode with the same noise figure (NF) $\textrm {4.5dB}$ and noise tilt (NT) $\textrm {0dB/Hz}$ according to [21]. The center frequency and bandwidth of both EDFAs are set to the same as the LD’s center frequency i.e., $\textrm {193.4145THz}$ and I or Q tributary’s bandwidth, i.e., $\textrm {260GHz}$, respectively. The bandwidth setting here is equivalent to assuming an OF after each EDFA to remove the out-of-band amplified spontaneous emission (ASE) noise. The output power of EDFA1 is set to $\textrm {0.5mW}$ while that of EDFA2 is $\textrm {10mW}$.

As for the Costas coherent receiver, the balanced PDs in the coherent receiver are both PIN-model as [18] defines. The bandwidth is $\textrm {105GHz}$ and the responsivity is $\textrm {0.25A}/\textrm {W}$. Detection currents of them will be influenced by the sum of the dark current of $\textrm {5nA}$, the thermal noise of $10\textrm {pA}/\sqrt {\textrm {Hz}}$, and shot noise. After a Costas loop with the loop bandwidth of $\textrm {4MHz}$ to compensate for the frequency and phase offset, a matched filter with the same parameters as the shaping filter is applied again before the pattern recognition results are demonstrated at the end.

A summary of the parameters abovementioned is displayed in Table 3.

Table 3. Parameters in cascaded IQMZMs setup

View Table | View all tables in this article

3.1.2 Results analysis

Firstly, we assign a certain source sequence of the QPSK modulation format to explain the reason why we employ a coherent receiver instead of a single PD like [9] to obtain the pattern recognition results. According to section 2, the proposed cascaded IQMZMs system is the same as executing the cross-correlation operation in terms of the result, therefore, we select the perfect QPSK sequence [22] with good autocorrelation to interpret the usage of a coherent receiver. The complex perfect QSPK symbol is $\left \{1,1,1,1,1,j,-1,-j,1,-1,1,-1,1,-j,-1,j\right \}$ as [22] proved. We adopt Gray-code mapping so that the source QPSK sequence should be 00000000000111100011001100101101. The target pattern is selected to be $\left \{j,-1,-j,1\right \}$, i.e., 01111000 of the target QPSK sequence. The presence of the target pattern in the complex perfect QSPK symbol is from the sixth symbol to the ninth symbol. Then the highest level of the recognition result should coincide with the last symbol of the target pattern, i.e., the ninth symbol according to Eq. (5). Figure 7(a) illustrates the theoretical recognition results of the abovementioned process. Here the result from the I tributary of a coherent receiver (the solid line) conforms to the analysis while the result from a single PD (the dashed line) does not demonstrate a unique highest level, which means we can not identify the specific symbol indicating the recognized position from the result of a single PD. Furthermore, the result from a single PD also demonstrates the highest level at the eighth symbol, indicating the pattern from the fifth symbol to the eighth symbol, i.e., $\left \{1,j,-1,-j\right \}$, which is only rotated through $-\pi /2$ from the anticipated target pattern. This reveals that the detected recognition result by a single PD may cause erroneous judgment when other patterns are only rotated through an angle from the target pattern. Unless a special source sequence is designed to avoid this situation, employing a coherent receiver is necessary.

Next, we demonstrate the numerical simulation QPSK pattern recognition results as Fig. 7(b) illustrates according to the parameters in Table 3. Obviously, we obtain the highest level at the ninth symbol (about $\textrm {30.769ps}\!\sim \!\textrm {34.615ps}$ in time) as the solid line illustrates, which indicates that the sixth symbol to the ninth symbol of the source signal describes the target pattern, conforming to the theory. We also assign the only changing-one-bit case of the target sequence to prove the highest level. Since only changing one bit in the target sequence has made minimal changes to the target pattern, this may achieve the second highest level of the recognition result. For the selected target pattern 01111000, although there are eight cases of only changing one bit, Fig. 7(b) merely lists the highest and lowest amplitude at the ninth symbol among the cases as the dashed and dash-dotted lines illustrate. In the two cases, the target sequences are modified to 00111000 and 11111000, which are both not present in the source sequence. The highest amplitude of the dashed line not achieved at the highest level of the solid line also proves this. Based on the three lines, we can easily set the threshold to judge the highest level, which could be just higher than the maximum of the dashed line (the second-highest level of the recognition result). Then only the target pattern that is present in the source signal can achieve the highest level higher than the threshold. Therefore, we set the threshold as the average of the maximum of the solid and dashed line, i.e., Threshold=$\textrm {0.041954A}$ in Fig. 7(b).

Then, we similarly demonstrate the 8PSK pattern recognition results in Fig. 8(a). The perfect 8PSK sequence is still selected according to [22], with the complex 8PSK symbol $\left \{1,1,1,1,1,1,1,1,1,e^{j\pi /4},j,e^{j3\pi /4},-1,e^{-j3\pi /4},-j,e^{-j\pi /4},1,j,-1,-j,1,j,-1,-j,1,\right.$

$e^{j3\pi /4},-j,e^{j\pi /4},-1,e^{-j\pi /4},j,e^{-j3\pi /4},1,-1,1,-1,1,-1,1,-1,1,e^{-j3\pi /4},j,e^{-j\pi /4},-1,$

 

Fig. 7. QPSK theoretical and simulation recognition results.

Download Full Size | PDF

 

Fig. 8. 8PSK and 16QAM pattern recognition results of the two cascaded IQMZMs architecture.

Download Full Size | PDF

 

Fig. 9. QPSK, 8PSK, and 16QAM pattern recognition results of the two cascaded IQMZMs architecture when the transmission fiber length changes.

Download Full Size | PDF

$\left.e^{j\pi /4},-j,e^{j3\pi /4},1,-j,-1,j,1,-j,-1,j,1,e^{-j\pi /4},-j,e^{-j3\pi /4},-1,e^{j3\pi /4},j,e^{j\pi /4}\right \}$. Gray-code mapping is still adopted and the target pattern is selected to be from the tenth symbol to the seventeenth symbol (about $\textrm {61.538ps}\!\sim \!\textrm {65.385ps}$ in time) of the source signal, i.e., $\{e^{j\pi /4}, j, e^{j3\pi /4}, -1, e^{-j3 \pi /4},-j, e^{-j\pi /4}, 1\}$, indicating 001011010110111101100000 of the target 8PSK sequence. The two additional changing-one-bit sequences are 000011010110111101100000 and 001011010110111101110000, respectively. Although the difference between the highest level and the second highest level of the recognition result is small, we can still set the threshold=$\textrm {0.096299A}$ like the abovementioned discussion and achieve the highest level of the matched sequence at the seventeenth symbol according to the solid line.

Finally, we demonstrate the 16QAM pattern recognition results in Fig. 8(b). For a perfect 16QAM sequence [23], not all of the constellation points could be traversed, to employ the constellation points as many as possible, we adopt an almost perfect 16QAM sequence with 15 constellation points according to [24], which owns good autocorrelation as well. The complex 16QAM symbol is $\left \{-1-1j,-3+3j,3+3j,-1+1j,3+3j,-1+1j,3+3j,-1+1j,1+3j,\right.$

$-1-3j,-1+3j,-1+3j,3+1j,3+1j,1-3j,1-3j,-3-3j,1-1j,-1-1j,-3+3j,1+1j,$

$\left.3-3j,-1-1j,-3+3j,3+1j,3+1j,3-1j,-3+1j,1+3j,-1-3j,-3+1j,3-1j\right \}$.

Gray-code mapping is adopted again and the target pattern is selected to be $\left \{-1-3j,-1+3j,\right.$$\left.-1+3j,3+1j,3+1j,1-3j,1-3j,-3-3j\right \}$, i.e., 01100100010010011001111011100010 of the target 16QAM sequence. The two additional changing-one-bit sequences are 01100100010010011000111011100010 and 01100100010010011001111011000010, respectively. The threshold is set to $\textrm {0.30368A}$ and a similar result can be achieved as the abovementioned modulation formats.

Additionally, some factors may cause distortions in the recognition results. It is necessary to analyze the tolerance of our proposed system against them. These factors include the transmission fiber length, the laser linewidth, the noise figure and bandwidth of EDFAs, and the received power of the coherent receiver. After our simulation, in terms of the two cascaded IQMZMs architecture, only the factors of the transmission fiber length and the received power can cause the influence. We illustrate the two types of influence for three modulation formats in Figs. 9 and 10.

 

Fig. 10. QPSK, 8PSK, and 16QAM pattern recognition results of the two cascaded IQMZMs architecture when the received power after the whole loop changes.

Download Full Size | PDF

When the transmission fiber length changes, the transmission fiber will introduce a delay to the source signal. According to the cross-correlation form in Eq. (5), the value of the recognition result will be maintained but the position of the highest level will be moved. Figure 9 precisely demonstrates this phenomenon. we increase the transmission fiber length until the highest level is moved to other symbols instead of the last symbol (overflows the time frame of $\textrm {30.769ps}\!\sim \!\textrm {34.615ps}$ or $\textrm {61.538ps}\!\sim \!\textrm {65.385ps}$, annotated as the blue value of X in Fig. 9). For each modulation format, the tolerance can be up to $\textrm {3300km}$, $\textrm {1300km}$, and $\textrm {3500km}$, respectively. However, the proposed system is expected to be a reconfigurable system. Therefore, the limit of the transmission fiber length should be $\textrm {1300km}$.

As for the received power after the whole loop, apparently in Fig. 10, when it decreases, the value of the recognition result should be lower. However, when it decreases to a similar level of the noise of the balanced PDs in the coherent receiver, the impact of the noise is unpredictable, i.e., the highest level will be moved to the time except for the time frame of $\textrm {30.769ps}\!\sim \!\textrm {34.615ps}$ or $\textrm {61.538ps}\!\sim \!\textrm {65.385ps}$, annotated as the blue value of X in Fig. 10. The proposed system can not recognize the pattern correctly at this time. The tolerance of the three modulation formats is $-\textrm {39.0dBm}$, $-\textrm {35.5dBm}$, and $-\textrm {40.1dBm}$, respectively. Similarly, the limit of the received power after the whole loop should be $-\textrm {35.5dBm}$.

To summarize, our proposed system employing the two cascaded IQMZMs architecture can achieve the all-optical pattern recognition of different modulation formats such as QPSK, 8PSK, and 16QAM by only modifying different source signals and target patterns. The attainable baud rate of 260GBaud is the same as that supported by the IQMZMs, which can apply to high-speed optoelectronic firewalls.

3.2 Performance of the FWM-based GXNOR

In Fig. 6, the repeated source sequence and slowed-down target sequence are both normally modulated by two IQMZMs with the conventional DC-bias configuration like Eq. (7). The difference is the input center frequencies of LD1 and LD2, i.e., $f_c$ and $f_c+\Delta f$, respectively. The source signal $S\left (t\right )$ at $f_c$ and the target signal $T\left (t\right )$ at $f_c+\Delta f$ will be modulated after these configurations. Still taking a real transmission scenario into account, EDFA1, SSMF, and DCF are the same as the two cascaded IQMZMs architecture following the IQMZM generating $S\left (t\right )$. We modify EDFA2 to amplify $T\left (t\right )$ instead of an in-line amplifier since the FWM process needs a small signal input coupled with two high-power pumps. One of the pumps is the amplified $T\left (t\right )$, and the other pump $P\left (t\right )$ is amplified by EDFA3 at $f_c-2\Delta f$ without any modulated information. Then the FWM process is stimulated over an HNLF through the multiplexing of $P\left (t\right )$, amplified $T\left (t\right )$, and remotely transmitted $S\left (t\right )$. The idle signal $I\left (t\right )$ at $f_c-\Delta f$ is generated according to Eq. (11), describing the conjugate multiplication of $S\left (t\right )$ and $T\left (t\right )$. Filtering $I\left (t\right )$ by an OF and inputting it to the subsequent recirculating loop and the Costas coherent receiver, the recognition results will be obtained. It is noteworthy that the idle signal generated from the FWM process is usually much smaller than any input signals, therefore, we add EDFA4 before the coherent receiver to avoid it being drowned in the noise.

3.2.1 Parameters configuration

We adopt the center frequency of LD1 $f_c=\textrm {193.4145THz}$, $\Delta f=\textrm {1.2THz}$, i.e., the center frequencies of LD2 $f_c+\Delta f=\textrm {193.4145THz}+\textrm {1.2THz}=\textrm {194.6145THz}$ and LD3 $f_c-2\Delta f=\textrm {193.4145THz}-\textrm {2.4THz}=\textrm {191.0145THz}$. The noise center frequency of each EDFA is set to the same as the center frequency of the input signal. The output power of EDFA1 is set to $\textrm {2mW}$ while that of EDFA2 and EDFA3 is $\textrm {250mW}$. For EDFA4, the power is set to $\textrm {150}\mu \textrm {W}$. As for the HNLF, we adopt the commercial product NL-1550-Zero [25] from Yangtze Optical Fiber and Cable Joint Stock Limited Company (YOFC) with zeros dispersion at $\textrm {1550nm}$, $\textrm {0.03ps}/\left (\textrm {nm}^2\cdot \textrm {km}\right )$ dispersion slope, $\textrm {13.23}\mu \textrm {m}^2$ effective core area and the nonlinear Kerr coefficient $n_2=\textrm {3.264}\times \textrm {10}^{\textrm {-20}}\textrm {m}^2/\textrm {W}$. The length of the HNLF is $\textrm {200m}$. In terms of the OF, it is configured as a 1-order Gaussian bandpass filter with the center frequency of $f_c-\Delta f=\textrm {193.4145THz}-\textrm {1.2THz}=\textrm {192.2145THz}$ and the bandwidth of $\textrm {260GHz}$. Other parameters employed in Fig. 6 are set the same as the two cascaded IQMZMs architecture, which will not repeat them here.

A summary of the new parameters abovementioned is presented in Table 4.

Table 4. New parameters in FWM setup

View Table | View all tables in this article

3.2.2 Results analysis

All source and target sequences are set the same as the first architecture. Firstly, we demonstrate the frequency conversion of the FWM process in Fig. 11(a). The QPSK modulation format is taken as an example. We can see a new frequency $\textrm {192.2145THz}$ describing $I\left (t\right )$ is generated after the FWM as the solid line illustrates. During this process, the zero dispersion at $\textrm {1550nm}$ of the HNLF makes the phase matching be achieved more easily. The phase matching described as $\kappa$ in Eq. (11) plays an important role, which could severely affect the quality of the generated idle signal. Therefore, the frequency distance $\Delta f$ and the power of each participating wavelength have been carefully configured as Table 4 presents.

 

Fig. 11. QPSK frequency conversion and pattern recognition results.

Download Full Size | PDF

Next, we demonstrate the pattern recognition results of the three modulation formats abovementioned as Figs. 11(b)–12(b) illustrate. Obviously, the three figures illustrate similar results with the first architecture: the highest levels are all located at the matched position and coincide with the last symbol of the target patterns. The difference is the threshold to judge the position of the highest level. In the FWM architecture, the three thresholds ($\textrm {0.035096A}$, $\textrm {0.056725A}$, and $\textrm {0.049305A}$) tend to the same order of magnitude rather than those ($\textrm {0.041954A}$, $\textrm {0.096299A}$, and $\textrm {0.30368A}$) in the two cascaded IQMZMs. This is because we adopt EDFA4 in power-controlled mode before the coherent receiver. For different small idle signals generated from the FWM process, they can be amplified to the same power before being demodulated.

 

Fig. 12. 8PSK and 16QAM pattern recognition results of the FWM architecture.

Download Full Size | PDF

Similarly, we demonstrate the factors that have impacts on our proposed system. Except for the factors in section 3.1.2, after our simulation, factors of the laser linewidth and the noise bandwidth of EDFAs are added for the FWM architecture. We illustrate the four types of influence for three modulation formats in Figs. 13–16.

 

Fig. 13. QPSK, 8PSK, and 16QAM pattern recognition results of the FWM architecture when the transmission fiber length changes.

Download Full Size | PDF

 

Fig. 14. QPSK, 8PSK, and 16QAM pattern recognition results of the FWM architecture when the received power after the whole loop changes.

Download Full Size | PDF

 

Fig. 15. 8PSK pattern recognition results of the FWM architecture when the laser linewidth changes.

Download Full Size | PDF

 

Fig. 16. QPSK, 8PSK, and 16QAM pattern recognition results of the FWM architecture when the noise bandwidth of the EDFAs changes.

Download Full Size | PDF

For the factors of the transmission fiber length and the received power after the whole loop, Figs. 13 and 14 demonstrate a similar phenomenon of the two cascaded IQMZMs architecture, which will not repeat here. For a reconfigurable system, the tolerance should be $\textrm {500km}$ and $-\textrm {34.6dBm}$, respectively.

For the influence of the laser linewidth, after our simulation, we found that only the 8PSK modulation format has been influenced illustrated in Fig. 15. The influence is based on a wide laser linewidth up to $\textrm {100MHz}$. The reason may be that the relatively close constellation of 8PSK is sensitive to the phase noise originally. Considering a narrow laser is generally employed for coherent communication, the influence based on the wide laser linewidth of the 8PSK modulation format can be ignored.

As for the impacts on the noise bandwidth of EDFAs in Fig. 16, according to Fig. 11(a), the reason is obvious. When the noise bandwidth increases, signals $S\left (t\right )$, $T\left (t\right )$, and $P\left (t\right )$ will be overlapped in frequency, which causes interference among them. In addition, $I\left (t\right )$ after the NFWM is usually small, which can tend to be drowned in the noise amplified from EDFA2 and EDFA3 in Fig. 6. Finally, the tolerance should be narrower than $\textrm {1.56THz}$ at least for the reconfigurable system.

To summarize, our proposed system employing the FWM architecture can achieve the all-optical pattern recognition of different modulation formats same as the two cascaded IQMZMs architecture. The attainable baud rate 260GBaud is the same as the input $S\left (t\right )$ or $T\left (t\right )$, no matter how $S\left (t\right )$ or $T\left (t\right )$ is modulated, which can apply to high-speed optoelectronic firewalls more widely than the two cascaded IQMZMs architecture.

4. Conclusion

In this work, a reconfigurable all-optical pattern recognition system implemented by two architectures for PSK and QAM signals with a baud rate of up to $\textrm {260GBaud}$ has been proposed. We elaborated on the system’s operating principle in detail, especially for the expansion of the concept of XNOR and its two implementation architectures: two cascaded IQMZMs and FWM. The results demonstrated that the two architectures can both recognize target patterns for reconfigurable modulation formats such as QPSK, 8PSK, and 16QAM. Such a high baud rate and the reconfigurable pattern recognition system supporting multiple modulation formats can be applied to the high-speed optoelectronic firewalls in F5G. Although we have merely demonstrated three modulation formats in this work, more modulation formats such as 8QAM, 64QAM, etc. can be scaled as well when modifying the input source and target sequences. Additionally, the position of the highest level in the whole signal time window indicates the last symbol of the target pattern, therefore, a precise synchronization technology may be required for real experiments in the future.