Abstract

In this paper, we propose a cost-efficient, polarization-insensitive and widely-tunable wavelength conversion scheme for orthogonal frequency division multiplexing (OFDM) signal based on four-wave mixing (FWM) in semiconductor optical amplifier (SOA). In this scheme, electrical OFDM signal directly drives directly modulated laser (DML) to achieve intensity modulation, then the modulated signal lightwave and pump are coupled and injected into a polarization-diversity structure for performing FWM in SOA. The analytical results show that the proposed scheme is polarization-insensitive and has a wider conversion range compared with the parallel pump scheme and orthogonal pump scheme. We have also numerically demonstrated wavelength conversion of 16QAM-OFDM signal by employing the proposed scheme. The results can be agreed with the theoretical analyses. In addition, the impact of input optical power, line-width of external cavity laser (ECL) and injection current of SOA on the system performance are also studied.

© 2019 Optical Society of America under the terms of the OSA Open Access Publishing Agreement

1. Introduction

Wavelength division multiplexing (WDM) technique has been widely applied in optical communication systems to exploit fully the huge bandwidth resources of optical fiber [1]. But actually, the number of wavelengths in WDM system is much smaller than that of nodes and users, causing problems such as wavelength contention and network jams. So wavelength conversion (WC) technique is proposed for offering flexible routing and improving the efficiency in optical networks. Conventional wavelength converter generally employs optical-electrical-optical (O/E/O) wavelength conversion technique. The input optical signal is first converted into electrical signal, and then the wavelength conversion can be achieved by modulating the wavelength tunable laser with electrical signal. This O/E/O converter is the mature technology and easy to implement, the electric signal can also be shaped and amplified after photoelectric conversion. But its transparency is limited, and delays are usually introduced into the system. In order to improve the performance, all optical wavelength conversions (AOWC) techniques are proposed. They can efficiently avoid wavelength contention and increase throughput of future optical networks [2,3]. Orthogonal frequency division multiplexing (OFDM) technique is widely employed in optical communication system due to its strong resistance to chromatic dispersion (CD) and polarization mode dispersion (PMD), high spectral efficiency and good scalability [48]. AOWC for OFDM signal is significant to realize information exchange of high rate and large capacity in optical networks. In particular, the wavelength converter with polarization insensitivity, wide tunability and low cost are quite necessary for practical implementation in future WDM network. Several efforts have been made on AOWC of OFDM signal based on four wave mixing (FWM) in semiconductor optical amplifier (SOA) by using direct-detection approach [911]. AOWC of OFDM signal using single-pump FWM scheme has been experimentally verified [9], but this scheme is polarization sensitive. Polarization insensitive AOWC can be achieved based on parallel dual-pump FWM [10] and orthogonal pump FWM schemes [11]. However, the wavelength tunability is only about 0.02 THz in [10], and the adoption of external modulator in the three schemes increase the system cost. Another approach using two-mode injection-locking (TMIL) in a Fabry-Pérot laser has been proposed in [12]. However, the TMIL typically requires accurate wavelength control and this approach is sensitive to polarization, which reduce greatly the flexibility of wavelength converter. Besides, several FWM-based AOWC schemes of OFDM signal have been reported by employing coherent detection approach [1316], including AOWC in highly nonlinear fiber (HNLF) [13,14], in silicon waveguide [15], and in SOA [16]. However, these schemes adopting complicated receiver can increase the cost of system. Moreover, AOWC can be realized using sum frequency generation (SFG) and difference frequency generation (DFG) nonlinear processes in a periodically-poled lithium-niobate (PPLN) waveguide has been demonstrated [17]. However, the optical frequency of the pump must be matched closely to the dispersion of the nonlinear waveguide to achieve acceptable conversion efficiency. Therefore, in almost all schemes, due to the advantages of low power cost, high conversion efficiency and easy for photonics integration, using FWM in SOA for AOWC may be the most promising approach.

In this paper, we propose and numerically demonstrate a cost-efficient, polarization-insensitive and widely-tunable FWM-based AOWC scheme for OFDM signal in SOA. In the scheme, the modulated signal lightwave is generated using directly modulated laser (DML) driven by electrical OFDM signal, the modulated signal lightwave and pump are coupled and injected into a polarization-diversity structure for performing FWM in SOA. The results show that the proposed scheme is polarization-insensitive and has larger conversion range compared with the parallel pump FWM scheme and orthogonal pump FWM scheme. Finally, the effects of the input optical power, the linewidth of ECL and the injection current of SOA on the system performance are discussed by simulation, and the optimal system performance is obtained.

This paper is organized as follows. In Section 2, we describe the principle and scalability of the proposed scheme. In Section 3, the simulation setup is described and tunability and polarization insensitive of the proposed scheme are verified. Several impact factors on system are studied in Section 4. A conclusion is drawn in Section 5.

2. Theory

2.1 Principle of the proposed AOWC scheme

The principle diagram of the proposed AOWC scheme is shown in Fig. 1. The pump and signal lightwave are generated from an external cavity laser (ECL) and a directly modulated laser (DML), respectively, which can be expressed as: as ${\vec{E}_i}({\omega _i},t) = {A_i}\exp [j({\omega _i}t + {\varphi _i})] (i = 1,2)$, where ${A_i}$, ${\omega _i}$ and ${\varphi _i}$ are amplitudes, angular frequencies and phases of the pump and signal lightwave, respectively. The electrical baseband OFDM signal $s(t)$ is directly modulated on the signal lightwave by DML, which can be expressed as: ${\vec{E}_{2M}}({\omega _2},t) = {A_{OFDM}}{A_2}\exp [j({\omega _2}t + {\varphi _2})]$, where ${A_{OFDM}}$ is the amplitude of OFDM signal. The pump and the modulated signal lightwave are coupled by an optical coupler (OC). The coupled lightwaves are injected into the polarization-diversity structure. The polarization-diversity structure is illustrated schematically in Fig. 1(i), which is consists of one polarizing beam splitter (PBS), two SOAs, and one polarizing beam combiner (PBC). Figure 1(ii) shows the polarization state at the input of PBS. Pump is polarized at ${45^ \circ }$ to PBS’s principal axis, so that the pump is divided into two parts with equal power. The modulated signal lightwave ${\vec{E}_{2M}}({\omega _2},t)$ has polarization angle with respect to $x$-polarized direction. Thus, the co-polarized components of pump field and signal field ($x$ /$y$- polarized direction) are injected into each SOA, as is shown in Fig. 1(iii). The SOA can be described as a “lumped” model for FWM, consisting of a lumped saturable gain, a lumped third-order nonlinearity and the amplified spontaneous emission (ASE) noise [18], as shown in Fig. 1(iv). According to the lumped model, the pump and modulated signal lightwave are amplified by the SOA’s gain, so that, the optical field at the input to the SOA-1’s nonlinearity can be expressed as:

$${\vec{E}_{1 - SOA1}}({\omega _1},t) = {A_1}\sqrt {\alpha {G_{x1}}} \cos {45^ \circ }\exp [j({\omega _1}t + {\varphi _1})]\hat{x}$$
$${\vec{E}_{2M - SOA1}}({\omega _2},t) = {A_{OFDM}}{A_2}\sqrt {\alpha {G_{x1}}} \cos \theta \exp [j({\omega _2}t + {\varphi _2})]\hat{x}$$
where $\alpha$ is the transmissivity of PBS and PBC, ${G_{x1}}$ is SOA-1’s gain for $x$-polarized direction. According to the principle of FWM, a phase grating with frequency ${\omega _1} - {\omega _2}$ generated, which modulate input fields to generate upper and lower sidebands because of the three-order nonlinear effect in SOA. In this case, two converted lightwaves with frequency $2{\omega _1} - {\omega _2}$ and $2{\omega _2} - {\omega _1}$ are generated, which is shown in Fig. 1(v). We only consider the converted lightwave with frequency $2{\omega _1} - {\omega _2}$ as follows:
$$\begin{aligned} {{\vec{E}}_{c1}}(2{\omega _1} - {\omega _2},t) &= {r_1}({\omega _1} - {\omega _2})({{\vec{E}}_{1 - SOA1}} \cdot \vec{E}_{2M - SOA1}^\ast ){{\vec{E}}_{1 - SOA1}}\\ & = \frac{1}{2}\alpha \sqrt \alpha A_1^2{A_2}{A_{OFDM}}{G_{x1}}\sqrt {{G_{x1}}} \cos \theta \cdot {r_1}({\omega _1} - {\omega _2}){e^{j({2{\omega_1} - {\omega_2}} )t}}{e^{j({2{\varphi_1} - {\varphi_2}} )}}\hat{x} \end{aligned}$$
where ${r_1}({\omega _1} - {\omega _2})$ is the relative conversion efficiency function that inversely proportional to frequency separation [19,20]. Then, the power of the converted lightwave ${\vec{E}_{c1}}(2{\omega _1} - {\omega _2},t)$ can be expressed as:
$${P_{c1}} = \frac{1}{4}{\alpha ^3}A_1^4A_\textrm{2}^2A_{OFDM}^2G_{x1}^3{\cos ^2}\theta \cdot {R_1}({\omega _1} - {\omega _2})$$
here ${R_1}({\omega _1} - {\omega _2}) = {|{{r_1}({\omega_1} - {\omega_2})} |^2}$. Similarly, the amplified pump and signal lightwave in SOA-2 can be expressed as:
$${\vec{E}_{1 - SOA\textrm{2}}} = {A_1}\sqrt {\alpha {G_{y2}}} \sin {45^ \circ }\exp [j({\omega _1}t + {\varphi _1})]\hat{y}$$
$${\vec{E}_{2M - SOA\textrm{2}}} = {A_{OFDM}}{A_\textrm{2}}\sqrt {\alpha {G_{y2}}} \sin \theta \cdot \exp [j({\omega _2}t + {\varphi _2})]\hat{y}$$
the converted lightwave with frequency $2{\omega _1} - {\omega _2}$ in SOA-2 can be expressed as:
$${\vec{E}_{c2}}(2{\omega _1} - {\omega _2},t) = \frac{1}{2}\alpha \sqrt \alpha A_1^2{A_\textrm{2}}{A_{OFDM}}{G_{y2}}\sqrt {{G_{y2}}} \sin \theta \cdot {r_2}({\omega _1} - {\omega _2}){e^{j({2{\omega_1} - {\omega_2}} )t}}{e^{j({2{\varphi_1} - {\varphi_2}} )}}\hat{y}$$
then, the power of the converted lightwave ${\vec{E}_{c2}}(2{\omega _1} - {\omega _2},t)$ can be expressed as:
$${P_{c2}} = \frac{1}{4}{\alpha ^3}A_1^4A_\textrm{2}^\textrm{2}A_{OFDM}^2G_{y2}^3{\sin ^2}\theta \cdot {R_2}({\omega _1} - {\omega _2})$$
where ${G_{y2}}$ is SOA-2’s gain for $y$-polarized direction and ${R_2}({\omega _1} - {\omega _2}) = {|{{r_2}({\omega_1} - {\omega_2})} |^2}$.

 figure: Fig. 1.

Fig. 1. Principle diagram of the proposed AOWC scheme for OFDM signal. (i) The structure of polarization-diversity; (ii) The polarization state of input lightwaves; (iii) The two orthogonal polarization modes after PBS; (iv) The model of SOA; (v) The output optical spectrum of the polarization-diversity structure. DML: directly modulated laser; ECL: external cavity laser; OC: optical coupler; PC: polarization controller; PBS: polarization beam splitter; PBC: polarization beam combiner; SOA: semiconductor optical amplifier; OBPF: optical band pass filter; PD: photoelectric detector.

Download Full Size | PPT Slide | PDF

The two orthogonal polarization modes are combined by a PBC. The output optical spectrum of the polarization-diversity structure is shown in Fig. 1(v). The converted lightwave with frequency $2{\omega _1} - {\omega _2}$ can be obtained by an optical band pass filter (OBPF), and the power of the converted lightwave is given by:

$${P_c} = \alpha ({P_{c1}} + {P_{c2}}) = \frac{1}{4}{\alpha ^4}A_1^4A_\textrm{2}^\textrm{2}A_{OFDM}^2[{G_{x1}^3{{\cos }^2}\theta \cdot {R_1}({\omega_1} - {\omega_2}) + G_{y\textrm{2}}^3{{\sin }^2}\theta \cdot {R_2}({\omega_1} - {\omega_2})} ]$$
If the two SOAs have identical polarization-insensitive gain (${G_{x1}} = {G_{y2}} = G$) and identical relative conversion efficiency functions (${R_\textrm{1}}({\omega _1} - {\omega _2})\textrm{ = }{R_\textrm{2}}({\omega _1} - {\omega _2})\textrm{ = }R({\omega _1} - {\omega _2})$), then Eq. (9) can be reduced to:
$${P_c} = \frac{1}{4}{\alpha ^4}A_1^4A_\textrm{2}^\textrm{2}A_{OFDM}^2{G^3}R({\omega _1} - {\omega _2})$$
Equation (10) shows that the output power of the converted lightwave at $2{\omega _1} - {\omega _2}$ is independent of the polarization angle $\theta$ of signal lightwave. Therefore, the converted lightwave with frequency $2{\omega _1} - {\omega _2}$ is polarization insensitive.

2.2 Investigation of wavelength tunability

In this sub-section, the wavelength tunability (i.e. the conversion range) of the parallel pump FWM scheme, the orthogonal pump FWM scheme and the proposed FWM scheme is investigated and compared. Figure 2 illustrates the output spectra of the three FWM schemes. In the parallel pump scheme, pump 1 and pump 2 produce a phase grating with frequency $|{{\omega_1} - {\omega_2}} |$, modulating signal lightwave to generate a converted lightwave with frequency ${\omega _1} - {\omega _2}\textrm{ + }{\omega _3}$. In the orthogonal pump scheme, pump 1 and the signal lightwave produce a phase grating with frequency $|{{\omega_1} - {\omega_3}} |$, modulating pump 2 to generate a converted lightwave with frequency ${\omega _1} + {\omega _2} - {\omega _3}$. In the proposed scheme, pump 1 and signal lightwave produce a phase grating with frequency $|{{\omega_1} - {\omega_2}} |$, resulting in a converted lightwave with frequency $2{\omega _1} - {\omega _2}$. Here, the conversion range $\Delta \omega$ is defined as the frequency separation between the signal lightwave and converted lightwave. Among the three FWM schemes, the conversion ranges $\Delta \omega$ are ${\omega _2} - {\omega _1}$, $\textrm{2}{\omega _\textrm{3}} - {\omega _2} - {\omega _1}$ and $\textrm{2}{\omega _2} - \textrm{2}{\omega _1}$, respectively.

 figure: Fig. 2.

Fig. 2. Schematic illustration of the output spectrum in three FWM schemes: (a) parallel pump scheme, (b) orthogonal pump scheme, (c) polarization-diversity scheme.

Download Full Size | PPT Slide | PDF

According to the lumped model, the signal to noise ratio (SNR) of three schemes are given by the following equations [18]:

Parallel pump scheme:

$$SN{R_{\textrm{pp}}} = H \cdot R(\Delta {\omega _{pp}}) \cdot {2^{\beta - 3\gamma - 1}}$$
Orthogonal pump scheme:
$$SN{R_{op}} = H \cdot R(\frac{{\Delta {\omega _{op}}}}{2}) \cdot {2^{\beta - 3\gamma - 1}}$$
Polarization-diversity scheme:
$$SN{R_{pd}} = H \cdot R(\frac{{\Delta {\omega _{pd}}}}{2}) \cdot \frac{{{\alpha ^{\beta - 3\gamma + 3}}}}{2}$$
where
$$H = \frac{{{a^3}A_\textrm{2}^\textrm{2}A_{OFDM}^2}}{{b \cdot \Delta f}} \cdot A_1^{4 + 2\beta - 6\gamma }$$
Here $a,\textrm{ }b,\textrm{ }\beta \textrm{ }$ and $\gamma$ are constants related to device characteristic, $\Delta f$ is the noise-equivalent bandwidth of the receiver, $R(\Delta \omega )$ is the relative conversion efficiency function that inversely proportional to conversion range $\Delta \omega$. Equations (11)–(13) show that, the relative conversion efficiency function $R(\Delta \omega )$ is inversely proportional to conversion range $\Delta \omega$, so the output $SNR$ decreases with the increase of conversion range $\Delta \omega$. In other words, the conversion range of wavelength conversion can be increased until the output SNR falls below the minimum SNR ($SN{R_{\min }}$) acceptable for reception. If the three FWM schemes have the same $SN{R_{\min }}$, the following relations between the maximum tunabilities ($\Delta {\omega _{pp\_\max }}$, $\Delta {\omega _{op\_\max }}$ and $\Delta {\omega _{pd\_\max }}$) of three schemes are given from Eqs. (11)–(13):
$$R(\Delta {\omega _{op\_\max }}/2) = R(\Delta {\omega _{pp\_\max }})$$
$$\frac{{R(\Delta {\omega _{op\_\max }}/2)}}{{R(\Delta {\omega _{pd\_\max }}/2)}} = \frac{{{\alpha ^{\beta - 3\gamma + 3}}}}{{{2^{\beta - 3\gamma }}}}$$
Equations (15)–(16) show that the conversion range of polarization-diversity scheme is wider than that of the parallel pump and orthogonal pump schemes if $\alpha > {\alpha _{\min }}$, where ${\alpha _{\min }} = {2^{\beta - 3\gamma /\beta - 3\gamma + 3}}$. According to the experimental measured values of $\gamma = 0.88$ and $\beta = 0.76$, we can obtain ${\alpha _{\min }} \approx \textrm{0}\textrm{.3}$ [18]. Generally the transmissivity of commercial PBS and PBC is $\alpha > 0.9$ [21]. Under these circumstances, the polarization-diversity scheme has the widest tunable range among three FWM schemes.

3. Simulation and results

3.1 Simulation setup

In order to verify the theory analysis, the simulation setup is established based on Fig. 1. OFDM signal is generated by Matlab program offline. Figure 3(a) shows the details of the digital signal processing (DSP) for OFDM modulation at the OFDM transmitter. The procedure of DSP at OFDM transmitter is as follows: firstly, a pseudo-random binary sequence (PRBS) with a length of 55296 bits is stored in local document, which is used to assess the transmission performance of the proposed scheme. Next, a parallel 216-bit sequence is mapped into 54 16-QAM complex-valued symbols. In this paper, the 1st–54th subcarriers (SCs) are modulated by the 54 complex-valued symbols, while the direct-current (DC) subcarrier (SC index is 0), the Nyquist SC (SC index is 64) and other 9 high-frequency SCs (SC indices from 55 to 63) are set as 0. Here, the DC subcarrier is easily interfered and the Nyquist SC has phase blur at recovery, so they are set as 0 and the 9 high-frequency zero-SCs are used for over-sampling. In addition, the 63 negative-frequency SCs (SC indices from −1 to −63) are the complex conjugates of the 63 positive-frequency SCs (SC indices from 1 to 63), which makes the input data satisfy Hermitian symmetry. A training sequence (TS) is inserted for timing synchronization and channel estimation. The real-valued OFDM symbol is produced after the 128-point inverse discrete Fourier transform (IFFT). In order to avoid inter-symbol interference (ISI), a 16-point cyclic prefix (CP) is added at the beginning of each IFFT output. The OFDM frame consists of a TS and 256 OFDM symbols. The effective sampling rate is 20 GSa/s, so the bandwidth of OFDM signal is $({54 + 1} )/128 \times 20\textrm{ }GHz \approx 8.6\textrm{ }GHz$ and the net signal bit rate is ${{(256 \times 54 \times 4)} \mathord{\left/ {\vphantom {{(256 \times 54 \times 4)} {(256 + 1) \times (128 + 16)}}} \right.} {(256 + 1) \times (128 + 16)}} \times 20 \approx 30\textrm{ }Gbit/s$. A continuous-wave (CW) lightwave emitted from a DML with a line-width of 100 kHz is utilized for signal lightwave at 193.5 THz. The DML is driven by OFDM signal to achieve intensity modulation and output the double-side-band OFDM signal lightwave. ECL with a line-width of 100 kHz is utilized for pump at 193. 47 THz. The polarization states of the pump and OFDM signal lightwave are controlled with polarization controllers PC1, and PC2, respectively. After passing through PCs, the signal lightwave and pump are coupled by an OC and are fed into the polarization-diversity structure for FWM. The injection power of pump and signal lightwave are 16 dBm and 2 dBm, respectively. Eeach SOA injection current is 0.32 A. The differential gain of SOA is 2.78×10−20 m2, the carrier density at transparent is 1.4×1024 m3 and the initial carrier density is 3×1024 m3. In the polarization-diversity structure, the coupled lightwaves are split into two orthogonal polarization modes by PBS, and two single-polarization FWMs performing in two SOAs, respectively. After FWM, converted lightwave is generated and the two orthogonal polarization modes are combined by a PBC. Then the converted lightwave with frequency 193.44 THz is filtered out by an optical band-pass filter (OBPF) and detected by a photodiode (PD) before sending into OFDM receiver. Figure 3(b) shows the details of the DSP for OFDM demodulation at the receiver. The main DSP procedure of OFDM receiver include TS-based symbol synchronization, serial to parallel conversion, the removal of CP and fast Fourier transformation (FFT), channel equalization, 16-QAM de-mapping et al.

 figure: Fig. 3.

Fig. 3. The flow of DSP at (a) transmitter and (b) receiver.

Download Full Size | PPT Slide | PDF

The optical spectra before and after the structure of polarization-diversity are described in Figs. 4(a) and 4(b), respectively. Also visible in Fig. 4(b) are undesired signals (e.g. ider1 and ider2) near the converted lightwave, produced by four wave mixing between the converted lightwave and signal lightwave. When the frequency separation $\Delta \omega$ is larger than the bandwidth of optical OOFDM signal (about 17.2 GHz), these undesired signals fall beside the desired converted lightwave, where they can be rejected by filtering. In addition, the power of signal lightwave and pump can be further optimized in order to guarantee signal quality of converted lightwave. The received constellation diagrams of 16QAM signal before and after FWM as shown in Figs. 4(c) and 4(d). Compared with the original OFDM signal, the constellation only makes a little divergent, which indicates that the polarization-diversity wavelength conversion has good performance. The slight degradation is mainly caused by the noises including from the ASE of the SOA and the fluctuation of laser sources.

 figure: Fig. 4.

Fig. 4. Optical spectrum (a) before and (b) after FWM process; constellations before (c) and after (d) FWM process.

Download Full Size | PPT Slide | PDF

3.2 Polarization sensitivity

Firstly, the polarization state of the pump is fixed at 45° to the PBS. In order to study the polarization sensitivity of the proposed scheme, we observe the power variation of converted lightwave by varying the polarization state of signal lightwave. The optical power of the converted lightwave as a function of the polarization angle for the signal lightwave and corresponding optical spectra are shown in Fig. 5. From Fig. 5, it can be seen that the power fluctuation of the converted lightwave is less than 0.5 dB when the polarization angle of signal lightwave changes from $- {90^ \circ }$ to ${90^ \circ }$. For instance, the power of the converted lightwave is 7.1, 7.4, 7.4 and 7.1 dBm when the polarization angle are −90°, −30°, 30° and ${90^ \circ }$, respectively (see Figs. 5(a)–5(d)). The simulation result is consistent with the theoretical analysis shown in Eq. (10).

 figure: Fig. 5.

Fig. 5. The power of converted lightwave as a function of polarization angle of signal lightwave. (a) $- {90^ \circ }$, (b) $- {30^ \circ }$, (c) ${30^ \circ }$, and (d) ${90^ \circ }$.

Download Full Size | PPT Slide | PDF

3.3 Wavelength tunability

In order to validate the tunability, the proposed scheme is compared with the other two FWM schemes (parallel-pump and orthogonal pump schemes) mentioned in Section 2.2. According the analysis in Section 2.2, changing ${\omega _1}$ of pump 1 will change the frequency of converted lightwave results in variation of frequency separation $\Delta \omega$. Therefore, we evaluate the performance of converted signal lightwave of the three schemes by changing the frequency ${\omega _1}$ of pump 1 to observe the maximum tunabilities of three schemes.

In the parallel pump scheme, the frequencies of signal lightwave and pump 2 are fixed at 193.5 and 193.22THz. Bit-error-ratio (BER) versus different frequency separations $\Delta \omega$ is obtained by changing the frequency of pump 1 from 193.2 THz to 193.16THz as shown in Fig. 6. It is observed that the BER is increased as the $\Delta \omega$ increases. And when the BER achieves the FEC limitation of $1 \times {10^{ - 3}}$, the $\Delta \omega$ varies from 0.02 to 0.07 THz (see Figs. 6(a)–(b)). For instance, the BER are $1 \times {10^{ - \textrm{4}\textrm{.14}}}$ and $1 \times {10^{ - 3.1}}$ when frequency separations are 0.02 and 0.07THz, respectively. We can see from Figs. 6(a)–6(b) that the power of converted lightwave varies from 1dBm to −11dBm as the $\Delta \omega$ increases. The reason is that the conversion efficiency function is inversely proportional to the frequency spacing between two pumps.

 figure: Fig. 6.

Fig. 6. BER curves versus different frequency separations and optical spectra at frequency separations of (a) 0.02THz and (b) 0.07THz of parallel pump scheme.

Download Full Size | PPT Slide | PDF

In the orthogonal pump scheme, the frequencies of signal lightwave and pump 2 are fixed at 193.5 and 193.48THz. BER versus different frequency separations $\Delta \omega$ is obtained by changing the frequency of pump 1 from 193.46 THz to 193.36THz, as shown in Fig. 7. It is observed that the BER is increased with the increasing $\Delta \omega$. And when the BER achieves the FEC limitation of $1 \times {10^{ - 3}}$, the $\Delta \omega$ varies from 0.06 to 0.14THz (see Figs. 7(a)–7(b)). For instance, the BER are $1 \times {10^{ - \textrm{4}\textrm{.14}}}$ and $1 \times {10^{ - \textrm{3}\textrm{.1}}}$ when frequency separations are 0.06 and 0.14THz, respectively. From Figs. 7(a)–7(b), the power of converted lightwave varies from −2dBm to −12dBm as the $\Delta \omega$ increases, because the conversion efficiency function is inversely proportional to the frequency spacing between pump and signal lightwave.

 figure: Fig. 7.

Fig. 7. BER curves versus different frequency separations and optical spectra at frequency separations of (a) 0.06THz and (b) 0.14THz of orthogonal pump scheme.

Download Full Size | PPT Slide | PDF

In the polarization-diversity scheme, the frequencies of signal lightwave and pump 2 are fixed at 193.5 and 193.48THz. BER versus different frequency separations $\Delta \omega$ of polarization-diversity scheme is obtained by changing the frequency of pump 1 from 193.48 THz to 193.4 THz, as shown in Fig. 8. It is observed that the BER is increased as the $\Delta \omega$ increases. And when the BER achieves the FEC limitation of $1 \times {10^{ - 3}}$, the $\Delta \omega$ varies from 0.04 to 0.18THz (see Figs. 8(a)–8(b)). For instance, the BER are $1 \times {10^{ - \textrm{3}\textrm{.96}}}$ and $1 \times {10^{ - \textrm{3}\textrm{.1}}}$ when frequency separations are 0.04 and 0.18THz, respectively (see Figs. 8(a)–8(b)). From Figs. 8(a)–8(b), the power of converted lightwave varies from 8.3dBm to −3.3dBm as the $\Delta \omega$ increases. Tthe reason is that the conversion efficiency function is inversely proportional to the frequency spacing between pump and signal lightwave.

 figure: Fig. 8.

Fig. 8. BER curves versus different frequency separations and optical spectra at frequency separations of (a) 0.04THz and (b) 0.18THz of polarization-diversity scheme.

Download Full Size | PPT Slide | PDF

In conclusion, the conversion range of parallel pump, orthogonal pump and polarization-diversity schemes are 0.05, 0.08 and 0.14 THz, respectively, as shown in Figs. 78. Therefore, the proposed polarization-diversity scheme enables widest wavelength tunability among three FWM schemes, which is in accord with the analysis of section 2.2.

4. Discussion

Based on the above simulation results, several key factors that affect system performance are discussed, such as input optical power, line-width of external cavity laser (ECL) and injection of SOA.

4.1 Input optical power

The influence of optical power on BER performance is studied by numerical simulation. Figure 9(a) shows the BER as a function of power of signal lightwave when pump power is fixed at 16 dBm. It is clear that the BER performance improves when the signal lightwave power is increased from −9 dBm, and reaches minimum at 2dBm. That is because a low signal lightwave power leads to insufficient FWM and low power of converted lightwave, yielding poor BER performance. Afterwards, FWM effects between subcarriers (in-band noise) start to dominate and BER increases. Figure 9(b) shows the BER as a function of pump power when signal lightwave power is fixed at 2 dBm. The trend is similar for different signal lightwave powers. The BER performance improves when the pump power is increased from 11 dBm, and reaches minimum at 22 dBm. That is because increased pump power results in sufficient conversion efficiency and consequently the lowest BER is obtained. When the power of pump is further increased to greater than 22 dBm, the higher pump power can cause SOA’s gain saturation that result in increased BER. To conclude, the optimal system performance with BER of 10−5 is obtained when the power difference between pump and signal lightwave ranges from 14 dB to 20 dB.

 figure: Fig. 9.

Fig. 9. BER curves versus input optical power of (a) signal lightwave and (b) pump.

Download Full Size | PPT Slide | PDF

4.2 Line-width of external cavity laser (ECL)

Laser’s phase noise is caused by fluctuation in the laser source, such as spontaneous emission, temperature, and stimulated emission. Consequently, the output spectrum of laser is not a single frequency, but having a spectral line-width ranging from hundreds of kHz to hundreds of MHz [22]. The relation between the variance of phase noise and the line-width of laser can be expressed as [23]:

$$\left\langle {\Delta {\phi^2}(t)} \right\rangle = 2\pi \Delta \upsilon t$$
where $\Delta \phi (t)$ represents the phase noise, it’s a function related with time t, $\Delta \upsilon$ is the line-width of laser.

According to Eq. (17), the wider the line-width is, the greater the phase noise is. Because large phase noise from pump can be transferred to converted lighwave after wavelength conversion based on FWM in SOA [24]. Here, we investigate the impact of line-width of ECL on system performance. Figure 10 shows the system BER versus line-width of ECL. It can be seen that as the line-width increases from 0.1 MHz to 1 MHz, the BER increases from $1\textrm{ } \times \textrm{ }{10^{ - 4.3}}$ to $1\textrm{ } \times \textrm{ }{10^{ - 2.5}}$. The constellation diagrams at a line-width of 0.1 MHz, 0.4 MHz, 0.7 MHz and 1 MHz are shown in Figs. 10(a)–10(d). It can be seen from the Fig. 10 that the constellation points become divergent with an increased linewidth. That is because phase noise can cause a spectrum spreading of subcarrier of received signal, leading to inter-carrier interference (ICI) in OFDM optical communication system [25]. Moreover, higher-order modulation with small distance between constellation points results in a low phase noise tolerance, presenting deterioration of signal quality.

 figure: Fig. 10.

Fig. 10. BER curve and constellations versus different line-width of ECL.

Download Full Size | PPT Slide | PDF

Thus, the line-width of ECL used in theory should be narrowed as much as possible to relieve the distortions caused by phase noise. However, considering practical application, ECL with line-width of 100 kHz available commercially can be selected to maintain an acceptable performance.

4.3 Injection current of SOA

Figure 11 shows the BER performance versus injection current of SOA. It can be seen that as the injection current of SOA increases from 0.18 A to 0.3 A, the BER decreases from $1\textrm{ } \times \textrm{ }{10^{ - 2.95}}$ to $1\textrm{ } \times \textrm{ }{10^{ - 3.84}}$, but there is an optimal injection current of 0.3 A. When the injection current is greater than the optimal value, the BER gradually increases. The result can be explained that the third-order nonlinearity is enhanced with the increase of injection current, but at the same time the gain of SOA will be reduced. These two effects interact with each other all the time, so there is an optimal injection current.

 figure: Fig. 11.

Fig. 11. BER curve and constellations versus different SOA injection current.

Download Full Size | PPT Slide | PDF

5. Conclusion

In this paper, a cost-efficient, polarization-insensitive and widely-tunable AOWC scheme for OFDM signal is proposed and numerically investigated. In the scheme, the modulated signal lightwave is generated using DML driven by electrical OFDM signal, and the modulated signal lightwave and pump are coupled and injected into a polarization-diversity structure for performing FWM in SOA. Wavelength conversion of 16QAM-OFDM signal is achieved by simulation. Results show that the power variation of the converted lightwave is less than 0.5 dB with polarization angle of the signal lightwave changed from $- {90^ \circ }$ to ${90^ \circ }$. The proposed scheme with conversion range of 0.14 THz is wider than parallel pump scheme of 0.05 THz and orthogonal pump of 0.08 THz under same conditions. The simulation results are consistent with the theoretical analysis. Furthermore, we found that the line-width of ECL, input optical power and injection current of SOA have great impacts on system performance through simulation. The optimal line-width of ECL is 100 kHz and the optimal SOA’s injection current is 0.3 A; when power difference of pump and signal between 14 dB to 20 dB, system gains the best performance.

Funding

National Natural Science Foundation of China (61701180, 61775054, 61805079); Natural Science Foundation of Hunan Province (2017JJ3212); Scientific Research Foundation of Hunan Provincial Education Department (18B026).

References

1. D. Chadha, Optical WDM Networks: From Static to Elastic Networks (Wiley-IEEE, 2019), Chap. 1.

2. T. Ohtsuki and M. Matsuura, “Wavelength Conversion of 25-Gbit/s PAM-4 Signals Using a Quantum-Dot SOA,” IEEE Photonics Technol. Lett. 30(5), 459–462 (2018). [CrossRef]  

3. J. X. Gong, J. Xu, M. Luo, X. Li, Y. Qiu, Q. Yang, X. L. Zhang, and S. Yu, “All-optical wavelength conversion for mode division multiplexed superchannels,” Opt. Express 24(8), 8926–8939 (2016). [CrossRef]  

4. N. E. Jolley, H. Kee, R. Rickard, J. Tang, and K. Cordina, “Generation and propagation of a 1550 nm 10 Gbit/s Optical Orthogonal Frequency Division Multiplexed signal over 1000 m of Multimode fibre using a directly modulated DFB,” in Optical Fiber Communication Conference and Exposition and The National Fiber Optic Engineers Conference, Technical Digest (CD) (Optical Society of America, 2005), paper OFP3.

5. B. Hongchun and S. William, “Transmission simulation of coherent optical OFDM signals in WDM systems,” Opt. Express 15(8), 4410–4418 (2007). [CrossRef]  

6. M. Chen, J. He, Q. Fan, Z. Dong, and L. Chen, “Experimental Demonstration of Real-Time High-Level QAM-Encoded Direct-Detection Optical OFDM Systems,” J. Lightwave Technol. 33(22), 4632–4639 (2015). [CrossRef]  

7. H. Zhou, Z. Zheng, and Q. Wan, “Radio over fiber system carrying OFDM signal based on optical octuple frequency technique,” Opt. Commun. 349, 54–59 (2015). [CrossRef]  

8. F. Li, J. Yu, Z. Cao, M. Chen, J. Zhang, and X. Li, “Demonstration of 520 Gb/s/lambda pre-equalized DFT-spread PDM-16QAM-OFDM signal transmission,” Opt. Express 24(3), 2648–2654 (2016). [CrossRef]  

9. Z. Dong, Z. Cao, J. Lu, L. Chen, and J. Yu, “All-Optical Wavelength Conversion Based on Four Wave Mixing in Semiconductor Optical Amplifier for OFDM Optical Signal,” Chin. J. Lasers 36(11), 2952–2956 (2009). [CrossRef]  

10. J. Lu, Y. Hu, J. Liu, X. Zeng, and J. Gao, “All-Optical Wavelength Conversion Based on Parallel Dual-Pump for Polarization Multiplexing OFDM Signal in SOA,” Chin. J. Lasers 42(2), 0205005 (2015). [CrossRef]  

11. Z. Cao, Z. Dong, J. Lu, L. Chen, and J. Yu, “All-optical Orthogonal-pump wavelength conversion of optical OFDM signal,” J. Optoelectronics. Laser. 20(5), 622–627 (2009).

12. J. T. Dang, X. W. Yi, J. Zhang, T. P. Ye, B. Xu, and K. Qiu, “Experimental characterization of an all-optical wavelength converter of OFDM signals using two-mode injection-locking in a Fabry–Pérot laser,” Opt. Express 24(15), 16711–16721 (2016). [CrossRef]  

13. S. H. You, C. Li, Q. Yang, M. Luo, Y. Qiu, X. Xiao, and S. Yu, “Seamless Sub-Band Wavelength Conversion of Tb/s-Class CO-OFDM Superchannels,” IEEE Photonics Technol. Lett. 26(8), 801–804 (2014). [CrossRef]  

14. C. Li, M. Luo, Z. He, H. Li, J. Xu, S. You, Q. Yang, and S. Yu, “Phase noise canceled polarization-insensitive all-optical wavelength conversion of 557-Gb/s PDM-OFDM signal using coherent dual-pump,” J. Lightwave Technol. 33(13), 2848–2854 (2015). [CrossRef]  

15. C. Li, C. Gui, X. Xiao, Q. Yang, S. Yu, and J. Wang, “On-chip all-optical wavelength conversion of multicarrier, multilevel modulation (OFDM m-QAM) signals using a silicon waveguide,” Opt. Lett. 39(15), 4583–4586 (2014). [CrossRef]  

16. J. Ma, J. Lu, J. F. Liu, and P. Wu, “The Cost-efficient All-optical Wavelength Conversion for 160 Gbps CO-OFDM Signal Based on SOA,” in International Conference on Optical Communications and Networks (ICOCN, 2016), pp. 1–3.

17. X. Wu, W. R. Peng, V. Arbab, J. Wang, and A. Willner, “Tunable optical wavelength conversion of OFDM signal using a periodically-poled lithium niobate waveguide,” Opt. Express 17(11), 9177–9182 (2009). [CrossRef]  

18. J. P. R. Lacey, M. A. Summerfield, and S. J. Madden, “Tunability of Polarization-Insensitive Wavelength Converters Based on Four-Wave Mixing in Semiconductor Optical Amplifiers,” J. Lightwave Technol. 16(12), 2419–2427 (1998). [CrossRef]  

19. J. Zhou, N. Park, J. W. Dawson, K. J. Vahala, M. A. Newkirk, and B. I. Miller, “Efficiency of broadband four-wave mixing wavelength conversion using semiconductor traveling-wave amplifiers,” IEEE Photonics Technol. Lett. 6(1), 50–52 (1994). [CrossRef]  

20. J. Zhou, N. Park, K. J. Vahala, M. A. Newkirk, and B. I. Miller, “Four-wave mixing wavelength conversion efficiency in semiconductor traveling-wave amplifiers measured to 65 nm of wavelength shift,” IEEE Photonics Technol. Lett. 6(8), 984–987 (1994). [CrossRef]  

21. L. Li and J. A. Dobrowolski, “Visible broadband, wide-angle, thin-film multilayer polarizing beam splitter,” Appl. Opt. 35(13), 2221–2225 (1996). [CrossRef]  

22. X. Yi, W. Shieh, and Y. Ma, “Phase Noise Effects on High Spectral Efficiency Coherent Optical OFDM Transmission,” J. Lightwave Technol. 26(10), 1309–1316 (2008). [CrossRef]  

23. C. Henry, “Theory of the line-width of semiconductor lasers,” IEEE J. Quantum Electron. 18(2), 259–264 (1982). [CrossRef]  

24. R. Hui and A. Mecozzi, “Phase noise of four-wave mixing in semiconductor lasers,” Appl. Phys. Lett. 60(20), 2454–2456 (1992). [CrossRef]  

25. D. Dhawan and N. Gupta, “Investigation of Tolerable Laser Line-width for Different Modulation Formats in CO-OFDM Systems,” Opt. Photonics J. 07(05), 92–100 (2017). [CrossRef]  

References

  • View by:

  1. D. Chadha, Optical WDM Networks: From Static to Elastic Networks (Wiley-IEEE, 2019), Chap. 1.
  2. T. Ohtsuki and M. Matsuura, “Wavelength Conversion of 25-Gbit/s PAM-4 Signals Using a Quantum-Dot SOA,” IEEE Photonics Technol. Lett. 30(5), 459–462 (2018).
    [Crossref]
  3. J. X. Gong, J. Xu, M. Luo, X. Li, Y. Qiu, Q. Yang, X. L. Zhang, and S. Yu, “All-optical wavelength conversion for mode division multiplexed superchannels,” Opt. Express 24(8), 8926–8939 (2016).
    [Crossref]
  4. N. E. Jolley, H. Kee, R. Rickard, J. Tang, and K. Cordina, “Generation and propagation of a 1550 nm 10 Gbit/s Optical Orthogonal Frequency Division Multiplexed signal over 1000 m of Multimode fibre using a directly modulated DFB,” in Optical Fiber Communication Conference and Exposition and The National Fiber Optic Engineers Conference, Technical Digest (CD) (Optical Society of America, 2005), paper OFP3.
  5. B. Hongchun and S. William, “Transmission simulation of coherent optical OFDM signals in WDM systems,” Opt. Express 15(8), 4410–4418 (2007).
    [Crossref]
  6. M. Chen, J. He, Q. Fan, Z. Dong, and L. Chen, “Experimental Demonstration of Real-Time High-Level QAM-Encoded Direct-Detection Optical OFDM Systems,” J. Lightwave Technol. 33(22), 4632–4639 (2015).
    [Crossref]
  7. H. Zhou, Z. Zheng, and Q. Wan, “Radio over fiber system carrying OFDM signal based on optical octuple frequency technique,” Opt. Commun. 349, 54–59 (2015).
    [Crossref]
  8. F. Li, J. Yu, Z. Cao, M. Chen, J. Zhang, and X. Li, “Demonstration of 520 Gb/s/lambda pre-equalized DFT-spread PDM-16QAM-OFDM signal transmission,” Opt. Express 24(3), 2648–2654 (2016).
    [Crossref]
  9. Z. Dong, Z. Cao, J. Lu, L. Chen, and J. Yu, “All-Optical Wavelength Conversion Based on Four Wave Mixing in Semiconductor Optical Amplifier for OFDM Optical Signal,” Chin. J. Lasers 36(11), 2952–2956 (2009).
    [Crossref]
  10. J. Lu, Y. Hu, J. Liu, X. Zeng, and J. Gao, “All-Optical Wavelength Conversion Based on Parallel Dual-Pump for Polarization Multiplexing OFDM Signal in SOA,” Chin. J. Lasers 42(2), 0205005 (2015).
    [Crossref]
  11. Z. Cao, Z. Dong, J. Lu, L. Chen, and J. Yu, “All-optical Orthogonal-pump wavelength conversion of optical OFDM signal,” J. Optoelectronics. Laser. 20(5), 622–627 (2009).
  12. J. T. Dang, X. W. Yi, J. Zhang, T. P. Ye, B. Xu, and K. Qiu, “Experimental characterization of an all-optical wavelength converter of OFDM signals using two-mode injection-locking in a Fabry–Pérot laser,” Opt. Express 24(15), 16711–16721 (2016).
    [Crossref]
  13. S. H. You, C. Li, Q. Yang, M. Luo, Y. Qiu, X. Xiao, and S. Yu, “Seamless Sub-Band Wavelength Conversion of Tb/s-Class CO-OFDM Superchannels,” IEEE Photonics Technol. Lett. 26(8), 801–804 (2014).
    [Crossref]
  14. C. Li, M. Luo, Z. He, H. Li, J. Xu, S. You, Q. Yang, and S. Yu, “Phase noise canceled polarization-insensitive all-optical wavelength conversion of 557-Gb/s PDM-OFDM signal using coherent dual-pump,” J. Lightwave Technol. 33(13), 2848–2854 (2015).
    [Crossref]
  15. C. Li, C. Gui, X. Xiao, Q. Yang, S. Yu, and J. Wang, “On-chip all-optical wavelength conversion of multicarrier, multilevel modulation (OFDM m-QAM) signals using a silicon waveguide,” Opt. Lett. 39(15), 4583–4586 (2014).
    [Crossref]
  16. J. Ma, J. Lu, J. F. Liu, and P. Wu, “The Cost-efficient All-optical Wavelength Conversion for 160 Gbps CO-OFDM Signal Based on SOA,” in International Conference on Optical Communications and Networks (ICOCN, 2016), pp. 1–3.
  17. X. Wu, W. R. Peng, V. Arbab, J. Wang, and A. Willner, “Tunable optical wavelength conversion of OFDM signal using a periodically-poled lithium niobate waveguide,” Opt. Express 17(11), 9177–9182 (2009).
    [Crossref]
  18. J. P. R. Lacey, M. A. Summerfield, and S. J. Madden, “Tunability of Polarization-Insensitive Wavelength Converters Based on Four-Wave Mixing in Semiconductor Optical Amplifiers,” J. Lightwave Technol. 16(12), 2419–2427 (1998).
    [Crossref]
  19. J. Zhou, N. Park, J. W. Dawson, K. J. Vahala, M. A. Newkirk, and B. I. Miller, “Efficiency of broadband four-wave mixing wavelength conversion using semiconductor traveling-wave amplifiers,” IEEE Photonics Technol. Lett. 6(1), 50–52 (1994).
    [Crossref]
  20. J. Zhou, N. Park, K. J. Vahala, M. A. Newkirk, and B. I. Miller, “Four-wave mixing wavelength conversion efficiency in semiconductor traveling-wave amplifiers measured to 65 nm of wavelength shift,” IEEE Photonics Technol. Lett. 6(8), 984–987 (1994).
    [Crossref]
  21. L. Li and J. A. Dobrowolski, “Visible broadband, wide-angle, thin-film multilayer polarizing beam splitter,” Appl. Opt. 35(13), 2221–2225 (1996).
    [Crossref]
  22. X. Yi, W. Shieh, and Y. Ma, “Phase Noise Effects on High Spectral Efficiency Coherent Optical OFDM Transmission,” J. Lightwave Technol. 26(10), 1309–1316 (2008).
    [Crossref]
  23. C. Henry, “Theory of the line-width of semiconductor lasers,” IEEE J. Quantum Electron. 18(2), 259–264 (1982).
    [Crossref]
  24. R. Hui and A. Mecozzi, “Phase noise of four-wave mixing in semiconductor lasers,” Appl. Phys. Lett. 60(20), 2454–2456 (1992).
    [Crossref]
  25. D. Dhawan and N. Gupta, “Investigation of Tolerable Laser Line-width for Different Modulation Formats in CO-OFDM Systems,” Opt. Photonics J. 07(05), 92–100 (2017).
    [Crossref]

2018 (1)

T. Ohtsuki and M. Matsuura, “Wavelength Conversion of 25-Gbit/s PAM-4 Signals Using a Quantum-Dot SOA,” IEEE Photonics Technol. Lett. 30(5), 459–462 (2018).
[Crossref]

2017 (1)

D. Dhawan and N. Gupta, “Investigation of Tolerable Laser Line-width for Different Modulation Formats in CO-OFDM Systems,” Opt. Photonics J. 07(05), 92–100 (2017).
[Crossref]

2016 (3)

2015 (4)

C. Li, M. Luo, Z. He, H. Li, J. Xu, S. You, Q. Yang, and S. Yu, “Phase noise canceled polarization-insensitive all-optical wavelength conversion of 557-Gb/s PDM-OFDM signal using coherent dual-pump,” J. Lightwave Technol. 33(13), 2848–2854 (2015).
[Crossref]

J. Lu, Y. Hu, J. Liu, X. Zeng, and J. Gao, “All-Optical Wavelength Conversion Based on Parallel Dual-Pump for Polarization Multiplexing OFDM Signal in SOA,” Chin. J. Lasers 42(2), 0205005 (2015).
[Crossref]

M. Chen, J. He, Q. Fan, Z. Dong, and L. Chen, “Experimental Demonstration of Real-Time High-Level QAM-Encoded Direct-Detection Optical OFDM Systems,” J. Lightwave Technol. 33(22), 4632–4639 (2015).
[Crossref]

H. Zhou, Z. Zheng, and Q. Wan, “Radio over fiber system carrying OFDM signal based on optical octuple frequency technique,” Opt. Commun. 349, 54–59 (2015).
[Crossref]

2014 (2)

C. Li, C. Gui, X. Xiao, Q. Yang, S. Yu, and J. Wang, “On-chip all-optical wavelength conversion of multicarrier, multilevel modulation (OFDM m-QAM) signals using a silicon waveguide,” Opt. Lett. 39(15), 4583–4586 (2014).
[Crossref]

S. H. You, C. Li, Q. Yang, M. Luo, Y. Qiu, X. Xiao, and S. Yu, “Seamless Sub-Band Wavelength Conversion of Tb/s-Class CO-OFDM Superchannels,” IEEE Photonics Technol. Lett. 26(8), 801–804 (2014).
[Crossref]

2009 (3)

X. Wu, W. R. Peng, V. Arbab, J. Wang, and A. Willner, “Tunable optical wavelength conversion of OFDM signal using a periodically-poled lithium niobate waveguide,” Opt. Express 17(11), 9177–9182 (2009).
[Crossref]

Z. Cao, Z. Dong, J. Lu, L. Chen, and J. Yu, “All-optical Orthogonal-pump wavelength conversion of optical OFDM signal,” J. Optoelectronics. Laser. 20(5), 622–627 (2009).

Z. Dong, Z. Cao, J. Lu, L. Chen, and J. Yu, “All-Optical Wavelength Conversion Based on Four Wave Mixing in Semiconductor Optical Amplifier for OFDM Optical Signal,” Chin. J. Lasers 36(11), 2952–2956 (2009).
[Crossref]

2008 (1)

2007 (1)

1998 (1)

1996 (1)

1994 (2)

J. Zhou, N. Park, J. W. Dawson, K. J. Vahala, M. A. Newkirk, and B. I. Miller, “Efficiency of broadband four-wave mixing wavelength conversion using semiconductor traveling-wave amplifiers,” IEEE Photonics Technol. Lett. 6(1), 50–52 (1994).
[Crossref]

J. Zhou, N. Park, K. J. Vahala, M. A. Newkirk, and B. I. Miller, “Four-wave mixing wavelength conversion efficiency in semiconductor traveling-wave amplifiers measured to 65 nm of wavelength shift,” IEEE Photonics Technol. Lett. 6(8), 984–987 (1994).
[Crossref]

1992 (1)

R. Hui and A. Mecozzi, “Phase noise of four-wave mixing in semiconductor lasers,” Appl. Phys. Lett. 60(20), 2454–2456 (1992).
[Crossref]

1982 (1)

C. Henry, “Theory of the line-width of semiconductor lasers,” IEEE J. Quantum Electron. 18(2), 259–264 (1982).
[Crossref]

Arbab, V.

Cao, Z.

F. Li, J. Yu, Z. Cao, M. Chen, J. Zhang, and X. Li, “Demonstration of 520 Gb/s/lambda pre-equalized DFT-spread PDM-16QAM-OFDM signal transmission,” Opt. Express 24(3), 2648–2654 (2016).
[Crossref]

Z. Dong, Z. Cao, J. Lu, L. Chen, and J. Yu, “All-Optical Wavelength Conversion Based on Four Wave Mixing in Semiconductor Optical Amplifier for OFDM Optical Signal,” Chin. J. Lasers 36(11), 2952–2956 (2009).
[Crossref]

Z. Cao, Z. Dong, J. Lu, L. Chen, and J. Yu, “All-optical Orthogonal-pump wavelength conversion of optical OFDM signal,” J. Optoelectronics. Laser. 20(5), 622–627 (2009).

Chadha, D.

D. Chadha, Optical WDM Networks: From Static to Elastic Networks (Wiley-IEEE, 2019), Chap. 1.

Chen, L.

M. Chen, J. He, Q. Fan, Z. Dong, and L. Chen, “Experimental Demonstration of Real-Time High-Level QAM-Encoded Direct-Detection Optical OFDM Systems,” J. Lightwave Technol. 33(22), 4632–4639 (2015).
[Crossref]

Z. Dong, Z. Cao, J. Lu, L. Chen, and J. Yu, “All-Optical Wavelength Conversion Based on Four Wave Mixing in Semiconductor Optical Amplifier for OFDM Optical Signal,” Chin. J. Lasers 36(11), 2952–2956 (2009).
[Crossref]

Z. Cao, Z. Dong, J. Lu, L. Chen, and J. Yu, “All-optical Orthogonal-pump wavelength conversion of optical OFDM signal,” J. Optoelectronics. Laser. 20(5), 622–627 (2009).

Chen, M.

Cordina, K.

N. E. Jolley, H. Kee, R. Rickard, J. Tang, and K. Cordina, “Generation and propagation of a 1550 nm 10 Gbit/s Optical Orthogonal Frequency Division Multiplexed signal over 1000 m of Multimode fibre using a directly modulated DFB,” in Optical Fiber Communication Conference and Exposition and The National Fiber Optic Engineers Conference, Technical Digest (CD) (Optical Society of America, 2005), paper OFP3.

Dang, J. T.

Dawson, J. W.

J. Zhou, N. Park, J. W. Dawson, K. J. Vahala, M. A. Newkirk, and B. I. Miller, “Efficiency of broadband four-wave mixing wavelength conversion using semiconductor traveling-wave amplifiers,” IEEE Photonics Technol. Lett. 6(1), 50–52 (1994).
[Crossref]

Dhawan, D.

D. Dhawan and N. Gupta, “Investigation of Tolerable Laser Line-width for Different Modulation Formats in CO-OFDM Systems,” Opt. Photonics J. 07(05), 92–100 (2017).
[Crossref]

Dobrowolski, J. A.

Dong, Z.

M. Chen, J. He, Q. Fan, Z. Dong, and L. Chen, “Experimental Demonstration of Real-Time High-Level QAM-Encoded Direct-Detection Optical OFDM Systems,” J. Lightwave Technol. 33(22), 4632–4639 (2015).
[Crossref]

Z. Dong, Z. Cao, J. Lu, L. Chen, and J. Yu, “All-Optical Wavelength Conversion Based on Four Wave Mixing in Semiconductor Optical Amplifier for OFDM Optical Signal,” Chin. J. Lasers 36(11), 2952–2956 (2009).
[Crossref]

Z. Cao, Z. Dong, J. Lu, L. Chen, and J. Yu, “All-optical Orthogonal-pump wavelength conversion of optical OFDM signal,” J. Optoelectronics. Laser. 20(5), 622–627 (2009).

Fan, Q.

Gao, J.

J. Lu, Y. Hu, J. Liu, X. Zeng, and J. Gao, “All-Optical Wavelength Conversion Based on Parallel Dual-Pump for Polarization Multiplexing OFDM Signal in SOA,” Chin. J. Lasers 42(2), 0205005 (2015).
[Crossref]

Gong, J. X.

Gui, C.

Gupta, N.

D. Dhawan and N. Gupta, “Investigation of Tolerable Laser Line-width for Different Modulation Formats in CO-OFDM Systems,” Opt. Photonics J. 07(05), 92–100 (2017).
[Crossref]

He, J.

He, Z.

Henry, C.

C. Henry, “Theory of the line-width of semiconductor lasers,” IEEE J. Quantum Electron. 18(2), 259–264 (1982).
[Crossref]

Hongchun, B.

Hu, Y.

J. Lu, Y. Hu, J. Liu, X. Zeng, and J. Gao, “All-Optical Wavelength Conversion Based on Parallel Dual-Pump for Polarization Multiplexing OFDM Signal in SOA,” Chin. J. Lasers 42(2), 0205005 (2015).
[Crossref]

Hui, R.

R. Hui and A. Mecozzi, “Phase noise of four-wave mixing in semiconductor lasers,” Appl. Phys. Lett. 60(20), 2454–2456 (1992).
[Crossref]

Jolley, N. E.

N. E. Jolley, H. Kee, R. Rickard, J. Tang, and K. Cordina, “Generation and propagation of a 1550 nm 10 Gbit/s Optical Orthogonal Frequency Division Multiplexed signal over 1000 m of Multimode fibre using a directly modulated DFB,” in Optical Fiber Communication Conference and Exposition and The National Fiber Optic Engineers Conference, Technical Digest (CD) (Optical Society of America, 2005), paper OFP3.

Kee, H.

N. E. Jolley, H. Kee, R. Rickard, J. Tang, and K. Cordina, “Generation and propagation of a 1550 nm 10 Gbit/s Optical Orthogonal Frequency Division Multiplexed signal over 1000 m of Multimode fibre using a directly modulated DFB,” in Optical Fiber Communication Conference and Exposition and The National Fiber Optic Engineers Conference, Technical Digest (CD) (Optical Society of America, 2005), paper OFP3.

Lacey, J. P. R.

Li, C.

Li, F.

Li, H.

Li, L.

Li, X.

Liu, J.

J. Lu, Y. Hu, J. Liu, X. Zeng, and J. Gao, “All-Optical Wavelength Conversion Based on Parallel Dual-Pump for Polarization Multiplexing OFDM Signal in SOA,” Chin. J. Lasers 42(2), 0205005 (2015).
[Crossref]

Liu, J. F.

J. Ma, J. Lu, J. F. Liu, and P. Wu, “The Cost-efficient All-optical Wavelength Conversion for 160 Gbps CO-OFDM Signal Based on SOA,” in International Conference on Optical Communications and Networks (ICOCN, 2016), pp. 1–3.

Lu, J.

J. Lu, Y. Hu, J. Liu, X. Zeng, and J. Gao, “All-Optical Wavelength Conversion Based on Parallel Dual-Pump for Polarization Multiplexing OFDM Signal in SOA,” Chin. J. Lasers 42(2), 0205005 (2015).
[Crossref]

Z. Cao, Z. Dong, J. Lu, L. Chen, and J. Yu, “All-optical Orthogonal-pump wavelength conversion of optical OFDM signal,” J. Optoelectronics. Laser. 20(5), 622–627 (2009).

Z. Dong, Z. Cao, J. Lu, L. Chen, and J. Yu, “All-Optical Wavelength Conversion Based on Four Wave Mixing in Semiconductor Optical Amplifier for OFDM Optical Signal,” Chin. J. Lasers 36(11), 2952–2956 (2009).
[Crossref]

J. Ma, J. Lu, J. F. Liu, and P. Wu, “The Cost-efficient All-optical Wavelength Conversion for 160 Gbps CO-OFDM Signal Based on SOA,” in International Conference on Optical Communications and Networks (ICOCN, 2016), pp. 1–3.

Luo, M.

Ma, J.

J. Ma, J. Lu, J. F. Liu, and P. Wu, “The Cost-efficient All-optical Wavelength Conversion for 160 Gbps CO-OFDM Signal Based on SOA,” in International Conference on Optical Communications and Networks (ICOCN, 2016), pp. 1–3.

Ma, Y.

Madden, S. J.

Matsuura, M.

T. Ohtsuki and M. Matsuura, “Wavelength Conversion of 25-Gbit/s PAM-4 Signals Using a Quantum-Dot SOA,” IEEE Photonics Technol. Lett. 30(5), 459–462 (2018).
[Crossref]

Mecozzi, A.

R. Hui and A. Mecozzi, “Phase noise of four-wave mixing in semiconductor lasers,” Appl. Phys. Lett. 60(20), 2454–2456 (1992).
[Crossref]

Miller, B. I.

J. Zhou, N. Park, K. J. Vahala, M. A. Newkirk, and B. I. Miller, “Four-wave mixing wavelength conversion efficiency in semiconductor traveling-wave amplifiers measured to 65 nm of wavelength shift,” IEEE Photonics Technol. Lett. 6(8), 984–987 (1994).
[Crossref]

J. Zhou, N. Park, J. W. Dawson, K. J. Vahala, M. A. Newkirk, and B. I. Miller, “Efficiency of broadband four-wave mixing wavelength conversion using semiconductor traveling-wave amplifiers,” IEEE Photonics Technol. Lett. 6(1), 50–52 (1994).
[Crossref]

Newkirk, M. A.

J. Zhou, N. Park, J. W. Dawson, K. J. Vahala, M. A. Newkirk, and B. I. Miller, “Efficiency of broadband four-wave mixing wavelength conversion using semiconductor traveling-wave amplifiers,” IEEE Photonics Technol. Lett. 6(1), 50–52 (1994).
[Crossref]

J. Zhou, N. Park, K. J. Vahala, M. A. Newkirk, and B. I. Miller, “Four-wave mixing wavelength conversion efficiency in semiconductor traveling-wave amplifiers measured to 65 nm of wavelength shift,” IEEE Photonics Technol. Lett. 6(8), 984–987 (1994).
[Crossref]

Ohtsuki, T.

T. Ohtsuki and M. Matsuura, “Wavelength Conversion of 25-Gbit/s PAM-4 Signals Using a Quantum-Dot SOA,” IEEE Photonics Technol. Lett. 30(5), 459–462 (2018).
[Crossref]

Park, N.

J. Zhou, N. Park, J. W. Dawson, K. J. Vahala, M. A. Newkirk, and B. I. Miller, “Efficiency of broadband four-wave mixing wavelength conversion using semiconductor traveling-wave amplifiers,” IEEE Photonics Technol. Lett. 6(1), 50–52 (1994).
[Crossref]

J. Zhou, N. Park, K. J. Vahala, M. A. Newkirk, and B. I. Miller, “Four-wave mixing wavelength conversion efficiency in semiconductor traveling-wave amplifiers measured to 65 nm of wavelength shift,” IEEE Photonics Technol. Lett. 6(8), 984–987 (1994).
[Crossref]

Peng, W. R.

Qiu, K.

Qiu, Y.

J. X. Gong, J. Xu, M. Luo, X. Li, Y. Qiu, Q. Yang, X. L. Zhang, and S. Yu, “All-optical wavelength conversion for mode division multiplexed superchannels,” Opt. Express 24(8), 8926–8939 (2016).
[Crossref]

S. H. You, C. Li, Q. Yang, M. Luo, Y. Qiu, X. Xiao, and S. Yu, “Seamless Sub-Band Wavelength Conversion of Tb/s-Class CO-OFDM Superchannels,” IEEE Photonics Technol. Lett. 26(8), 801–804 (2014).
[Crossref]

Rickard, R.

N. E. Jolley, H. Kee, R. Rickard, J. Tang, and K. Cordina, “Generation and propagation of a 1550 nm 10 Gbit/s Optical Orthogonal Frequency Division Multiplexed signal over 1000 m of Multimode fibre using a directly modulated DFB,” in Optical Fiber Communication Conference and Exposition and The National Fiber Optic Engineers Conference, Technical Digest (CD) (Optical Society of America, 2005), paper OFP3.

Shieh, W.

Summerfield, M. A.

Tang, J.

N. E. Jolley, H. Kee, R. Rickard, J. Tang, and K. Cordina, “Generation and propagation of a 1550 nm 10 Gbit/s Optical Orthogonal Frequency Division Multiplexed signal over 1000 m of Multimode fibre using a directly modulated DFB,” in Optical Fiber Communication Conference and Exposition and The National Fiber Optic Engineers Conference, Technical Digest (CD) (Optical Society of America, 2005), paper OFP3.

Vahala, K. J.

J. Zhou, N. Park, K. J. Vahala, M. A. Newkirk, and B. I. Miller, “Four-wave mixing wavelength conversion efficiency in semiconductor traveling-wave amplifiers measured to 65 nm of wavelength shift,” IEEE Photonics Technol. Lett. 6(8), 984–987 (1994).
[Crossref]

J. Zhou, N. Park, J. W. Dawson, K. J. Vahala, M. A. Newkirk, and B. I. Miller, “Efficiency of broadband four-wave mixing wavelength conversion using semiconductor traveling-wave amplifiers,” IEEE Photonics Technol. Lett. 6(1), 50–52 (1994).
[Crossref]

Wan, Q.

H. Zhou, Z. Zheng, and Q. Wan, “Radio over fiber system carrying OFDM signal based on optical octuple frequency technique,” Opt. Commun. 349, 54–59 (2015).
[Crossref]

Wang, J.

William, S.

Willner, A.

Wu, P.

J. Ma, J. Lu, J. F. Liu, and P. Wu, “The Cost-efficient All-optical Wavelength Conversion for 160 Gbps CO-OFDM Signal Based on SOA,” in International Conference on Optical Communications and Networks (ICOCN, 2016), pp. 1–3.

Wu, X.

Xiao, X.

C. Li, C. Gui, X. Xiao, Q. Yang, S. Yu, and J. Wang, “On-chip all-optical wavelength conversion of multicarrier, multilevel modulation (OFDM m-QAM) signals using a silicon waveguide,” Opt. Lett. 39(15), 4583–4586 (2014).
[Crossref]

S. H. You, C. Li, Q. Yang, M. Luo, Y. Qiu, X. Xiao, and S. Yu, “Seamless Sub-Band Wavelength Conversion of Tb/s-Class CO-OFDM Superchannels,” IEEE Photonics Technol. Lett. 26(8), 801–804 (2014).
[Crossref]

Xu, B.

Xu, J.

Yang, Q.

Ye, T. P.

Yi, X.

Yi, X. W.

You, S.

You, S. H.

S. H. You, C. Li, Q. Yang, M. Luo, Y. Qiu, X. Xiao, and S. Yu, “Seamless Sub-Band Wavelength Conversion of Tb/s-Class CO-OFDM Superchannels,” IEEE Photonics Technol. Lett. 26(8), 801–804 (2014).
[Crossref]

Yu, J.

F. Li, J. Yu, Z. Cao, M. Chen, J. Zhang, and X. Li, “Demonstration of 520 Gb/s/lambda pre-equalized DFT-spread PDM-16QAM-OFDM signal transmission,” Opt. Express 24(3), 2648–2654 (2016).
[Crossref]

Z. Cao, Z. Dong, J. Lu, L. Chen, and J. Yu, “All-optical Orthogonal-pump wavelength conversion of optical OFDM signal,” J. Optoelectronics. Laser. 20(5), 622–627 (2009).

Z. Dong, Z. Cao, J. Lu, L. Chen, and J. Yu, “All-Optical Wavelength Conversion Based on Four Wave Mixing in Semiconductor Optical Amplifier for OFDM Optical Signal,” Chin. J. Lasers 36(11), 2952–2956 (2009).
[Crossref]

Yu, S.

Zeng, X.

J. Lu, Y. Hu, J. Liu, X. Zeng, and J. Gao, “All-Optical Wavelength Conversion Based on Parallel Dual-Pump for Polarization Multiplexing OFDM Signal in SOA,” Chin. J. Lasers 42(2), 0205005 (2015).
[Crossref]

Zhang, J.

Zhang, X. L.

Zheng, Z.

H. Zhou, Z. Zheng, and Q. Wan, “Radio over fiber system carrying OFDM signal based on optical octuple frequency technique,” Opt. Commun. 349, 54–59 (2015).
[Crossref]

Zhou, H.

H. Zhou, Z. Zheng, and Q. Wan, “Radio over fiber system carrying OFDM signal based on optical octuple frequency technique,” Opt. Commun. 349, 54–59 (2015).
[Crossref]

Zhou, J.

J. Zhou, N. Park, J. W. Dawson, K. J. Vahala, M. A. Newkirk, and B. I. Miller, “Efficiency of broadband four-wave mixing wavelength conversion using semiconductor traveling-wave amplifiers,” IEEE Photonics Technol. Lett. 6(1), 50–52 (1994).
[Crossref]

J. Zhou, N. Park, K. J. Vahala, M. A. Newkirk, and B. I. Miller, “Four-wave mixing wavelength conversion efficiency in semiconductor traveling-wave amplifiers measured to 65 nm of wavelength shift,” IEEE Photonics Technol. Lett. 6(8), 984–987 (1994).
[Crossref]

Appl. Opt. (1)

Appl. Phys. Lett. (1)

R. Hui and A. Mecozzi, “Phase noise of four-wave mixing in semiconductor lasers,” Appl. Phys. Lett. 60(20), 2454–2456 (1992).
[Crossref]

Chin. J. Lasers (2)

Z. Dong, Z. Cao, J. Lu, L. Chen, and J. Yu, “All-Optical Wavelength Conversion Based on Four Wave Mixing in Semiconductor Optical Amplifier for OFDM Optical Signal,” Chin. J. Lasers 36(11), 2952–2956 (2009).
[Crossref]

J. Lu, Y. Hu, J. Liu, X. Zeng, and J. Gao, “All-Optical Wavelength Conversion Based on Parallel Dual-Pump for Polarization Multiplexing OFDM Signal in SOA,” Chin. J. Lasers 42(2), 0205005 (2015).
[Crossref]

IEEE J. Quantum Electron. (1)

C. Henry, “Theory of the line-width of semiconductor lasers,” IEEE J. Quantum Electron. 18(2), 259–264 (1982).
[Crossref]

IEEE Photonics Technol. Lett. (4)

J. Zhou, N. Park, J. W. Dawson, K. J. Vahala, M. A. Newkirk, and B. I. Miller, “Efficiency of broadband four-wave mixing wavelength conversion using semiconductor traveling-wave amplifiers,” IEEE Photonics Technol. Lett. 6(1), 50–52 (1994).
[Crossref]

J. Zhou, N. Park, K. J. Vahala, M. A. Newkirk, and B. I. Miller, “Four-wave mixing wavelength conversion efficiency in semiconductor traveling-wave amplifiers measured to 65 nm of wavelength shift,” IEEE Photonics Technol. Lett. 6(8), 984–987 (1994).
[Crossref]

T. Ohtsuki and M. Matsuura, “Wavelength Conversion of 25-Gbit/s PAM-4 Signals Using a Quantum-Dot SOA,” IEEE Photonics Technol. Lett. 30(5), 459–462 (2018).
[Crossref]

S. H. You, C. Li, Q. Yang, M. Luo, Y. Qiu, X. Xiao, and S. Yu, “Seamless Sub-Band Wavelength Conversion of Tb/s-Class CO-OFDM Superchannels,” IEEE Photonics Technol. Lett. 26(8), 801–804 (2014).
[Crossref]

J. Lightwave Technol. (4)

J. Optoelectronics. Laser. (1)

Z. Cao, Z. Dong, J. Lu, L. Chen, and J. Yu, “All-optical Orthogonal-pump wavelength conversion of optical OFDM signal,” J. Optoelectronics. Laser. 20(5), 622–627 (2009).

Opt. Commun. (1)

H. Zhou, Z. Zheng, and Q. Wan, “Radio over fiber system carrying OFDM signal based on optical octuple frequency technique,” Opt. Commun. 349, 54–59 (2015).
[Crossref]

Opt. Express (5)

Opt. Lett. (1)

Opt. Photonics J. (1)

D. Dhawan and N. Gupta, “Investigation of Tolerable Laser Line-width for Different Modulation Formats in CO-OFDM Systems,” Opt. Photonics J. 07(05), 92–100 (2017).
[Crossref]

Other (3)

J. Ma, J. Lu, J. F. Liu, and P. Wu, “The Cost-efficient All-optical Wavelength Conversion for 160 Gbps CO-OFDM Signal Based on SOA,” in International Conference on Optical Communications and Networks (ICOCN, 2016), pp. 1–3.

D. Chadha, Optical WDM Networks: From Static to Elastic Networks (Wiley-IEEE, 2019), Chap. 1.

N. E. Jolley, H. Kee, R. Rickard, J. Tang, and K. Cordina, “Generation and propagation of a 1550 nm 10 Gbit/s Optical Orthogonal Frequency Division Multiplexed signal over 1000 m of Multimode fibre using a directly modulated DFB,” in Optical Fiber Communication Conference and Exposition and The National Fiber Optic Engineers Conference, Technical Digest (CD) (Optical Society of America, 2005), paper OFP3.

Cited By

Optica participates in Crossref's Cited-By Linking service. Citing articles from Optica Publishing Group journals and other participating publishers are listed here.

Alert me when this article is cited.


Figures (11)

Fig. 1.
Fig. 1. Principle diagram of the proposed AOWC scheme for OFDM signal. (i) The structure of polarization-diversity; (ii) The polarization state of input lightwaves; (iii) The two orthogonal polarization modes after PBS; (iv) The model of SOA; (v) The output optical spectrum of the polarization-diversity structure. DML: directly modulated laser; ECL: external cavity laser; OC: optical coupler; PC: polarization controller; PBS: polarization beam splitter; PBC: polarization beam combiner; SOA: semiconductor optical amplifier; OBPF: optical band pass filter; PD: photoelectric detector.
Fig. 2.
Fig. 2. Schematic illustration of the output spectrum in three FWM schemes: (a) parallel pump scheme, (b) orthogonal pump scheme, (c) polarization-diversity scheme.
Fig. 3.
Fig. 3. The flow of DSP at (a) transmitter and (b) receiver.
Fig. 4.
Fig. 4. Optical spectrum (a) before and (b) after FWM process; constellations before (c) and after (d) FWM process.
Fig. 5.
Fig. 5. The power of converted lightwave as a function of polarization angle of signal lightwave. (a) $- {90^ \circ }$, (b) $- {30^ \circ }$, (c) ${30^ \circ }$, and (d) ${90^ \circ }$.
Fig. 6.
Fig. 6. BER curves versus different frequency separations and optical spectra at frequency separations of (a) 0.02THz and (b) 0.07THz of parallel pump scheme.
Fig. 7.
Fig. 7. BER curves versus different frequency separations and optical spectra at frequency separations of (a) 0.06THz and (b) 0.14THz of orthogonal pump scheme.
Fig. 8.
Fig. 8. BER curves versus different frequency separations and optical spectra at frequency separations of (a) 0.04THz and (b) 0.18THz of polarization-diversity scheme.
Fig. 9.
Fig. 9. BER curves versus input optical power of (a) signal lightwave and (b) pump.
Fig. 10.
Fig. 10. BER curve and constellations versus different line-width of ECL.
Fig. 11.
Fig. 11. BER curve and constellations versus different SOA injection current.

Equations (17)

Equations on this page are rendered with MathJax. Learn more.

E 1 S O A 1 ( ω 1 , t ) = A 1 α G x 1 cos 45 exp [ j ( ω 1 t + φ 1 ) ] x ^
E 2 M S O A 1 ( ω 2 , t ) = A O F D M A 2 α G x 1 cos θ exp [ j ( ω 2 t + φ 2 ) ] x ^
E c 1 ( 2 ω 1 ω 2 , t ) = r 1 ( ω 1 ω 2 ) ( E 1 S O A 1 E 2 M S O A 1 ) E 1 S O A 1 = 1 2 α α A 1 2 A 2 A O F D M G x 1 G x 1 cos θ r 1 ( ω 1 ω 2 ) e j ( 2 ω 1 ω 2 ) t e j ( 2 φ 1 φ 2 ) x ^
P c 1 = 1 4 α 3 A 1 4 A 2 2 A O F D M 2 G x 1 3 cos 2 θ R 1 ( ω 1 ω 2 )
E 1 S O A 2 = A 1 α G y 2 sin 45 exp [ j ( ω 1 t + φ 1 ) ] y ^
E 2 M S O A 2 = A O F D M A 2 α G y 2 sin θ exp [ j ( ω 2 t + φ 2 ) ] y ^
E c 2 ( 2 ω 1 ω 2 , t ) = 1 2 α α A 1 2 A 2 A O F D M G y 2 G y 2 sin θ r 2 ( ω 1 ω 2 ) e j ( 2 ω 1 ω 2 ) t e j ( 2 φ 1 φ 2 ) y ^
P c 2 = 1 4 α 3 A 1 4 A 2 2 A O F D M 2 G y 2 3 sin 2 θ R 2 ( ω 1 ω 2 )
P c = α ( P c 1 + P c 2 ) = 1 4 α 4 A 1 4 A 2 2 A O F D M 2 [ G x 1 3 cos 2 θ R 1 ( ω 1 ω 2 ) + G y 2 3 sin 2 θ R 2 ( ω 1 ω 2 ) ]
P c = 1 4 α 4 A 1 4 A 2 2 A O F D M 2 G 3 R ( ω 1 ω 2 )
S N R pp = H R ( Δ ω p p ) 2 β 3 γ 1
S N R o p = H R ( Δ ω o p 2 ) 2 β 3 γ 1
S N R p d = H R ( Δ ω p d 2 ) α β 3 γ + 3 2
H = a 3 A 2 2 A O F D M 2 b Δ f A 1 4 + 2 β 6 γ
R ( Δ ω o p _ max / 2 ) = R ( Δ ω p p _ max )
R ( Δ ω o p _ max / 2 ) R ( Δ ω p d _ max / 2 ) = α β 3 γ + 3 2 β 3 γ
Δ ϕ 2 ( t ) = 2 π Δ υ t

Metrics