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Frequency-offset-tolerant optical frequency comb-based coherent transmission for intra-datacenter interconnections

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Abstract

In recent years, in order to increase the capacity and scalability of intra-datacenter (DC) transmission, the optical frequency comb (OFC) source has been considered promising to replace discrete lasers, aiming to reduce the cost of wavelength division multiplexing (WDM) transmission within DC. In this paper, an OFC based coherent architecture is proposed. An OFC, in the receiver side, is split by a splitter with a uniform power ratio and separately used as local oscillators (LOs) to detect the demultiplexed signals. The signal spectrum is copied onto every tone of the LO-OFC, and a large frequency offset (FO) tolerance is achieved. In addition, the required ADC sampling rate is the same as a system without FO. Extensive simulations are conducted. In the simulated coherent WDM transmission system, a 3-tone-OFC is used to provide 3 carriers, and an 11-tone-OFC is split and used to provide LO-OFCs. For a 64GBd polarization multiplexing 16 quadrature amplitude modulation (PM-16QAM) WDM transmission, the tolerances of FO are up to about ±0.3THz and ±0.374THz for the 1st/3rd signal, and the 2nd signal, respectively, below the pre-forward error correction (FEC) bit error rate (BER) level of 1.25×10−2. Moreover, the maximum tolerance of FO linearly increases with the number of effective tones in LO-OFC. Further, extensive experiments with back-to-back connection are conducted to verify the performance. The tolerance of FO is up to >36 GHz for 36GBd PM-16QAM transmission with a 3-tone-LO-OFC below the BER level of 1.25×10−2. The proposed OFC based coherent architecture is a promising solution for intra-DC interconnections with a large FO.

© 2021 Optical Society of America under the terms of the OSA Open Access Publishing Agreement

1. Introduction

With the wider adoption of 5G, internet of things (IoT), cloud computing, and machine learning based applications, the required data rate within datacenter (DC) has been increasing rapidly [16]. Intra-DC optical interconnections, unlike long-haul transmission, have much shorter reach (typically < 2 km) with numerous connections [2,4,7]. Thus, the capital and operational expenditures (i.e., CAPEX and OPEX) are largely dominated by optical transceivers, having much more stringent requirements on the cost, power consumption and footprint [4]. These requirements are mainly reflected in the limitations on laser, analog-to-digital converter (ADC) and digital-to-analog converter (ADC), modulator, receiver, etc. Thus, how to realize the coexistence of high data rate and low cost is a great challenge for next generation DC interconnections [4,6,8].

In the past few years, intensity modulation and direct detection (IMDD) was still a popular architecture within DC because of its simplicity and relatively low cost [9]. However, scaling IMDD links to >200Gbps/lane will require a great increase in complexity and power consumption [10]. And the limited prospects have driven substantial interests in developing a new generation of energy-efficient coherent links for intra-DC interconnections. Compared to IMDD, coherent transmission with a much higher spectral efficiency is a promising alternative architecture [1,4]. However, the cost, power consumption and footprint need to be significantly reduced, which have been widely investigated in recent years. For example, in [11], a hardware efficient adaptive equalizer is proposed for short-reach coherent optical interconnects. In [12], a homodyne DSP-free coherent receiver architecture is proposed.

In addition, increasing the number of parallel channels per fiber (i.e. WDM) has been considered as an option to increase the data rate per transceiver [1,4,8]. In particular, coarse-WDM (CWDM) based IMDD transceivers with uncooled laser have been widely adopted within DC [2]. And WDM based coherent detection is also investigated in recent years [10]. These solutions are based on discrete lasers, and the laser cost increases linearly with the number of WDM channels. An optical frequency comb (OFC) source has been considered as a replacement of multiple discrete lasers to reduce the cost of WDM-based transceivers [1316]. Several OFC based WDM transmissions have been reported for long-haul scenarios [1,1619], where two OFC sources with stabilized wavelengths are demultiplexed and used as carriers and local oscillators (LOs) at the transmitter and receiver sides, respectively. However, these traditional architectures will face challenges within DC, because the seed lasers with stabilized wavelength will increase cost [2]. A laser without a wavelength stabilization subsystem (e.g., temperature-controller) suffers from a random frequency drift. And the FO range can reach ${\pm} {0.25}{\textrm {THz}}$ [20]. Moreover, it is subject to a temperature-induced wavelength drift in the order of 0.1 nm/°C [20,21]. This will lead to a large FO in coherent systems, resulting in a large electrical bandwidth penalty or incomplete detection of signal spectrum at the coherent receiver. In [22], an OFC is also used to perform colorless reception, but it requires several times excess receiver electrical bandwidth compared to a standard coherent receiver. This is not acceptable for the application within DC, since the high transmission rate is strictly limited by electrical bandwidth.

In this paper, a frequency-offset-tolerant OFC based coherent-WDM architecture for intra-DCI interconnects is proposed. An OFC with several tones is used as LO (i.e., LO-OFC), and after coherent detection the signal is copied onto every tone of LO-OFC. In this case, a complete spectrum is obtained even with a large FO. In the digital signal processing (DSP), we propose a signal reconstruction algorithm, via which no additional electrical bandwidth at the receiver is required. Therefore, wavelength stabilization is not required for the lasers in this system. In addition, the sampling rate of the ADCs can be minimized to reduce power consumption. Extensive simulations and experiments are conducted to demonstrate the performance of the proposed architecture. In the simulations, a 3-tone-OFC and a 11-tone-OFC are respectively used as WDM signal carriers and LO-OFC sources. For 64GBd PM-16QAM WDM transmission, the system can tolerate a FO up to about ${\pm} {0.3}{ \textrm{THz}}$ and ${\pm} {0.374}{ \textrm{THz}}$ for the 1st/3rd signal, and 2nd signal, respectively, below the 14.8% concatenated forward error correction (C-FEC) threshold (bit error rate (BER) = 1.25×10−2). Moreover, the maximum tolerable FO of a demultiplexed signal linearly increases with the number of effective tones in LO-OFC. In the experiments, we demonstrate that the tolerance of FO is up to >36 GHz for 36GBd PM-16QAM transmission with a 3-tone-LO-OFC below the pre-FEC BER level of 1.25×10−2. Finally, the power sensitivity and cost of the proposed architecture are discussed.

This paper is organized as follows. In Section 2, the principle of the proposed OFC based cost-effective coherent architecture is derived. In Section 3, the simulation setup is described, and the results are analyzed. The experimental demonstration is presented in Section 4. The power sensitivity and cost are discussed in Section 5. Finally, the conclusions are given in Section 6.

2. Principle

2.1 Proposed OFC-based coherent-WDM architecture

The proposed OFC based coherent-WDM architecture for intra-DC interconnects is illustrated in Fig. 1. At the transmitter side, the tones of an OFC are demultiplexed by a wavelength demultiplexer (De-MUX). They are individually modulated in each transmitter (i.e., Tx 1∼N), multiplexed by a multiplexer (MUX), and then injected into the fiber channel. At the receiver side, the WDM signal is demultiplexed, and individually detected by the receivers (i.e., Rx 1∼N) along with LO-OFCs. These LO-OFCs are provided by an OFC source followed by a splitter with a uniform power ratio. In this architecture, the demultiplexed signal is copied onto every tone of the LO-OFC to achieve a large FO tolerance, as shown in the inset of Fig. 1, where MUX/De-MUX just indicate functional blocks, which can be realized by different schemes, such as serially cascaded micro-ring [13] or cascaded Mach-Zehnder based schemes [23]. In practical applications, all components should be integrated into a single transceiver. In addition, for next generation 800Gbps/1.6Tbps/3.2Tbps standards, a few-tone OFC is a reasonable choice based on the recommendation of equipment bandwidth in 400ZR implementation agreement of OIF and the expected FO range of ${\pm} 0.25\textrm{THz}$.

 figure: Fig. 1.

Fig. 1. The proposed OFC-based coherent-WDM architecture. MUX: multiplexer; De-MUX: demultiplexer.

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In the remaining part of this section, the characteristics of an OFC are firstly described and illustrated. Then, the principle of using the proposed OFC-based coherent detection to achieve a large FO tolerance is derived, followed by the description of the needed digital signal processing.

2.2 Optical frequency comb

An OFC source can be used as an alternative to an array of discrete lasers to reduce the cost of the WDM transmission within DC. An OFC source generates a set of tones. They are equidistantly separated in frequency [1,14]. Typically, the tones of OFC are coherent in phase [15,16]. In this case, the frequency of the $k$-th tones, ${f_{OFC,\; k}}$, can be fully defined by only two parameters: free-spectral range (${f_{FSR}}$) and central frequency (${f_{CF}})$ [15,16] as

$${f_{OFC,\; \; k}} = ({{f_{CF}} + \varDelta f} )+ k \cdot {f_{FSR}},k \in \{{ - N, \ldots ,0, \ldots ,N} \}$$
where $\varDelta f$ is the random FO due to the frequency drift of the seed laser centered at ${f_{CF}}$. k is the index of tones. The electric field of the OFC can be expressed as
$${E_{OFC}}(t )= \textrm{exp}({i{\varphi_{OFC}}(t )} )\cdot \mathop \sum \nolimits_{k ={-} N}^N {A_{OFC,\; k}}(t )\textrm{exp}({i2\pi t{f_{OFC,\; k}}} )$$
where ${\varphi _{OFC}}(t )$ is the phase of the seed laser. ${A_{OFC,k}}(t )$ and ${f_{OFC,k}}$ are the amplitude and frequency of the k-th tone of the OFC, respectively.

Many methods to build an OFC have been proposed during the past years [14]. In the experiments of this work, an electro-optic modulation (EOM) method based on only one intensity modulator (IM) is adopted to generate an OFC with three tones. A spectral flatness of <1 dB can be realized by carefully adjusting the voltage of oscillation signal from a microwave source, and the bias voltage of IM. Specifically, the ${f_{FSR}}$ can be defined by the frequency of oscillation signal.

2.3 Principle of the proposed coherent detection based on LO-OFC

For the proposed OFC-based coherent-WDM architecture, an OFC with multiple tones is used as LO-OFC, and injected into the coherent receiver along with a demultiplexed signal. By doing so, the signal is copied onto every tone of LO-OFC, as illustrated in Fig. 2(a). The detailed derivations are described as follows.

 figure: Fig. 2.

Fig. 2. (a) Spectrum evolution throughout the LO-OFC based coherent receiver; (b) Spectrum evolution of the signal reconstruction processing in the Rx DSP.

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The baseband signal at the transmitter side can be expressed as

$${E_S}(t )= {A_S}(t )\textrm{exp}({i{\varphi_S}(t )} )$$
where ${A_S}(t )$ and ${\varphi _S}(t )$ are the amplitude and phase of the signal, respectively.

The optical carrier at a certain frequency demultiplexed from an OFC at the transmitter side can be written as

$${E_C}(t )= {A_C}(t )\textrm{exp}({i({2\pi t{f_C} + {\varphi_C}(t )} )} )$$
where ${A_C}(t )$ and ${\varphi _C}(t )$ are the amplitude and phase of the optical carrier with a central frequency of ${f_C}$ in OFC at the transmitter side, respectively. Thus, the modulated signal can be derived from Eq. (3) and (4) in a complex format [24] and expressed as
$${E_M}(t )= {A_M}(t )\textrm{exp}({i({2\pi t{f_C} + {\varphi_M}(t )} )} )$$
where ${A_M}(t )$ and ${\varphi _M}(t )$ are the amplitude and phase of the modulated signal. Then, N modulated signals from N transmitters are multiplexed by a MUX, and injected into the fiber channel. At the receiver side, a WDM signal is demultiplexed. Due to the equivalence of WDM channels, the m-th signal centered at ${f_{C,\; \; \textrm{m}}}$ is selected as illustrated in Fig. 2(a(i)), without loss of generality, to describe the derivation as follows.

According to the principle of coherent detection [25], with Eq. (2) and (5), the detected signal before the bandlimited electrical devices in a coherent receiver is given as

$$\begin{aligned}{E_{Det}}(t )= {A_{Dem, m}}(t )\textrm{exp}({i({ - {\varphi_{LO - OFC}}(t )+ {\varphi_{Dem, m}}(t )} )} )\cdot\\ \mathop \sum \nolimits_{k ={-} N}^N {A_{LO - OFC,\; k}}(t )\textrm{exp}({i2\pi t({ - {f_{LO - OFC,\; k}} + {f_{C,m}}} )} )\end{aligned}$$
where ${A_{Dem,m}}(t )$ and ${\varphi _{Dem,m}}(t )$ are the amplitude and phase of the m-th demultiplexed signal, respectively. ${A_{LO - OFC,k}}(t )$ and ${f_{LO - OFC,k}}$ are the amplitude and frequency of the k-th tone in LO-OFC seeded by a laser with phase of ${\varphi _{LO - OFC}}(t )$ at the receiver side, respectively. And the spectrum evolution of the selected signal is illustrated as figures from Fig. 2(a(i)) to Fig. 2(a(ii)) corresponding to ${E_{Dem,m}}(t )$ and ${E_{Det}}(t )$, respectively. As expressed in Eq. (6), the spectrum of ${E_{Dem,m}}(t )$ is copied and up-converted periodically with a period of ${f_{FSR}}$. These spectra are centered at $\varDelta F + {f_{OFC,\; k}},\; k \in \{{ - N, \ldots ,0, \ldots ,N} \}$, and marked with index, ${E_{Det.,k}}(t )$, according to the index of tones in OFC as illustrated in Fig. 2(a(ii)). $\varDelta \textrm{F}$ is defined as
$$\mathrm{\varDelta }F = \textrm{mod}({|{{f_{C,\; \; m}} - {f_{CF,\; LO - OFC}}} |,\; {B_S}} )$$
where ${f_{C,m}}$ and ${f_{CF,LO - OFC}}$ are the central frequency of the m-th demultiplexed signal and LO-OFC, respectively. ${B_S}$ is the bandwidth of baseband signal. $\; |\cdot |$ is the absolute operation. ${f_{FSR,LO - OFC}}$ should be equal to ${B_S}$. $\mathrm{\varDelta }F$ can be estimated in digital signal processer (DSP) as shown in Fig. 3.

 figure: Fig. 3.

Fig. 3. Algorithm flow of signal reconstruction in the proposed system.

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After that, the detected signal is filtered by the electrical modules with limited bandwidth in a coherent receiver, and converted to a digital signal by ADC with limited bandwidth and sampling rate, which can be expressed as

$${E_D}(n )\mathop \Leftarrow \limits^{\textrm{ADC}} {E_A}(t )= {E_{Det}}(t )\ast h(t )$$
where * is the convolutional operation. And $h(t )$ is the cascade impulse response of electrical modules in the coherent receiver and ADC. The spectrum of ${E_D}(n )$ can be illustrated as Fig. 2(a(iii)), where ${E_{Det.,0}}(n )$ and ${E_{Det.,1}}(n )$ are the digital counterpart of ${E_{Det.,0}}(t )$ and ${E_{Det.,1}}(t )$, respectively. Then, the digital signal suffered from FO and band limitation can be reconstructed in Rx-DSP.

The digital signal ${E_D}(n )$ is firstly processed by Gram-Schmidt orthogonalization and normalization as shown in the Rx-DSP of Fig. (4)(c). And the processed signal is denoted by ${E_O}(n )$. Then, the signal reconstruction is implemented in the time domain as shown in Fig. 3, where ${E_R}(n )$ is the reconstructed signal. ${B_{{S_p}}}$ indicates the bandwidth covering signal and pilot-tone. ${B_S}$ indicates the signal bandwidth.

The detailed process is described as follows and the signal spectrum evolution is plotted in Fig. 2(b).

Step 1: The received signal ${E_O}(n )$ passes a low pass filter with a bandwidth of ${B_{{S_P}}}$ to filter out the redundant signal. A root-raised-cosine (RRC) filter with 8 taps is used as the low pass filter.

Step 2: The signal after low pass filter is multiplied with frequency-dependent coefficients to realize the frequency shift in the time domain. With the frequency shift of $|{\Delta F} |- {B_{{S_P}}}$ and $|{\varDelta F} |$, we can obtain two signals. Adding these two signals together, we can construct a frequency-continuous spectrum.

Step 3: The obtained signal passes another low pass filter with a bandwidth of ${B_S}$ to filter out the redundant signal. Another RRC filter with 8 taps is adopted again.

The signal reconstruction algorithm should cooperate with the frequency offset estimation (FOE) module to obtain the $|{\Delta F} |$. A pilot-tone based FOE [26] is adopted as an example.

3. Simulation setup and results

3.1 Simulation setup

To validate the effectiveness of the proposed OFC based coherent architecture for intra-DC interconnections, extensive simulations are conducted. The relationship between the WDM channels, expected FO range, signal bandwidth and the number of tones in LO-OFC is given as

$${N_{tone}} \ge \frac{{|{F{O_{Max}}} |}}{{{B_s}}} \times 2 + {N_{ch}}$$
where ${N_{tone}}$ is the number of flat tones in LO-OFC. $\; {N_{ch}}$ is the number of WDM channels. $F{O_{Max}}$ is the expected maximum FO range. ${B_s}$ is the bandwidth of signal. $\lceil\cdot \rceil $ is the ceiling operation.

In simulation, the comparisons between a conventional OFC based WDM system and the proposed architecture are carried out. For the former, the tones of two OFCs seeded by two separated lasers located at the transmitter and receiver sides are demultiplexed. And they are used as carriers and LOs, respectively. Due to the one-to-one mapping between the demultiplexed carrier and LO, the FO should be small in the conventional system. In the Rx side of the proposed system, a splitter with a uniform power ratio is used to split the LO-OFC, as illustrated in Fig. 4(a).

 figure: Fig. 4.

Fig. 4. (a) Simulation setup; (b) Tx DSP flow; (c) Rx DSP flow; (d) Spectrum of the 3 multiplexed signals; (e) Spectrum of LO-OFC with 11 flat tones in the Rx side. The side-tones are not shown. PRBS: pseudorandom bit sequence; G.-S.: Gram-Schmidt; FOC: frequency offset correction; CPR: carrier phase recovery.

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Specifically, at the Tx the OFC provides 3 carrier tones into IQ modulators through a De-MUX. Then, the 3 modulated signals are multiplexed by a MUX, as illustrated in Fig. 4(d), and injected into a fiber channel with a length of 2 km. In order to cover the expected FO range of ${\pm} 0.25\textrm{THz}$, at the Rx, the OFC with 11 flat tones illustrated in Fig. 4(e) is adopted and split into 3 parts with a power ratio of 1:1:1, and separately used as LO-OFCs. The LO-OFC and a demultiplexed signal (i.e., Sig. 1, 2, or 3) are input into the coherent receivers. It is worth noted that the ${f_{FSR}}$ of LO-OFC equals to ${B_S}$. And the DSP flows at the Tx and Rx side are listed as Fig. 4(b) and (c), respectively.

For a fair comparison, the same parameters are set for both systems. Specifically, a 64GBd DP-16QAM signal is employed, and a RRC filter with a roll-off factor of 0.1 is employed to shape the signal. Thus, the ${f_{FSR}}$ of LO-OFCs should be set to be 70.4 GHz. In order to estimate the FO, a pilot tone was adopted and inserted into the pulse-shaped signal with a frequency gap of 1 GHz. In addition, the spectral flatness of OFC tones in the Tx and Rx sides is < 1 dB. In this paper, the concatenated forward error correction (C-FEC) was assumed with a 14.8% overhead (pre-BER=1.25×10−2) [27].

3.2 Frequency offset tolerance

As described in the previous Section, the coherently detected signal suffered from a random FO can be reconstructed by the Rx-DSP illustrated in Fig. 4(c). A large FO tolerance can be achieved. Thus, wavelength stabilization is not required for the lasers in this system. In the simulation, the LO (conventional system) and LO-OFC (proposed system) are set to have the same power of 14.4dBm. And the power per line after splitting LO-OFC is −0.8dBm. The received optical power (ROP) of the demultiplexed signal in the conventional system and proposed system is set to −18dBm and −8dBm, respectively. As illustrated in Fig. 5(a), the proposed system has a much better tolerance than the conventional one among the absolute value of FO ($|{FO} |$) from 0 to 0.4THz. Figure 5(a) reveals that the FO tolerances of the proposed system are about ${\pm} 0.3\textrm{THz}$ and ${\pm} 0.374\textrm{THz}$ for Signal 1 and 2 below the pre-FEC BER level of 1.25×10−2, respectively. And the FO tolerance of Signal 3 shown in Fig. 4(e) is same as that of Signal 1. However, the FO tolerance of the conventional system is very small as expected. In addition, Fig. 5 also illustrates that the FO tolerance of the proposed system increases linearly with the number of effective tones, $N = \textrm{min}({{N_L},\; \; {N_R}} )$, in LO-OFC. The relationship between the maximum tolerable FO (i.e., $\textrm{Max}({|{{f_{FO}}} |} )$) of the signal and N can be expressed as

$$\textrm{Max}({|{{f_{FO}}} |} )= ({N - 1} )\cdot {B_S} = ({\textrm{min}({{N_L},\; \; {N_R}} )- 1} )\cdot {B_S}$$
where ${N_L}\; and\; {N_R}$ is the number of tones in the left and right of a signal, respectively, as shown in Fig. 5(b). Thus, the FO tolerance of Signal 2 is better than that of Signal 1/3.

 figure: Fig. 5.

Fig. 5. (a) BER versus the absolute value of FO in the proposed system and the conventional system; (b) Illustration of relationship between demultiplexed signals and LO-OFC.

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3.3 Impacts of ADC sampling rate on the performance

As expressed in Eq. (8), the signals are converted into digital counterparts by ADC with limited bandwidth and sampling rate. Then the Rx-DSP is used to recover the signals. In a conventional coherent system, the ADC sampling rate should be increased to tolerate a larger FO. However, a higher sampling rate leads to higher power consumption. Thus, it is necessary to minimize the ADC sampling rate.

As illustrated in Fig. 6(a), compared to the conventional system, the requirements of the ADC sampling rate in the proposed system with |FO|=100 GHz/250 GHz can be reduced to about 1.2 times symbol rate, and is independent of the FO within the tolerance. The demand of ADC sampling rate of Signal 3 is same as that of Signal 1. It can be forecasted that the required sampling rate can remain constant over the entire range of FO tolerance for the proposed system. The performance is slightly better in Fig. 6(a) with FO=0 GHz than |FO|=100 GHz/250 GHz, when the oversampling ratio is higher than 1.1. This is because that due to the frequency gap between the pilot-tone and signal, there is a larger penalty in signal with |FO|=100 GHz/250 GHz than that of signal with FO=0 GHz, as explained in Fig. 6(b). To conclude, the required ADC sampling rate of the proposed system is almost the same as a conventional coherent system without FO, which is an advantage in saving power consumption.

 figure: Fig. 6.

Fig. 6. (a) BER versus the ADC sampling rate in the proposed system and conventional system.

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4. Experimental results

4.1 Experimental setup

Experiments are conducted to verify the FO tolerance of the proposed system. Figure 7(a) shows the experimental setup. Limited by experiment equipment, a single channel signal with a symbol rate of 36GBd is employed, and a three-tone LO-OFC is adopted. At the transmitter side, an external cavity laser (ECL) with a linewidth of <100 kHz and a wavelength of 1550 nm is used as carrier, imitating the demultiplexed OFC tone. Pseudorandom bit sequences (PRBSs) are processed offline in MATLAB. A signal with a length of 262144 is generated via an 80GSa/s arbitrary waveform generator (AWG). A dual polarization inphase-quadrature LiNbO3 Mach-Zehnder modulator (DP-IQ-MZM) is used. The carrier is modulated by an electric field with 4 amplitude levels in each quadrature of both polarizations. The signal with 36GBd polarization multiplexed 16-ary quadrature amplitude modulation (PM-16QAM) is generated. A RRC filter with a roll-off factor of 0.1 is employed to shape the signal. Thus ${B_S}$ is 39.6 GHz. Due to the limited power of laser, an Erbium-doped fiber amplifier (EDFA (1)) is used to compensate the loss of the DP-IQ-MZM. Passing through 2 m standard single mode fiber, the ROP of signal is adjusted by a variable optical attenuator (VOA). At the receiver side, a 3-tone-LO-OFC with a spectral flatness of < 1 dB and the received signal are injected into a coherent receiver (Fujitsu, FIM24706/301). Then, the detected signals are sampled by a real-time oscilloscope (Tektronix, DPO75902SX) with a sampling rate of 50GSa/s, and converted into digital signals. Finally, the digital signal is processed by Rx-DSP flow shown in Fig. 4(c) offline in MATLAB.

 figure: Fig. 7.

Fig. 7. (a) Experimental setup; (b) LO-OFC generator; (c) Example spectrum of LO-OFC.

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As mentioned before, the LO-OFC generator consists of an IM (FTM7938EZ), an ECL with a linewidth of <100 kHz and a wavelength of 1550 nm, and an oscillator (Agilent, N5183A) with a frequency of $39.6\textrm{GHz}({ = {B_S}} )$, as illustrated in Fig. 7(b). Due to the limited power of oscillation signal and the seed laser of LO-OFC, EDFA (2) is used to amplify the tones. The power splitting of LO-OFC is merged into the adjustment of output power of EDFA (2). The spectrum of LO-OFC is plotted as Fig. 7(c). For the conventional system, a standalone ECL laser is used as LO. And the powers of received signal (i.e., ROP) and LO/LO-OFC are carefully adjusted to guarantee the fair comparison against the proposed system.

4.2 Frequency offset tolerance

For the experiment, the ROP of signal is set to about −10dBm for both systems. The power of LO (conventional system) and LO-OFC (proposed system) is both set to about 10dBm. The received signal is copied onto 3 tones of the LO-OFC centered at 1550 nm. And a large FO tolerance is achieved. Due to the limited bandwidth of electrical modules in the coherent receivers and oscilloscope, the received signal suffered from FO is severely filtered as shown in Fig. 8(b) with FO=20 GHz. However, the complete spectrum can be obtained by the proposed reconstruction algorithm listed in Fig. 4(c). The reconstructed signal is plotted as Fig. 8(c). As shown in Fig. 8(a), for the proposed system, the performance is almost identical among the $|{FO} |$ ranging from 0 to 36 GHz below the pre-FEC BER level of 1.25×10−2. However, the conventional system does not work when the FO is large. This is consistent with the conclusions of the theoretical derivations and numerical simulations in the previous sections.

 figure: Fig. 8.

Fig. 8. (a) BER versus the absolute of FO in proposed system and conventional system; (b) Spectrum of the received digital signal with FO=20 GHz; (c) Spectrum of the reconstructed signal.

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In the experiment, the total power of LO input into the coherent receiver is set to be consistent for both systems. Thus, the power of a standalone laser is larger than that of a single flat tone in LO-OFC. As a result, the conventional system shows a smaller BER than the proposed system with FO = 0 GHz. In addition, the side-tones with much low power on both sides of central flat tones cause a power penalty about 1 dB. And the amplified spontaneous emission (ASE) noise induced by EDFA (2) also causes a penalty for the proposed system in the experiment.

5. Discussions on power budget penalty

For the proposed OFC-based coherent WDM system, there is a trade-off between the FO tolerance, optical power penalty and cost. In this section, a quantitative analysis for the advantages and disadvantages is given as follows.

An LO-OFC and a splitter are used in the proposed system to provide LOs for all WDM signals, which achieves a large tolerance of FO. There is a trade-off between the FO tolerance and power penalty. The relationship between the WDM channels, FO tolerance range, signal bandwidth and the number of tones in LO-OFC is given as Eq. (9).

In the proposed system, the LO-OFC is firstly split into ${N_{ch}}\; $ part evenly in terms of power. After the coherent detection, the signal with its neighboring copies of ${N_{tone}}$ are filtered by the coherent receiver and ADCs with limited bandwidth. The power penalty of the proposed system is the effective power loss between the power of one flat tone in LO-OFC and the original power of a seed laser used to generate LO-OFC, and it can be expressed as

$${P_1}({\textrm{dB}} )= 10{\log _{10}}\left( {\frac{1}{{{N_{ch}} \cdot {N_{tone}}}}} \right) + {L_1}$$
where ${L_1}$ includes the insertion-loss induced by the generator of LO-OFC, and the total power of the side-tones with much lower power on both sides of central flat tones.

In the conventional OFC based system, the LO tones are demultiplexed from an OFC by a DEMUX, and separately sent into the coherent receivers. The power penalty of the proposed system is the effective power loss between the power of a demultiplexed tone and the original power of a seed laser used to generate OFC. Thus, the power penalty can be expressed as

$${P_2}({\textrm{dB}} )= 10{\log _{10}}\left( {\frac{1}{{{N_{ch}}}}} \right) + {L_2}$$
where ${L_2}$ includes the insertion-loss induced by the generator of OFC, and the total power of the side-tones with much lower power on both sides of central flat tones. And the number of tones in the OFC is equal to the number of WDM channels.

Based on the above analysis, the power budget penalty is the difference between ${P_1}({\textrm{dB}} )$ and ${P_2}({\textrm{dB}} )$. In addition, ${L_1}$ is approximately equal to ${L_2}$. In the following, the penalty of the proposed system is quantitatively evaluated in the configuration of three 64/75/80GBd channels. A RRC filter with a roll-off factor of 0.1 is employed. The FO range is from 10 GHz to 0.25THz. The results are shown is Fig. 9. As expected, there is a trade-off between the FO tolerance and power penalty for the proposed system. For a certain FO tolerance, the higher symbol rate can lead to lower power budget penalty. For the high-rate transmission which has enough power supply but sensitive to the device cost, the proposed scheme is a promising novel candidate.

 figure: Fig. 9.

Fig. 9. The power budget penalty and tone number versus the FO tolerance for symbol rate of (a) 64GBd, (b) 75GBd, and (c) 80GBd.

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6. Conclusion

In this paper, a frequency-offset-tolerant OFC based coherent transmission within DC is proposed. An OFC, in the receiver side, is split with a uniform power ratio, and separately used as LOs to detect the demultiplexed signals. The signal spectrum is copied onto every tone of the LO-OFC, and a large FO tolerance is achieved. Extensive simulations are conducted. The FO tolerance of the proposed system increases linearly with the number of effective tones of LO-OFC. The required ADC sampling rate of the proposed system is almost the same as a conventional coherent system without FO. Extensive experiments are conducted to confirm the conclusions in terms of FO tolerance. Further, the power budget penalty of the proposed system is analyzed.

Funding

National Key Research and Development Program of China (2018YFB1801200); National Natural Science Foundation of China (61801291); Shanghai Rising-Star Program (19QA1404600).

Disclosures

The authors declare no conflicts of interest.

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Figures (9)

Fig. 1.
Fig. 1. The proposed OFC-based coherent-WDM architecture. MUX: multiplexer; De-MUX: demultiplexer.
Fig. 2.
Fig. 2. (a) Spectrum evolution throughout the LO-OFC based coherent receiver; (b) Spectrum evolution of the signal reconstruction processing in the Rx DSP.
Fig. 3.
Fig. 3. Algorithm flow of signal reconstruction in the proposed system.
Fig. 4.
Fig. 4. (a) Simulation setup; (b) Tx DSP flow; (c) Rx DSP flow; (d) Spectrum of the 3 multiplexed signals; (e) Spectrum of LO-OFC with 11 flat tones in the Rx side. The side-tones are not shown. PRBS: pseudorandom bit sequence; G.-S.: Gram-Schmidt; FOC: frequency offset correction; CPR: carrier phase recovery.
Fig. 5.
Fig. 5. (a) BER versus the absolute value of FO in the proposed system and the conventional system; (b) Illustration of relationship between demultiplexed signals and LO-OFC.
Fig. 6.
Fig. 6. (a) BER versus the ADC sampling rate in the proposed system and conventional system.
Fig. 7.
Fig. 7. (a) Experimental setup; (b) LO-OFC generator; (c) Example spectrum of LO-OFC.
Fig. 8.
Fig. 8. (a) BER versus the absolute of FO in proposed system and conventional system; (b) Spectrum of the received digital signal with FO=20 GHz; (c) Spectrum of the reconstructed signal.
Fig. 9.
Fig. 9. The power budget penalty and tone number versus the FO tolerance for symbol rate of (a) 64GBd, (b) 75GBd, and (c) 80GBd.

Equations (12)

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f O F C , k = ( f C F + Δ f ) + k f F S R , k { N , , 0 , , N }
E O F C ( t ) = exp ( i φ O F C ( t ) ) k = N N A O F C , k ( t ) exp ( i 2 π t f O F C , k )
E S ( t ) = A S ( t ) exp ( i φ S ( t ) )
E C ( t ) = A C ( t ) exp ( i ( 2 π t f C + φ C ( t ) ) )
E M ( t ) = A M ( t ) exp ( i ( 2 π t f C + φ M ( t ) ) )
E D e t ( t ) = A D e m , m ( t ) exp ( i ( φ L O O F C ( t ) + φ D e m , m ( t ) ) ) k = N N A L O O F C , k ( t ) exp ( i 2 π t ( f L O O F C , k + f C , m ) )
Δ F = mod ( | f C , m f C F , L O O F C | , B S )
E D ( n ) ADC E A ( t ) = E D e t ( t ) h ( t )
N t o n e | F O M a x | B s × 2 + N c h
Max ( | f F O | ) = ( N 1 ) B S = ( min ( N L , N R ) 1 ) B S
P 1 ( dB ) = 10 log 10 ( 1 N c h N t o n e ) + L 1
P 2 ( dB ) = 10 log 10 ( 1 N c h ) + L 2
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