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Abstract
Due to their simple structures and high robustness to fibre dispersion, single-sideband transmission systems using Kramer–Kronig (KK) receivers are an attractive solution for 80 km data centre interconnects. However, a major problem with KK receivers is that the optimal carrier signal power ratio (CSPR) needs to be large, due to the existence of signal-signal beat interference (SSBI), but this results in low receiver sensitivity. We propose two modified KK receivers that can estimate and eliminate SSBI and allow for signal detection when the CSPR is less than 0 dB. After transmission over an 80 km optical fibre, our modified KK receivers were able to increase the receiver sensitivity by 3 dB compared with a traditional KK receiver while the CSPR was reduced by 6 dB, and improvements of 1.16 and 1.60 dB in the OSNR were achieved with a reduction in the CSPR of 8 dB. Our improved KK receivers can greatly reduce the carrier power and CSPR necessary for the system, and thus reduce the cost of the system transmitter.
© 2022 Optica Publishing Group under the terms of the Optica Open Access Publishing Agreement
1. Introduction
Distributed data centre architectures are increasingly being used in order to support performance-critical applications such as commercial cloud services and big data [1]. A large number of machine-to-machine input/outputs (I/Os) are generated between servers. Global content network and network-scale companies need to connect these data centres in the form of a distributed cluster (within 80 km), which requires a large connection bandwidth and low cost [2]. Of the possible solutions, direct detection (DD) has been the preferred choice for a long time, due to its easy implementation, low power consumption, and low complexity. However, the radio frequency power fading caused by chromatic dispersion (CD) and the complex field loss in the power detection process results in lower spectral efficiency (SE) and a limited transmission distance compared with coherent systems [3,4]. In this context, single-sideband (SSB) modulation can solve the problems of power fading and SE, although the deterioration in the signal-to-noise ratio caused by signal-signal beat interference (SSBI) has always restricted the development of SSB systems. In 2016, Mecozzi proposed the KK receiver scheme, and theoretically proved that if a sufficiently large continuous wave was added, the KK receiver could eliminate the influence of SSBI on the SSB signal [5]. Since the development of the KK receiver, numerous researchers all over the world have conducted verification experiments and research studies on its application in various systems [6–13]. The traditional KK transmission system has the advantage of being able to reconstruct the phase information from the strength information of a signal that meets the minimum phase (MP) condition, meaning that a single photodiode (PD) can be used to achieve functions that could previously only be achieved with a coherent receiver (containing four PDs). After the signal has been reconstructed, DSP technology can then be used for various purposes, for example in traditional digital coherent receivers, dispersion compensation, polarisation demultiplexing, and even mode demultiplexing. The most direct application of KK receivers is to improve the receiver sensitivity of SSB systems. Experimental research by Li [6] has shown that compared with existing receivers based on the SSBI cancellation algorithm, the KK receiver can achieve better receiver sensitivity. Representative verification experiments have also been carried out. For example, in a single-wavelength transmission system, Chen used a KK receiver for the first time to demonstrate a single-wavelength 218 Gbit/s transmission rate over 100 km [7]. In terms of multiplexing technology, Le reported singlefibre transmission of 1.72 Tbit/s using wavelength division multiplexing (WDM) technology [8]. Kong transmitted 99 WDM wavelengths per core over a 37-core fibre, and finally transmitted 3,663 channels at a total rate of 909.5 Tbit/s [9]. Hong and Che each combined a KK receiver with a Stokes receiver [10,11], and used polarisation multiplexing to achieve a single-wavelength transmission rate of >400 Gbit/s, in the same way as in previous work on polarisation multiplexing [12]. The KK receiver can also be used for fibre nonlinear compensation; for example, Li used a KK receiver to recover phase information, and the digital backward propagation algorithm was applied to greatly improve the system tolerance [13].
The MP condition required by the KK algorithm is usually achieved through a sufficiently large carrier-to-signal power ratio (CSPR), and the optimum value of this key parameter is between 6 and 10 dB [14,15]. Xie, Sun and Bo have pointed out that when the optical signal is affected by CD and nonlinear effects, a larger CSPR (or, in other words, a higher carrier power) is needed for the signal to meet the MP condition [16–18]. However, the amplifier in a KK optical communication system with high CSPR requires a wide linear amplification area to ensure the quality of transmission. If the carrier power is too large, the signal will be distorted after nonlinear amplification. In particular, in multi-carrier systems, the signal distortion caused by amplifier nonlinearity will further aggravate sub-carrier crosstalk and channel aliasing, and excessive CSPR can also increase the cost of transmitters, amplifiers and other devices. When the signal is transmitted in an optical fibre, an optical signal with high CSPR will reduce the transmission performance of the system due to the strong nonlinear effect of the optical fibre on the overall signal due to the excessive carrier power. Hence a very meaningful research direction is to further reduce the CSPR based on the premise of ensuring transmission quality, and many researchers have worked on reducing the lowest CSPR of KK receivers [19–22]. Clipping-enhanced KK receivers were proposed by Lowery; this kind of receiver can reduce the carrier power by several dB, or the SNR can be substantially reduced for low CSPRs [19–21]. This method cleverly sets an amplitude threshold and performs amplitude limit processing on the signal below the threshold, thereby avoiding the error phase jump caused by the large rate of change of the logarithmic operation in the region where the independent variable is close to zero in the KK algorithm. Another representative work performed nonlinear shaping of the transmitted signal through exponential calculations, so that the signal reserves more redundant space when the MP condition is met [15]. Other researchers have focused on decreasing the negative impact of SSBI to reduce the CSPR [22–26].
In this paper, we propose two modified KK receivers that contain an optical bandpass filter (OBPF) or wavelength blocker (WB). These receivers can estimate the SSBI and eliminate its influence on MP signals, reduce the CSPR, and improve receiver sensitivity. We refer to the first modified KK receiver, which uses two OBPFs, as DF-KK, and the second, which uses a WB, as WB-KK. After transmission over 80 km optical fibre, compared with a traditional KK receiver (referred to as C-KK in this paper), our modified two KK receivers DF-KK and WB-KK were able to increase the receiver sensitivity by 3 dB when the CSPR was reduced by 6 dB, and improvements of 1.16 and 1.60 dB were achieved in the OSNR while the CSPR was reduced by 8 dB. Of the two proposed approaches, the DF-KK receiver showed a higher sensitivity when the carrier power in the MP signal was weak, while the WB-KK receiver had a higher OSNR gain. Compared with the C-KK for a CSPR of 10 dB, the sensitivity of the DF-KK system for a CSPR of 4 dB was improved by at least 3 dB, and the OSNR gain for the WB-KK system for a CSPR of 10 dB was 1.87 dB.
2. Structure and principle of operation of the two modified KK receivers
The KK algorithm is a DSP procedure that can reconstruct the full complex received optical field from the beats in the signal with a continuous wave (CW) tone, as shown in Fig. 1(a).
Details of the principle of operation of a KK receiver can be found in [5], and the necessary and sufficient condition for MP is mathematically proven in [27]. The classical KK receiver is shown in Fig. 1(b). The complex envelope of the MP optical field impinging on the PD is given by [28]:
where the CW ${E_0}$ is the optical carrier, $E_0^\ast $ is the conjugated field and is the signal component, and ${f_0}$ is the difference between the center frequencies of the optical carrier ${E_0}$ and the signal component ${E_S}$. The current $I(t )$ produced by the photodiode (PD) is proportional to the optical intensity:The first term in Eq. (2) is the carrier-to-carrier beat term, which appears as a DC component. The second term is the desired signal-to-carrier beat component, while the third term is the unwanted SSBI component. A necessary condition for implementing the KK algorithm is that ${E_0}$ must be large enough to satisfy the MP condition. One of the key system parameters of a system using a KK receiver is the CSPR [29], which can be expressed as:
It is crucial to optimise this parameter for each system, since a large CSPR reduces the sensitivity of the receiver, and a low CSPR causes the system to suffer from SSBI, or nonlinear distortions inherent in the direct detection of the signal [30].
Our two modified KK receivers can estimate and eliminate the SSBI and reduce the necessary CSPR of the KK algorithm. The structure of each is shown in Fig. 2. The modified KK receivers, DF-KK and WB-KK, divide the optical signal into two optical fibre links through an optical coupler (OC), and the signal detected by PD2 after the carrier of the second link has been removed by OBPF2 or WB, forms the estimated SSBI for the first link. At the DSP stage, the signal of the first link is subtracted from the signal of the second link; that is, the estimate of the SSBI is used to remove the SSBI and a constant A is added to ensure that the signal satisfies the MP condition in order to apply the KK algorithm and other algorithms. Figure 3 shows a schematic diagram of the bandpass and bandstop of the two modified KK receivers marked D1–D4 in Fig. 2. Green is used to represent the bandpass, and orange to indicate a bandstop. The bandwidth of OBPF2 in DF-KK is less than $2 \times {f_0}$, and the bandwidth of WB in WB-KK is less than $2 \times ({{f_0} - B} )$, where the centre frequency is equal to the carrier ${E_0}$. The bandwidth of OBPF1 in DF-KK and WB-KK is twice as high as the optical signal bandwidth. Its purpose is to remove high-frequency optical noise interference. OPBF1 and OPBF2 in DF-KK and WB-KK are centred at the centre frequency of the data signal ${E_S}$. The optical signal in DF-KK or WB-KK is divided into 1,2 two parts as ${E_1}$ and ${E_2}$ using a 50:50 OC, as follows:
Fig. 3. Schematic diagrams of the bandpass and bandstop for two modified KK receivers at D1–D4 (green represents a bandpass; orange represents a bandstop).
The purpose of OBPF2 and WB is to reduce the intensity of the optical carrier ${E_0}$. When the optical signal of the second link passes through OBPF2 and WB, it can be expressed as:
where ${E^{\prime}_0}$ represents the intensity of ${E_0}$ blocked by OBPF2 or WB. The currents ${I_1}$ and ${I_2}$ produced by PD1 and PD2 are proportional to ${E_1}$ and ${E^{\prime}_2}$:When the difference between the two signals, after removing most of the SSBI, it is assumed that the size of the remaining SSBI is $\alpha \cdot {|{{E_S}(t )} |^2}$. Then, $I(t )\textrm{ = }{I_1}(t )- {I_2}(t )$ can be expressed as:
Equation (8) can be regarded as the signal $\frac{{{E_0}}}{{\sqrt \alpha }} + \sqrt \alpha \cdot {E_S}(t )\exp ({i\pi {f_0}t} )$ obtained after the square rate detection of the PD, and a DC component of size $\left( {1 - \frac{1}{\alpha }} \right){|{{E_0}} |^2}$ is added at the DSP. According to the calculation method in Eq. (3), the CSPR of this signal becomes $1/\alpha$ times the previous value. In general, $\alpha$ is less than 1 and close to 0, and the CSPR of the original signal is amplified. Removing most of the SSBI is equivalent to reconstructing a low CSPR signal to form a high CSPR signal.
However, it may be necessary to add an intensity value A to ensure that the minimum value of $I(t )$ is greater than zero, since ${I_1}(t )$ minus ${I_2}(t )$ makes the minimum value of $I(t )$ less than zero, so that the MP condition is met.
The parameters of OBPF2 and WB both affect the suppression effect on the carrier and thus affect the estimation of SSBI. For both DF-KK and WB-KK, in addition to the parameters of OBPF2 and WB directly affecting the DC suppression in the second link, an excessively large bandwidth will also introduce additional noise by removing the necessary information from the optical signal. In the next section, the impact of OBPF2 and WB on the CSPR of the system due to the difference in bandwidth and other parameters will be analyzed in detail through simulation.
Before the KK algorithm was proposed, Peng and Alireza achieved low-CSPR transmission by removing the carrier and then estimating and removing the SSBI of the signal to be processed [25,26]. Equation (8) shows that after removing most of the SSBI, the signal to be processed can be reconstructed into a high-CSPR signal. Since Li reported that the lowest BER could be obtained with a KK receiver when the CSPR was high [6], we chose to use the KK algorithm to process the reconstructed signal. After the SSBI of the system is removed based on the estimated SSBI, there will be a residual SSBI, which is difficult to model in a simulation. The experiments in Section 4 demonstrate that our proposed scheme can achieve a low BER at lower CSPR signals compared to the scheme proposed by Peng and Alireza [25,26].
3. Simulation setup and results
The control group C-KK simulated in this paper was the Kramers Kronig Receiver demo from VPIphotonics VPItransmissionMaker 11.1 (in Application Example→Optical Systems Demos→Modulation Multilevel). A 32 Gbaud Nyquist-shaped 16-QAM (root-raised cosine IQ filters) signal was converted to minimum phase by adding at its output a CW laser with sufficient power, positioned outside the signal bandwidth. After transmission over an single-mode fibre (SMF), a single PD was used for detection and the signal was digitized with an analog-to-digital converter (ADC). It was then passed to the KK DSP block to reconstruct the in-phase and quadrature components of the signal before being processed by the DSP chain. Without special instructions, the key parameters of the simulation setup are given in Table 1, and the structure is shown in Fig. 4. Figure 5 shows the simulation setup for the DF-KK and WB-KK systems. The modified DF-KK and WB-KK receivers divide the optical signal into two optical fibre links via the coupler, and these two optical signals are then converted into electrical signals by PD1 and PD2 after passing through OBPF1, OBPF2 or WB. The estimated SSBI in the second link is subtracted from the signal of the first optical link, and a real constant A, a value that is 10 times the signal in the first link, is added to the differential signal to satisfy the MP condition. Following this, the signal is demodulated by the DSP algorithm of the C-KK system and the BER is calculated.
Table 1. Simulation setup
Fig. 4. Simulation setup for the C–KK system; DFBL – distributed feedback laser; AWG – arbitrary waveform generator; IQM – IQ modulator; EDFA – erbium doped fibre amplifier; ELPF – electric low-pass filter; MMA – multiple modulus algorithm; BPS – blind phase search algorithm.
We count the symbol errors over 217 bits and set a distance of 80 km as one span. At point A, we set the specified OSNR by adding depolarised noise to the input signal to reach a specific value. Unless otherwise specified, the transmitter optical signal power (TSOP) of the 32-Gbaud Nyquist-shaped 16QAM optical signal at point A is 0 dBm, the transfer function for OBPF2 is Gaussian, its Gaussian order is eight, its bandwidth is 36 GHz, and the OSNR at point A in each KK system is set to 20 dB. The minimum bandwidth resolution of a WB based on liquid crystal on silicon is usually 6 GHz [31], so unless the impact of the WB bandwidth on the system is specified, the WB bandwidth is set to 6 GHz in these experiments. The optical signal is divided into two parts at the receiving end, and in the second path in the two systems shown in Fig. 5, optical devices are used to remove the carrier signal, which causes a delay in the two parts passing through the PD. The strength of the estimated SSBI varies with time. If the signals are out of sync following PD square rate detection, not only can the SSBI not be removed from the signal, but more noise will be introduced. If the signal to be demodulated can be optically synchronized with the carrier-removed SSBI signal in the optical path, then a balanced receiver and a single ADC can be used at the receiving end. If optical synchronization is not applied, the signals demodulated by the two PDs will need to be synchronized via DSP, and the signals can then be subtracted after synchronization with the SSBI to remove the SSBI. We chose to use DSP for synchronization, as this is more practical.
Figures 6(a) and 6-(b) show comparisons of the BER for DF-KK and C-KK, and WB-KK and C-KK, for different values of the CSPR after transmission over one to four spans. It can be clearly seen that the two modified KK receiving systems not only have a lower BER than the C-KK system for the same CSPR, but also have good transmission quality when the CSPR is lower or even less than zero, with a BER of less than the 7% HD-FEC threshold.
Fig. 6. Changes in the BER with CSPR for (a) DF-KK and (b) WB-KK (b) after being transmitted over different numbers of spans.
Comparing the three KK systems, we see that when the CSPR is less than 8 dB, the BER for the DF-KK and WB-KK systems is much lower than for C-KK, and when the CSPR is greater than 10 dB, the values of the BER for the three systems become closer as the CSPR increases. Higher values of CSPR will suppress the influence of the SSBI on the system; however, when the signal is transmitted via the optical fibre, it will suffer from nonlinear crosstalk from the fibre due to cross-phase modulation of the carrier and the signal, and due to nonlinear crosstalk from devices such as the EDFA and PD. It can be observed from Fig. 6 that the larger the CSPR, the greater the influence of these sources of nonlinear crosstalk on the signal. Hence, by comparing the BER curves with the CSPR for these three KK systems, it can be found that when the CSPR is low, the effect of nonlinear crosstalk is small, and the SSBI directly affects the BER. The values of BER for the DF-KK and WB-KK systems are much smaller than for the C-KK system. When the CSPR is high, the SSBI is suppressed, and the nonlinear string generated by the cross-phase modulation becomes the main factor affecting the BER; the values of the BER for all three systems then gradually become closer, and in particular, the two red curves for the system after two spans almost coincide when the CSPR is 16 dB. By comparing Figs. 6(a) and (b), it can be seen that the inhibitory effect of WB-KK on SSBI is better than that of DF-KK under the conditions specified by the above parameters. After transmission over one span, the BER for the DF-KK system is lower than the KP4-FEC threshold (2.3×10−4 [19]) when the CSPR is 5 dB, whereas the BER for WB-KK (2.27×10−4) is lower than the KP4-FEC threshold when the CSPR is 2 dB. The BER for the WB-KK system for transmission over two to four spans is always lower than the 7% HD-FEC threshold when the CSPR is −4 dB, while for the DF-KK system after fibre transmission over two spans, the BER has already exceeded the 7% HD-FEC threshold when the CSPR is−4 dB. This shows that under these conditions, WB-KK has a stronger ability to estimate the SSBI than DF-KK, and can therefore better eliminate the SSBI from the signal and achieve better performance than DF-KK. In the following, we discuss the effects of different parameters for the two optical devices OBPF2 and WB in the two modified KK receiving systems on the estimation and elimination of SSBI.
3.1 Optimal parameters for OBPF 2
Figures 7(a) and 7(b) show the changes in the BER with CSPR for OBPF2 in the DF-KK system with Gaussian filters of different orders, after B2B or one span transmission. The small graphs in Figs. 7(a) and 7(b) show that the BER is lowest when the Gaussian order is 8 and the CSPR is less than –4 dB. From the overall changes in these seven curves, the transfer function of OBPF2 is a square wave; in other words, when the Gaussian order is close to positive infinity, the lowest BER compared to other Gaussian orders cannot be obtained when the CSPR <−4 dB. As shown in Fig. 7(b), when the CSPR is −2 and the Gaussian order is between 2 and 8, the BER decreases as the Gaussian order increases; however, when the Gaussian order is between 8 and 12, the BER increases as the Gaussian order increases. When the CSPR is less than 6 dB and the Gaussian order is 8, the lowest BER is always seen compared to other Gaussian orders. For B2B and after one span transmission, the values of the BER for the DF-KK system are 2.36×10−3 and 2.92×10−3 lower than the 7% HD-FEC threshold when the CSPR is −4dB.
Fig. 7. Variation in the BER for DF-KK with CSPR after (a) B2B and (b) one span transmission for different Gaussian orders of OBPF2.
Figures 8(a) and 8(b) show the changes in the BER with the CSPR for DF-KK after B2B and one span transmission, for different bandwidths of OBPF2. The dotted line in Figs. 8 represents C-KK. Although the transmission performance of the DF-KK system is better than for C-KK for an OBPF2 bandwidth in the range 32–39 GHz, the choice of the OBPF bandwidth affects the BER of the DF-KK system at different CSPR values. Figures 8(a) and 8(b) show that when the CSPR is less than 0 dB, the BER is lowest when the OBPF2 bandwidth is 36 GHz. When the OBPF2 bandwidth is set to 35, 36, and 37 GHz, the BER is less than 10−2 when the CSPR is –5 and –4 dB. For a CSPR of –3 dB, the BER decreases as the bandwidth increases in the range 32–36 GHz, while in the range 37–39 GHz, the BER increases as the bandwidth increases. By combining the results shown Figs. 7 and 8, we set the bandwidth for OBPF2 to 36 GHz and the Gaussian order to 8.
Fig. 8. Variation in BER with CSPR for the DF-KK system, for different bandwidths for OBPF2, after (a) B2B and (b) one span transmission.
3.2 Optimal parameters for WB
Figures 9(a) and (b) show the variation in BER with CSPR after B2B transmission and one span transmission, for the WB-KK and C-KK systems. All the curves in Figs. 9(a) and (b) indicate that the smaller the WB bandwidth in B2B or WB-KK transmission over one span, the better the suppression effect on the SSBI. WB-KK can achieve a BER lower than 10−2 at lower values of CSPR, meaning that a WB with lower bandwidth can block direct current, and that less noise is introduced by blocking the optical signals when estimating the SSBI.
Fig. 9. Variation in the BER of WB-KK with CSPR after (a) B2B or (b) one span transmission, for different bandwidths of WB.
3.3 Effects of insertion loss on the system
Both OBPF2 and WB have certain insertion losses, and the power of the 16QAM signal in the second links of the DF-KK and WB-KK systems will be reduced due to these insertion losses. In DF-KK, the optical signal separated by the OC is passed through an OBPF in the first and second links, and the insertion loss can be compensated by adjusting the filter loss when setting the filter function. For the WB-KK system, there is no additional optical filter or WB in the first link, and the second link contains a WB that introduces an insertion loss, meaning that the insertion loss must be compensated after the ADC.
In this paper, we set all OBPFs and WBs to zero insertion loss, and add attenuators at the points marked D2 and D4 in Fig. 5 to simulate the insertion losses introduced by the OBPF and WB. Figures 10(a)–10(d) show the variation in the BER with CSPR when the OFBF2 or WB have insertion losses of 0–5 dB in the DF-KK and WB-KK systems, respectively. Figures 10(a) and 10(b) show the results for B2B transmission, while Figs. 10(c) and 10(d) show the results for one span transmission. The dotted line in each of these four figures represents the results for C-KK. By comparing the changes in BER with CSPR for DF-KK after transmission over B2B and one span in Fig. 10, we see that these two systems use an OBPF or WB to block the CW when estimating the SSBI, but also introduce noise when blocking the CW. When dispersion is present, the performance will be affected unless the SSBI estimation is accurate. When the insertion loss introduced by the OBPF and WB causes the estimated SSBI to be less than the actual value, the effect of eliminating the SSBI will be poor, and the noise generated during the CW blocking process will increase the overall error in the system.
Fig. 10. Variation in the BER with CSPR for DF-KK and WB-KK, after B2B or one span transmission, for different insertion losses for OBPF2 and WB.
The variation in BER with CSPR for the three KK receiver systems after B2B and one span transmission (Figs. 10(a) and 10(b)) shows that when the insertion loss is 0–2 dB, the two modified KK receivers can achieve a BER lower than 10–2 at a lower CSPR; when the insertion loss is 4–5 dB, the BER for the two modified KK receivers is higher than C-KK. Figures 10(a) and 10(b) also show that the BER for the DF-KK system is less than for C-KK under the same CSPR conditions when the insertion loss is 3 dB. However, it can be seen from Figs. 10(c) and 10(d) that when the insertion loss is 3 dB and the CSPR is 9 dB, the BERs for DF-KK, WB-KK, and C-KK are 2.37×10–3, 2.58×10–3, and 2.16×10–3, respectively, meaning that the values of the BER for the two improved KK systems are already higher than for the C-KK system. Fibre transmission errors such as dispersion and nonlinear effects not only affect the optimal CSPR of the C-KK system, but also change the acceptable insertion loss values for DF-KK and WB-KK. As shown in Fig. 10, an additional SSBI estimation error is caused by the insertion loss. It is therefore necessary to adjust the power of the two optical signals to compensate for the insertion losses caused by OBPF and WB in order to accurately estimate and eliminate the SSBI.
3.4 Comparison of DF-KK and WB-KK
Figures. 11(a) and 11(b) show the variation in the BER with TSOP after one span transmission for the DF-KK and WB-KK systems. The dotted lines in Fig. 11 represent the results for C-KK. Figure 11 shows that for a CSPR of 10 dB, both DF-KK and WB-KK have the lowest BER when the TSOP is 0 dBm, and this is the main reason for setting the TSOP to 0 dBm in the remaining simulations in this paper. It can also be seen from Figs. 11(a) and 11(b) that when the TSOP is less than 0 dB, the BER decreases as the CSPR and TSOP increase. When the TSOP is greater than 0 dBm, the nonlinear effect becomes the main factor determining the BER for the three KK systems. When the CSPR is 10 dB, the values of the BER for the three KK receiving systems increase with the TSOP in the interval 0–5 dBm. When the CSPR is in the range 4–10 dB, the DF-KK system can achieve a BER lower than 10−2 when the TSOP is greater than −14 dB, and the WB-KK system can achieve a BER lower than 10−2 when the TSOP is greater than −12 dBm. For the C-KK system with a CSPR of 10 dB, the BER is lower than 10−2 in the range >−10dBm. This indicates that the two improved KK receiving systems greatly improve the sensitivity of the KK receiving system after eliminating the SSBI. In the range of TSOP from −14 to −11 dBm, the BER of the DF-KK system with a CSPR of 4 dB is lower than 10−2, while the BER for the WB-KK system with a CSPR of 4 dB at TSOP is much greater than 10−2 at −14 to −13 dBm. This shows that when the CSPR is greater than 4 dB, the sensitivity of the DF-KK receiver is higher than that of the WB-KK receiver. In the range of −3 to 2 dBm TSOP, the BER of the WB-KK system with a CSPR of 4 dB is lower than the KP4-FEC threshold, while the TSOP of the DF-KK system needs 7 dB to make the BER lower than KP4-FEC threshold when the CSPR is in the same range. WB-KK can achieve a low error transmission for a BER lower than the KP4-FEC threshold when the CSPR is lower than DF-KK by at least 3 dB.
Fig. 11. Variation in BER with TSOP for (a) DF-KK and (b) WB-KK for different values of CSPR, after one span transmission.
The solid and dashed lines in Fig. 12 show the changes in the BER with OSNR after one span transmission for the WB-KK system and DF-KK systems, respectively, with different values of the CSPR. The dotted line in Fig. 12 represents C-KK. We set KP4-FEC as the threshold. For a CSPR of 10 dB, the two improved KK receiving systems have a gain of 1.87 dB compared to the C-KK system. Compared with C-KK with a CSPR of 10 dB, WB-KK has a gain of 1.60 dB when the CSPR is 2 dB, and DF-KK has a gain of 1.16 dB. For the WB-KK system with a CSPR of −6 dB, the same decision threshold as the C-KK system with a CSPR of 10 dB can be achieved at the cost of an OSNR increase of 0.08 dB, while for the DF-KK system, the cost is 2.29 dB.
Fig. 12. Variation in BER with OSNR for the three KK receivers with different CSPRs after one span transmission.
The solid and dashed lines in Fig. 13 show the variation in BER with OSNR for the WB-KK and DF-KK systems, respectively, when they transmit over 40 km SMF without dispersion compensation, with different values of CSPR. Figure 13 shows that with KP4-FEC as the threshold and a CSPR of 10 dB, DF-KK has a gain of 2.23 dB compared to the C-KK system, whereas WB-KK has a gain of 2.35 dB. Compared with the C-KK system for a CSPR of 10 dB, WB-KK has a gain of 2.14 dB for a CSPR of 2 dB, DF-KK has a gain of 1.61 dB for a CSPR of 2 dB, and WB-KK has a gain of 0.35 dB for a CSPR of −6 dB. For the DF-KK system with a CSPR of −6 dB, the same decision threshold can be achieved as for the C-KK system with a CSPR of 10 dB at the cost of an OSNR increase of 1.85 dB.
Fig. 13. Variation in BER with OSNR for the three KK receivers with different CSPRs, without dispersion compensation, after transmission over 40 km.
4. Experimental setup and results
We carried out a set of experiments to compare the performance of our proposed scheme with that of Peng and Alireza [25,26]. Our results show that the proposed scheme achieves a lower BER for signals with residual SSBI. Figure 14 shows the experimental setup, consisting of two SSB-16QAM coherent optical communication systems in which SSBI is removed to achieve low-CSPR detection. The CWs are generated by external cavity lasers (ECLs) with a line width of less than 100 kHz and an output power of less than 15 dBm. The 1550 nm light source is then modulated by the I/Q modulator to realize photoelectric conversion. The I/Q modulator has a 3 dB bandwidth of 33 GHz and an insertion loss of 6 dB. An AWG of 64 GSa/s is used to convert the two independent sequences of digital symbols into analogue 10 GBaud 16QAM signals (raised cosine IQ filters, roll-off = 0.2). An EDFA with a noise value of 5.5 dB and a variable optical attenuator (VOA) is used to adjust the transmitted signal power to a 1×2 OC. CW light is generated by another external cavity laser (ECL2), which can adjust the frequency to give a guard band between the CW and 16QAM signals. The output power of ECL2 is adjusted by another VOA, and it is then coupled to the other side of the 1×2 coupler. The transmission link is composed of 10 km SMF (G 652, The fibre loss, dispersion, and nonlinearity coefficient are 0.18 dB/km, 17 ps/(nm.km), and 1.3 W−1 km−1, respectively. The bandwidth of OBPF1 is 20 GHz, including the 16QAM signal and CW. The bandwidth of OBPF2 is 12 GHz, and the centre frequency domain is the same as for the 16QAM signal. A four-channel digital phosphor oscilloscope with a sampling rate of 100 GSa/s and a bandwidth of 20 GHz as ADC is used to receive the signal. The offline digital signal is then processed by MATLAB. Offline DSP includes the KK algorithm, resampling, CD, a Nyquist filter, a frequency shift, clock phase recovery, MMA, and BPS.
Fig. 14. Experimental setup for two SSB-16QAM coherent optical communication systems in which SSBI is removed to achieve low-CSPR detection.
In Figs. 15 and 16, “w KK” represents our proposed DF-KK scheme, “w/o KK” represents the CSPR without the use of the KK algorithm reduction scheme proposed in [25,26], and “C” represents the classical unimproved KK receiver. Figure 15 shows a comparison of the BER for the DF-KK and the SSBI cancellation receiver proposed in [25,26] for different values of the CSPR after transmission over 10 km, where the carrier offset is 0.08 nm (10 GHz). It can be clearly seen from Fig. 15 that when ROP = 1 dBm, the two CSPR reduction schemes can still reach the 20% SD decision threshold with a CSPR reduction of 6 dB compared with the classic KK receiving scheme. The DF-KK receiver system not only has a lower BER than the SSBI cancellation system proposed in [25,26] for the same CSPR, but also achieves good transmission quality when the CSPR is −1 dB and the ROP is 1 dBm, with a BER of less than the 7% HD–FEC threshold. To meet the 20% SD-FEC threshold, the DF-KK system with an ROP of −3 dBm can reduce the CSPR by 1.2 dB compared with the system without KK in [25,26]. The results in Fig. 15 demonstrate that the modified DF-KK receiver proposed in this manuscript can further reduce the CSPR.
Figure 16 illustrates the relationship between the BER and the carrier offset when the ROP is 0 dBm. It can be clearly seen that the BER of the DF-KK system is lower than for the SSBI cancellation receiver in [25,26] when the carrier offset is between 0.05 and 0.11 nm. It can be seen from Fig. 16 that in the range 0.05–0.08 nm, the BER for the two systems decreases with an increase in the carrier offset. This reflects the same phenomenon as reported in [25,26]; as the frequency separation between the CW and the signal increases, the accuracy of the SSBI estimation gradually improves, and the reconstructed signal becomes more linear. The bandwidth of the ADC used here was 20 GHz. Due to limitations on the ADC bandwidth, the optimal carrier offset of the two systems for different CSPRs was 0.08 nm. The noise introduced by the ADC bandwidth limitation becomes obvious with an increase in the carrier offset, and DF-KK also produces errors in the estimation of SSBI due to this noise. Hence, the BER for both systems increases for a carrier offset greater than 0.08 nm. It can be clearly seen from Fig. 16 that when the carrier offset is less than 0.07 nm, the BER of the signal for a CSPR of 0 dB after using the KK algorithm is lower than for a signal with a CSPR of 2 dB without the KK algorithm. This reflects the importance of the KK algorithm, and shows that our proposed scheme can better handle the residual SSBI, thus enabling the system to obtain a lower BER at a lower CSPR.
5. Conclusion
We propose two KK receivers that can estimate and eliminate the SSBI to achieve good transmission performance for CSPR < 0 dB. Our modified KK receivers, DF-KK and WB-KK, divide the optical signal into two optical fibre links via an OC. The signal detected by PD2 after the CW of the second link has been removed by OBPF or WB forms the estimated SSBI for the first link. Unlike the classical KK algorithm, our two improved KK receivers use the estimated value of the SSBI to remove it from the other signal, and add a virtual CW to satisfy the MP condition. Compared with the traditional KK receiver, the CSPR required by the two modified KK receivers is reduced by at least 10 dB. After transmission over an 80 km optical fibre, our modified KK receivers were able to increase the receiver sensitivity by 3 dB compared with a traditional KK receiver while the CSPR was reduced by 6 dB, and improvements of 1.16 and 1.60 dB in the OSNR were achieved with a reduction in the CSPR of 8 dB. DF-KK and WB-KK have different characteristics. After one span transmission, when the CSPR is greater than 4 dB, the sensitivity of the DF-KK receiver is higher than that of the WB-KK receiver; however, when the TSOP is between −3 and 2 dBm, the BER for the WB-KK receiver is lower than for DF-KK.
Funding
National Key R&D Program of China from Ministry of Science and Technology (2021YFB2800903); National Natural Science Foundation of China for Excellent Young Scholars (62022016); National Natural Science Foundation of China (61727817, 61835002); Funds for Creative Research Groups of China (62021005).
Disclosures
The authors declare no conflicts of interest.
Data availability
Data underlying the results presented in this paper are not publicly available at this time but may be obtained from the authors upon reasonable request.
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