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Abstract
Four system frameworks based on carrier assisted differential detection (CADD) receivers for offset double sideband (DSB) signal transmission, including offset DSB asymmetric CADD (offset DSB A-CADD), offset DSB symmetric CADD (offset DSB S-CADD), offset DSB parallel double delay asymmetric CADD (offset DSB PDD-A-CADD), and offset DSB parallel double delay symmetric CADD (offset DSB PDD-S-CADD) are proposed to reduce the requirement for carrier-to-signal power ratio (CSPR) and improve the spectral efficiency (SE) of the self-coherent detection. These frameworks accommodate signal-signal beat interference (SSBI) and efficiently solve the noise enhancement by placing a frequency gap as wide as the signal bandwidth in the middle of the left and right sideband signal. Massive theoretical derivation and simulation verification illustrated that compared with previous interleaved A-CADD, our system achieve field recovery under the condition of 0 dB CSPR with the improvement of SE by 5%, and the OSNR sensitivity is improved by 4.5 dB with 20% forward error correction (FEC) threshold. In addition, due to the devices’ limited bandwidth (BW), the information-bearing signal is attenuated at the high-frequency region. And since SSBI has less influence on the signal in the high-frequency region, the frequency gap of the four offset DSB CADD schemes are compressed to utilize as much low-frequency resource as possible and improve the SE. Efficient compression of the frequency gap from 50% to 32.3% with 20% FEC threshold and 50% to 37.7% with 7% FEC threshold at 0 dB CSPR is achieved, and only a slight performance degradation is observed. At this time, the SE is improved by 22.7% and 17.3% with different FEC thresholds, respectively, compared with the 5% frequency gap interleaved A-CADD.
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1. Introduction
With the development of cloud computing, mobile internet, and virtual reality, the realization of high-speed transmission for cost-sensitive short-reach and medium-reach data center interconnection and metro networks has attracted considerable interest from the communication engineering community [1–3]. Despite the advantages of superior sensitivity, high spectral efficiency (SE), and linear optical field recovery for coherent detection [4], the requirement of narrow-linewidth local oscillator (LO) lasers with wavelength alignment remains a major obstacle to their application [5,6]. The simple structure and low cost of conventional intensity modulation and direct detection (IM-DD) enable them good options for short-reach transmission. However, the power fading problem caused by dispersion limits its transmission distance [7]. Self-coherent detection is considered as a promising solution to overcome the chromatic dispersion (CD) induced power fading problem in IM-DD system and achieve field recovery cost-effectively, which can potentially bridge the gap between direct and coherent detection [8–13].
Self-coherent systems typically utilize single sideband (SSB) modulation, and main influencing factor in these systems is the signal-signal beat interference (SSBI) generated by the receiver. In 2006, the Armstrong group proposed an offset SSB scheme to accommodate SSBI by placing a frequency gap [14], however, half of the SE is reduced. In 2009 and 2015, the Winzer and Chi group proposed a self-coherent scheme to remove SSBI by iterative cancellation algorithm to improve the SE [15,16]. But the iterative cancellation algorithm may suffer from the increased complexity of receiver design [17]. During 2016-2019, Mecozzi, Su and Shieh introduced Kramers-Kronig (KK) into the system which effectively mitigates SSBI under minimum phase conditions without an iterative elimination algorithm [18–20]. However, it should be noted that high power (about 6 dB) is required in the above two schemes for the inserted carrier to satisfy the minimum phase condition of the KK relation or to avoid error propagation during iterative cancellation receiver iterations [21], in addition, high carrier-to-signal power ratio (CSPR) in the system also limits the power efficiency and increases nonlinear effects. Very recently, Shieh and co-workers proposed an interleaved subcarrier loading scheme [22,23] for double-sideband (DSB) signals in CADD receivers [24–27]. The SSBI is accommodated by unused even subcarriers, which occupy 50% of all spectrum resources, and the field recovery at 3 dB CSPR is achieved when another 5% frequency gap is inserted. It is worth noting that the main contributing factor to the higher CSPR is the noise enhancement in the vicinity of zero frequency. The effect of noise enhancement decreases as the frequency gap increases, and the optimal CSPR gradually decreases to about 0 dB. However, frequency gap and unused even subcarriers may cause excessive waste of spectrum resources.
Herein, we report four system frameworks based on CADD receivers for offset DSB signal transmission, including offset DSB A-CADD, offset DSB S-CADD, offset DSB PDD-A-CADD and offset DSB PDD-S-CADD to reduce the requirement for CSPR and improve the SE. These frameworks accommodate SSBI and solve the noise enhancement in the vicinity of zero frequency by placing a frequency gap as wide as the signal bandwidth in the middle of the left and right sideband signal. In addition, considering that the insertion of a frequency gap renders the signal in the high-frequency region, the response of semiconductor devices in high-frequency is usually worse than that in low-frequency. Therefore, compression of the frequency gap should be carried out to restrict the offset DSB signal in the low-frequency region as much as possible. But partial overlap of the signal and SSBI is not negligible in the high-frequency region, which caused by compression and degrades the performance. Fortunately, the triangular-shaped SSBI has less impact on the received signal in the overlapping region. After weighing up the pros and cons of performance and SE, the optical field recovery at 0 dB CSPR is achieved within an acceptable performance sacrifice. Compared with interleaved A-CADD [22,23], the proposed scheme has three obvious advantages: (1) it achieves field recovery at 0 dB CSPR; (2) combined with frequency gap compression, it has higher SE; (3) the OSNR sensitivity is improved by about 4.5 dB under the 20% FEC threshold (BER = 2.4e-2) condition. Additionally, compared with the offset SSB scheme [14], the proposed offset DSB CADD scheme improves SE by more than half. The BER penalty after 1000 km of transmission is negligible showing the effectiveness of the offset DSB CADD schemes in recovering the phase information and CD compensation. Herein, the frequency gap compression is defined as the reduction of the frequency gap to reduce the overall bandwidth requirement of the system. The percentage of frequency gaps is defined as the ratio of frequency gap to the total bandwidth. And the spectrum resource penalty (SRP) is defined in this paper as the proportion of sacrificed effective bandwidth to the total bandwidth.
The rest of this paper is organized as follows. In Section 2, the theoretical description of the offset DSB CADD scheme is given. Section 3 verifies the effectiveness and superiority of the offset DSB CADD scheme through MATLAB and VPItransmissionMaker11.1 co-simulation, and discusses the optimization process of optical delay, CSPR and frequency gap. In Section 4, the simulation results are presented and analyzed. Finally, Section 5 concludes the article.
2. Principle of offset DSB CADD scheme
As shown in Figs. 1(a) and (b), the operation principle of interleaved A-CADD and offset DSB CADD schemes is introduced. Specifically, Fig. 1(a) shows the operation principle of interleaved A-CADD scheme reported by Shieh et al. [23], while Fig. 1(b) shows the proposed offset DSB CADD scheme.
Fig. 1. Operation principles for (a) previous interleaved A-CADD scheme; (b) proposed offset DSB CADD scheme.
The principle of interleaved A-CADD in Fig. 1(a) can be briefly stated as follows. At the transmitter end, only odd subcarriers are filled with data, and even subcarriers are left unused. Another 5% frequency gap needs to be inserted to overcome the noise enhancement in the vicinity of zero frequency. At the receiving end, the SSBI generated by the interleaved A-CADD receiver fall on the unused even subcarriers. As a result, the signal can be extracted without interference caused by the SSBI, which allows the interleaved A-CADD scheme to recover the optical field at 3 dB CSPR. The effect of noise enhancement decrease as the frequency gap increases, resulting in the optimal CSPR gradually decreasing to about 0 dB. However, it causes more than 75% of spectrum resources penalty (SRP). In this case, the 75%-SRP of the interleaved A-CADD scheme consists of 25% frequency gap and even subcarriers.
The proposed offset DSB CADD scheme accommodates SSBI and resolve the noise enhancement in the vicinity of zero frequency by inserting a frequency gap as wide as the signal bandwidth. The corresponding operation principle is shown in Fig. 1 (b). The left and right sideband signals at the transmitter side are up-converted to the center frequency ${\pm} {f_h}$ respectively, thus leaving a frequency gap as wide as the signal bandwidth, which only causes 50% spectrum resources penalty (SRP), and no extra penalty. The signal bandwidth is set to 2B and ${f_h}$ is set to 1.5B. As such, the left and right sideband signals occupy bandwidths of [-2B, -B] and [B, 2B], respectively, and the bandwidth occupied by the frequency gap is [-B, B]. The optical field E(t) of the offset DSB signal at the transmitter can be expressed as follow
The four offset DSB CADD schemes differs from each other mainly in the receiver structures as shown in Figs. 2(a)-(d). The offset DSB S-CADD/PDD-S-CADD removes single-ended photodiode (SPD) and has lower implementation complexity compared with offset DSB A-CADD/PDD-A-CADD. Moreover, the offset DSB PDD-A-CADD/ PDD-S-CADD places an additional delay in parallel to the original delay in the offset DSB A-CADD/S-CADD receiver, which improves the system performance. It is worth noting that the four CADD receivers are a special case of generalized CADD receiver [28–31], and we believe that the concept of proposed offset DSB may also be extended to generalized CADD receiver in future work. The specific derivation of the four offset DSB CADD receivers can be found in the Appendix A, and the SSBIs generated by them are as follows
Fig. 2. Structures of offset DSB CADD receivers. (a) offset DSB A-CADD receiver; (b) offset DSB S-CADD receiver; (c) offset DSB PDD-A-CADD receiver; (d) offset DSB PDD-S-CADD receiver. OC: optical coupler.
It can be seen from the exponential term containing t in Eqs. (2a)–(2d) that the center frequency of SSBI are 0 and ${\pm} 2{f_h}$,and the frequency bands occupied by SSBI are [-B, B], [-4B, -2B] and [2B,4B]. Besides, the bandwidth of the offset DSB electrical signal obtained by the offset DSB CADD receiver is constant, and still occupy the frequency bands [-2B,-B] and [B, 2B]. Therefore, the signal and SSBI are located in different frequency bands and the noise enhancement in the vicinity of zero frequency is solved by placing the frequency gap. In other words, signal can be extracted without interference caused by the SSBI and enhanced noise, so that the proposed scheme can achieve field recovery under the condition of 0 dB CSPR. Further, the SSBI of the offset DSB CADD receivers has approximately a triangle shape in the frequency domain, and it has less influence on signal in the high frequency region. Based on this characteristic, the frequency gap can be further compressed to utilize as much low-frequency resource as possible and improve the SE of the system.
The key characteristic of the offset DSB CADD is the unique transfer function, which is only determined by the optical delay. And the insertion of the frequency gap moves the offset DSB signal far from the zero-magnitude of the transfer function at 0 GHz, so the only thing left is to move the signal away from the second zero-magnitude by choosing an appropriate optical delay, which means the needs for optimization. Herein, the transfer functions corresponding to the two sets of optical delays shown in Fig. 3 are taken as an example. According to the steepness of the transfer function around 0 GHz and the noise enhancement caused by the magnitude of transfer function less than 1 of the signal region, it can be seen that setting the values of ${\tau _1}$, ${\tau _2}$, ${\tau _1}^\prime$ and ${\tau _2}^\prime $ to 26 ps, 63 ps, 13 ps, and 44.5 ps is better than 16 ps, 43 ps, 8 ps, and 29.5 ps. Furthermore, arranging in descending order, the steepness of the transfer function around 0 GHz is sorted as follows: offset DSB PDD-S-CADD, offset DSB PDD-A-CADD, offset DSB A-CADD/S-CADD. Remarkably, the optical delay of the offset DSB A-CADD receiver is twice as much as the offset DSB S-CADD receiver with the same transfer function.
3. Parameter optimization of offset DSB CADD system
3.1 Simulation setup
As shown in Fig. 4, the establishment of four offset DSB CADD systems by co-simulation using MATLAB and VPI transmissionMaker11.1 is accomplished. At the transmitter, the header of each frame has 1024 symbols for synchronization and equalization, and a total of 220 bits are transmitted for the final BER calculation. The bit rate of the signal is 100 Gb/s and the modulation format is 16-QAM. The two pseudo-random binary sequence (PRBS) bit streams are mapped to generate the symbol sequences respectively. The symbol sequences are pulse shaped using root-raised cosine (RRC) filter with roll-off of 0.01, and the signals is up-converted to obtain left and right sideband signals, which occupying the frequency bands [-25GHz, -12.5GHz] and [12.5GHz, 25GHz], respectively. The center frequency of the left and right sideband signals are ${\pm} 18.75$ GHz, and the frequency gap occupies the middle bandwidth of [-12.5GHz, 12.5GHz]. Then the left and right sideband signals are summed to obtain the offset twin-SSB electrical signal, and the transmitted optical signal is obtained by IQ modulation after adding the virtual carrier. Herein, the virtual carrier is used to facilitate the control of CSPR. In this case, the center frequency of the laser is 193.46 THz, and the laser linewidth is set to 0 Hz to reduce the complexity of the analysis problem. Only the effects of CD and additive white Gaussian noise (AWGN) are considered in the channel. The transmission distance is 1000 km with 17 ps/nm/km dispersion coefficient. Note that the 1000 km transmission reach is only used to evaluate the dispersion tolerance of offset DSB CADD. In short reach optical communications, the transmission distance is normally tens of kilometers. At the receiver side, four offset DSB CADD receivers shown in Fig. 2 are used for reception, and their performance can be improved by optimizing three receiver parameters such as optical delay, CSPR, and frequency gap, which are described in subsections 3.2, 3.3, and 3.4. Low-pass filters (LPFs) are used to simulate the modulator bandwidth and photodetector (PD) bandwidth. And the LPFs adopt fourth-order Bessel filters, and the bandwidth of all LPFs is set to the same parameter. In order to facilitate comparison with the interleaved A-CADD scheme, it is set to 33 GHz [23]. The DSP include the inverse transfer function, dispersion compensation, down-conversion, matched RRC filter, synchronization, equalization, symbolic decision, and finally the BER calculation module. The role of the equalization module is to mitigate the inter-symbol interference (ISI) caused by bandwidth (BW) limitation and link dispersion.
Fig. 4. Simulation setup. IQ Mod: IQ modulator; SSMF: standard single-mode fiber. Inset: Optical spectrum of the generated 25-GBaud 16-QAM offset DSB signal with 50% frequency gap.
3.2 Optimum optical delay
Since the offset DSB CADD receiver achieves field recovery of the signal by using differential information, the choice of the optical delay of the receiver is critical. A larger optical delay contributes to frequency gap compression, however, when the delay becomes too large, the 2nd null point of the transfer function will move into the signal spectrum, degrading the system performance. The three parameters of the offset DSB CADD receiver are closely related. Therefore, we need to set the values of CSPR and frequency gap before optimizing optical delay. To meet the goal of low CSPR, we set the CSPR to 0 dB. As for the frequency gap, the value is preferably set to 50%, thus achieving field recovery of the signal without interference from the SSBI. Figure 5(a) shows the system performance at different delay values. According to the structural characteristics of the proposed offset DSB CADD receiver shown in Fig. 2, only four optical delays need to be optimized in the four offset DSB CADD systems. In addition, system performance is mainly determined by the steepness of the transfer function around 0 GHz and the noise enhancement caused by the magnitude of transfer function less than 1 of the signal region. By comparison, it can be found that the best BER performance of the offset DSB A-CADD scheme is obtained when the optical delay ${\tau _1}$ set as 26 ps. For the offset DSB PDD-A-CADD scheme, an additional optical delay ${\tau _2}$ is placed parallel to the original delay ${\tau _1}$ in the offset DSB A-CADD, and the results imply that the optimal system performance is obtained when the ${\tau _2}$ set as 63 ps. The simulation results in Fig. 5(b) show that the optimal optical delay ${\tau _1}^\prime $ for the offset DSB S-CADD receiver is 13 ps. The additional optical delay ${\tau _2}^\prime $ of the offset DSB PDD-S-CADD receiver is set to 44.5 ps to achieve the optimal performance. The above results are obtained in back-to-back (BTB) scenario. Further, we optimize the optical delay for the offset DSB CADD receiver after 1000 km fiber transmission. The optimized results are shown in Figs. 5 (c) and (d), and the obtained optimal delay is consistent with that of BTB scenario. Besides, the optical delay of the system is kept constant when frequency gap compression is performed in order to reduce the complexity for system design.
Fig. 5. BER performance versus OSNR of various delays for (a) ${\tau _1}$and${\tau _2}$ in BTB scenario; (b) ${\tau _1}^\prime $and${\tau _2}^\prime $ in BTB scenario; (c) ${\tau _1}$and${\tau _2}$ after 1000 km transmission; (d) ${\tau _1}^\prime $and${\tau _2}^\prime $ after 1000 km transmission.
3.3 Optimum CSPR
CSPR is another key parameter for optimizing offset DSB CADD receivers. A higher CSPR means a higher proportion of the carrier and a lower proportion of the signal power, which brings about poor tolerance to noise and reduce the OSNR sensitivity for the transmission system. Therefore, it is of great importance to reduce the CSPR requirement for system. When searching for optimal CSPR, we should first fix the optical delay of the receiver to the optimal optical delay found in subsections 3.2, the frequency gap is set to 50%, the BER threshold is set to 2.4e-2. For the convenience of comparison, two interleaved A-CADD systems with a frequency gap of 5% and 15% are considered. For interleaved A-CADD, OFDM modulation format is adopted. In contrast, single carrier modulation is adopted for the offset DSB CADD due to the low peak-to-average power ratio (PAPR) and better tolerance to Mach-Zehnder modulator (MZM) nonlinearity. No optical noise-rejection filters are used in all of the interleaved A-CADD and offset DSB CADD schemes as the most practical low-cost applications. With the same data rate, as shown in Fig. 6, the optimal CSPRs of the four offset DSB CADD schemes are around 0 dB for both at BTB and after 1000 km fiber transmission. Among them, the OSNR sensitivity of offset DSB CADD receivers is sorted in descending order as follows: offset DSB PDD-A-CADD, offset DSB PDD-S-CADD, and offset DSB A-CADD/S-CADD. The main reason is that the transfer functions of the four offset DSB CADD receivers have different suppression effects on amplifier spontaneous eousemission (ASE) noise. In addition, we can see from Fig. 6(a), the system performance of the 5%-gap (55%SRP) interleaved A-CADD is affected by the noise enhancement. Thus, the optimal CSPR is only about 3 dB, and the OSNR sensitivity is 23 dB. Although the system performance of the 15%-gap (65%SRP) interleaved A-CADD scheme is improved, the 65%-SRP is too high, and the CSPR is only reduced to about 2 dB. In contrast, as shown in Fig. 6(a), the proposed 50%-gap (50%SRP) offset DSB CADD scheme which can reduce the optimal CSPR to about 0 dB, and the OSNR sensitivity is improved by up to 4.5 dB compared with 5%-gap (55%SRP) interleaved A-CADD.
Fig. 6. Required OSNR versus CSPR for different offset DSB CADD schemes (a) at BTB scenario; (b) after 1000 km transmission. Note: Since the transfer functions of offset DSB A-CADD and offset DSB S-CADD receivers are the same, their curves (black and red lines) basically coincide.
3.4 Frequency gap
In addition to the optical delay and CSPR, the frequency gap is another key factor to optimize for the offset DSB CADD receivers. A smaller frequency gap may lead to a little degradation of system performance, but it improves the SE of the system and mitigates the problem of BW limitation. For this reason, we optimize the offset DSB CADD system by compressing the frequency gap under the premise of ensuring performance. Figure 7 shows the relationship between mutual information (MI) and OSNR based on the simulation of selecting different frequency gaps under the conditions of BTB scenario and 1000 km transmission. In order to meet the low CSPR target, the CSPR value of the offset DSB CADD system is fixed to 0 dB and that of the interleaved A-CADD is set to the optimal CSPR, and other parameters remain unchanged. By analyzing Fig. 7, we can make the following conclusions: (1) The BER performance of the four offset DSB CADD systems is optimal when the frequency gap set as 50%, and this system with the advantage of 5% SE performs much better than the 5%-gap (55%SRP) interleaved A-CADD. (2) When OSNR is equal to 20 dB, compared with the 5%-gap (55%SRP) interleaved A-CADD, the 46%-gap (46%SRP) offset DSB A-CADD/S-CADD has an MI improvement of 0.15 bit/symbol, and the 44%-gap (44%SRP) offset DSB PDD-CADD system has 0.33/0.37 bit/symbol MI improvements.
Fig. 7. (a) MI versus OSNR for different offset DSB A-CADD/PDD-A-CADD schemes in BTB scenario; (b) MI versus OSNR for different offset DSB S-CADD/PDD-S-CADD schemes in BTB scenario; (c) MI versus OSNR for different offset DSB A-CADD/PDD-A-CADD schemes after 1000 km transmission; (d) MI versus OSNR for different offset DSB S-CADD/PDD-S-CADD schemes after 1000 km transmission.
These results imply that the proposed scheme can achieve a higher SE than the 5%-gap (55%SRP) interleaved A-CADD by compressing the frequency gap. The level of frequency gap compression will be further discussed in Section 4, and the above optimized optical delay, CSPR, and frequency gap parameters will also be used for the simulation study in Section 4.
4. Results and discussion
For the offset DSB CADD scheme, insertion of the frequency gap transfers the signal to the high-frequency region, the bandwidth of practical electro-optic devices is limited, and the information-bearing signal is usually attenuated at the high-frequency region. Therefore, for further exploration of the tolerance of the offset DSB CADD scheme to bandwidth limitations, the bandwidth of LPF is adjusted to vary in the range of 15 GHz-33 GHz. Figure 8 shows the required OSNR to meet the 20% FEC threshold at different bandwidths of LPF, where Figs. 8(a) and (b) represent the BTB and 1000 km transmission scenarios, respectively. The parameters of the receiver are set to the optimal values obtained in section 3. It can be found that the performance of the offset DSB CADD system declines at an increased rate as the bandwidth decreases. However, the interleaved A-CADD with 5% frequency gap requires a 23 dB OSNR to reach the 20% FEC threshold. The proposed offset DSB CADD scheme has a higher sensitivity in terms of OSNR even when the CSPR is equal to 0 with a 15 GHz bandwidth of LPF.
Fig. 8. BER of different offset DSB CADD schemes versus bandwidth of LPF (a) at BTB; (b) after 1000 km transmission.
The type of PDs discussed in this paragraph is PIN and be modeled with responsivity of 0.7A/W, dark current of 3 × 10−9 A, and thermal noise of 10−11 A/Hz1/2, respectively. The contribution of shot noise to PD noise is also considered, but the effect of optical noise is not added for the time being. Figure 9 shows the receiver power sensitivity of the four offset DSB CADD schemes at BTB and after 1000 km transmission scenarios. For all cases, the sensitivity of CADD receivers can be sorted from the most to the least sensitive as follows: 50%-gap offset DSB S-CADD, 50%-gap offset DSB A-CADD, 50%-gap offset DSB PDD-S-CADD, 50%-gap offset DSB PDD-A-CADD. Specifically, 50%-gap offset DSB S-CADD can meet the 7% FEC threshold (BER = 3.8e-3) at received optical power (ROP) equal to -12.2 dBm. Compared with the 50%-gap offset DSB A-CADD/PDD-S-CADD/PDD-A-CADD scheme, it has a receiver power sensitivity improvement of about 0.5 dB/1.3 dB/2.4 dB. It should be noted that the 50% frequency gap offset DSB CADD can ignore the influence of SSBI, so the sensitivity difference of the four offset DSB CADD receivers mainly comes from the thermal noise of PDs [26].
Fig. 9. BER of different offset DSB CADD schemes versus ROP (a) at BTB; (b) after 1000 km transmission.
As far as we know, the interleaved A-CADD is more robust to the fiber nonlinearities possibly due to the larger subcarrier spacing which can suppress the four wave mixing (FWM) [32]. In order to test the fiber nonlinear tolerance of the offset DSB CADD scheme, the performance curve shown in Fig. 10 is given. The simulation's 1000 km SSMF is changed to a fiber loop and each fiber span in the loop has a length of 80 km. An erbium-doped fiber amplifier (EDFA) is added to each fiber span to compensate the loss in the link and the ASE noise is introduced. The nonlinear coefficient of the fiber is set to 1.3 W-1/km, and the noise figure of the EDFA is set to 6 dB. No fiber nonlinearity mitigation and compensation are implemented. Figure 10(a) shows the BER performance of the system at different launch powers after 400 km fiber transmission. When the launch power is equal to 6.5 dBm/8.2 dBm, the BER meets the 7%/20% FEC threshold. Figure 10(b) shows the BER versus transmission distance when the launch power is fixed at 6 dBm. It can be seen from the figure that BER still meets the 20% FEC threshold after a transmission distance of 800 km. Furthermore, the four offset DSB CADD systems have comparable tolerance to fiber nonlinearity.
Fig. 10. (a) BER of different offset DSB CADD schemes versus launch powers after 400 km transmission; (b) BER of different offset DSB CADD schemes versus transmission distances at launch power of 6 dBm.
In order to utilize as much low-frequency resource as possible and improve the SE of the system, we compress the frequency gap to reduce the total bandwidth required while keeping the signal bandwidth constant. Figure 11 shows the relationship between BER and frequency gap in different offset DSB CADD schemes, which simulation block diagram are shown in Fig. 4. Through in-depth analysis of the simulation results under CSPR set as 0 dB, we can make the following conclusions: (1) The frequency gap of the offset DSB PDD S-CADD can be compressed from 50% to 32.3% with 20% FEC threshold and 50% to 37.7% with 7% FEC threshold. At this time, the SE is improved by 22.7% and 17.3% at different FEC threshold, respectively, compared with the 5% frequency gap interleaved A-CADD. (2) When the BER of the system meets the 7% FEC threshold, the SE of offset DSB PDD S-CADD is improved by 1.7% and 7.6% compared with the offset DSB PDD A-CADD and the offset DSB A-CADD/S-CADD. (3) The BER of 1000 km fiber transmission is similar to that of BTB scenario, which proves the effectiveness of the offset DSB CADD schemes in recovering the phase information and CD compensation.
Fig. 11. BER versus gap with different offset DSB CADD schemes (a) at BTB; (b) after 1000 km transmission.
Figure 12 presents the level of the frequency gap compression for different CSPRs with 7% FEC threshold. The results show that the level of frequency gap compression is significantly improved as the CSPR increases. The compression advantage of the offset DSB PDD-S-CADD over offset DSB A-CADD increased from 7.6% to 10.55% as the CSPR increased from 0 dB to 6 dB. And the frequency gap is compressed by the offset DSB PDD-S-CADD system to 28.4% at 7% FEC threshold with the allowed maximum CSPR set as 6 dB. Under the condition of 6 dB CSPR, the frequency gap of the offset DSB PDD-S-CADD can still be compressed to 28.6% after 1000 km fiber transmission. Consequently, the SE of system is significantly improved and the problem of BW limitation is effectively mitigated. In addition, it can be observed that the CSPR curve of offset DSB A-CADD just coincides with that of offset DSB S-CADD. This implies that the effects of different CSPRs are the same when the transfer function is the same.
Fig. 12. Gap versus CSPR with different offset DSB CADD schemes (a) at BTB. (b) after 1000 km transmission. Note: Since the transfer functions of offset DSB A-CADD and offset DSB S-CADD receivers are the same, their curves (black and red lines) basically coincide.
5. Conclusion
In this paper, we have proposed and investigated the offset DSB A-CADD, offset DSB S-CADD, offset DSB PDD-A-CADD, and offset DSB PDD-S-CADD schemes for offset DSB signal transmission. The solution accommodates SSBI and solves the noise enhancement by inserting a frequency gap as wide as the signal bandwidth in the middle of the left and right sideband signal. Specifically, the optimal CSPR for the 5%-gap (55%SRP) interleaved A-CADD is only reduced to about 3 dB, and the proposed offset DSB CADD scheme successfully achieves field recovery at 0 dB CSPR with 50-gap (50%SRP). Additionally, we also effectively utilize as much low-frequency resource as possible and improve the SE of the system by compressing the frequency gap, which the maximum level of compression is 37.7% at 0 dB CSPR. Compared with 5%-gap (55%SRP) interleaved A-CADD, SE is improved by 17.3%. The BER of 1000 km fiber transmission is similar to that of BTB scenario, which proves the effectiveness of the offset DSB CADD schemes in recovering the phase information and CD compensation. Consequently, the offset DSB CADD schemes provide an efficient approach for field recovery at 0 dB CSPR, and their feasibility have been verified by theory and simulation. It is worth noting in order to analyze simple and easy to compare with the interleaved A-CADD, we only consider the 16-QAM and 25 Gbaud of the offset DSB CADD scheme, in fact, the proposed scheme could be applied to a variety of modulation formats and baud rate.
A. Appendix
A.1 Offset DSB A-CADD Receiver
The structure of the offset DSB A-CADD receiver is shown in Fig. 2 (a). To simplify the theoretical description, the optical signal entering the offset DSB CADD receiver is denoted by $[A + S(t)]{e^{j2\pi {f_c}t}}$, where S(t) is the offset DSB electrical signal. Then the optical signal is uniformly divided into two branches by the coupler. The upper branch is further divided into two branches after passing the optical delay τ1. After photodiodes (PD) detection, the detected three photocurrents are given as follows
The first term in Eq. (4) is the carrier-signal beating term, and the second term is the interference term SSBI. Taking the Fourier transform of Eq. (4), we obtain
A.2 Offset DSB S-CADD Receiver
The structure of offset DSB S-CADD receiver is relatively simple, as shown in Fig. 2(b), and its two detected photocurrents can be expressed as follows
The combination of the two photocurrents I1 and I2 yields a complex-valued signal R2(t)
The delay ${\tau _1}^\prime $ can be applied to the waveform R2(t) to get${R_2}(t - {\tau _1}^\prime )$, and then by subtracting the conjugation of ${R_2}(t - {\tau _1}^\prime )$ from R2(t) yields the following formula
Taking the Fourier transform of Eq. (9), the signal is recovered as follows
The transfer function of the offset DSB S-CADD receiver is $H(f) = 1 - {e^{ - j2\pi f2{\tau _1}^\prime }}$. Note that when the delay ${\tau _1}$ is set to twice${\tau _1}^\prime $, the offset DSB CADD and the offset DSB S-CADD have the same transfer function. Strictly, the signal S(t) should be expressed as ${S_L}(t){e^{j2\pi ( - {f_h})t}} + {S_R}(t){e^{j2\pi {f_h}t}}$, and therefore the SSBI in Eq. (10) can be written as
A.3 Offset DSB PDD-A-CADD Receiver
The difference between the offset DSB PDD-A-CADD receiver and the offset DSB A-CADD receiver is that an additional optical delay is employed. It is parallel to the original delay, as shown in Fig. 2(c). It should be noted that the value of the original delay ${\tau _1}$ is unchanged and it has been optimized in the offset DSB A-CADD receiver. Therefore, offset DSB PDD-A-CADD only needs to optimize delay ${\tau _2}$ to get the best system performance. Three photocurrents Y0, Y1, and Y2 are obtained through the receiver
The signal R3(t) can be obtained by linear combination of the three photocurrents
Taking the Fourier transform of Eq. (13), the signal is recovered as follows
The transfer function of the offset DSB PDD-A-CADD receiver is $H(f) = 1 - {e^{ - j2\pi f{\tau _1}}}/(1 + {e^{j2\pi {f_c}({\tau _1} - {\tau _2})}}) - {e^{ - j2\pi f{\tau _2}}}/(1 + {e^{j2\pi {f_c}({\tau _2} - {\tau _1})}})$. If the signal S(t) is replaced with a more strictly expression${S_L}(t){e^{j2\pi ( - {f_h})t}} + {S_R}(t){e^{j2\pi {f_h}t}}$, and then the SSBI in Eq. (14) is modified as
A.4 Offset DSB PDD-S-CADD Receiver
The structure of the offset DSB PDD-S-CADD receiver is shown in Fig. 2 (d), where delay ${\tau _1}^\prime $ is consistent with the delay in the offset DSB S-CADD receiver. After photoelectric conversion, two photocurrents can be obtained
In order to recover the optical field, we reconstruct a complex-valued signal R4(t) by using the two photocurrents ${Y_1}$ and ${Y_2}$
The parallel delays ${\tau _1}^\prime $ and ${\tau _2}^\prime $ are applied to the complex-valued signal ${R_4}(t)$respectively to obtain${R_4}(t - {\tau _1}^\prime )$,${R_4}(t - {\tau _2}^\prime )$, and then we can acquire R4'(t) as below
Taking the Fourier transform of Eq. (18), the signal is recovered as follows
The transfer function of the offset DSB S-CADD receiver is $H(f) =$$1 - \frac{{{e^{ - j2\pi f2{\tau _1}^\prime }} + ({e^{j2\pi {f_c}({\tau _1}^\prime - {\tau _2}^\prime )}} + {e^{j2\pi {f_c}({\tau _2}^\prime - {\tau _1}^\prime )}}){e^{ - j2\pi f({\tau _1}^\prime + {\tau _2}^\prime )}} + {e^{ - j2\pi f2{\tau _2}^\prime }}}}{{({e^{j2\pi {f_c}{\tau _1}^\prime }} + {e^{j2\pi {f_c}{\tau _2}^\prime }})({e^{ - j2\pi {f_c}{\tau _1}^\prime }} + {e^{ - j2\pi {f_c}{\tau _2}^\prime }})}}$. Strictly, the signal S(t) should be expressed as ${S_L}(t){e^{j2\pi ( - {f_h})t}} + {S_R}(t){e^{j2\pi {f_h}t}}$, the SSBI in Eq. (19) can be modified as
Funding
This research was supported by National Natural Science Foundation of China (61501213, 61671227); Natural Science Foundation of Shandong Province (ZR2020MF012 ZR2020QF005), and Doctorial Research Start-up Foundation of Liaocheng University (318051834, 318051835.
Acknowledgments
The authors would like to thank Prof. Weisheng Hu and Dr. Yixiao Zhu for their enthusiastic help, and they also would like to express their sincere thanks to the reviewers for their many helpful advice and suggestions.
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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