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Abstract
For high-capacity and short-reach applications, carrier-assisted differential detection (CADD) has been proposed, in which the optical field of a complex-valued double sideband (DSB) signal is reconstructed without using a sharp-edge optical bandpass filter or local oscillator laser. The CADD receiver features a transfer function with periodical nulls in the frequency domain, while the signal-signal beat interference (SSBI) is severely amplified around the frequency nulls of the transfer function. Since the null magnitude at the zero frequency is inevitable, a guard band is required between the carrier and the signal, leading to a higher receiver bandwidth and implementation cost. To reduce the needed guard band, we propose a parallel dual delay-based CADD (PDD-CADD), in which an additional delay is placed parallel to the original delay in the conventional CADD. By this means, the modified transfer function has a sharper roll-off edge around the zero frequency. Consequently, the requirement on the guard band can be relaxed, which maximizes the bandwidth utilization of the system. The parallel delay is first optimized through numerical simulation. We then perform a proof-of-concept experiment to transmit a 100-Gb/s orthogonal frequency division multiplexing (OFDM) 16-ary quadrature amplitude modulation (16-QAM) signal over an 80-km single-mode fiber (SMF). After the fiber transmission, the proposed PDD-CADD can reduce the required guard band from 3 to about 1.2 GHz compared with the single delay-based conventional CADD. To our best knowledge, for the direct detection of a single polarization complex-valued DSB signal without using a sharp-roll-off optical filter, we achieve a record electrical spectral efficiency of 5.9 b/s/Hz.
© 2021 Optical Society of America under the terms of the OSA Open Access Publishing Agreement
1. Introduction
The explosive internet traffic growth in data centers and metro networks has driven the increasing demands on high-capacity optical transmission systems while maintaining the low implementation cost. Compared with intensity modulation/direct detection (IM/DD) [1–4], single-sideband self-coherent detection (SSB-SCD) [5–13], and coherent detection [14–16], DD of complex-valued double-sideband (DSB) signal is a more promising scheme for high capacity and low-cost transmission since the optical field of a complex-valued DSB signal can be recovered without using narrow-linewidth local oscillator (LO) laser. In [17], a dual-SSB modulation scheme was put forward to detect a complex-valued DSB signal, but at the expense of optical bandpass filters (OBPFs) with sharp edges; thus it requires a high-wavelength-stability laser source. In [18], Gerchberg-Saxton (GS) algorithm is applied to retrieve the optical field by detecting signal-signal beat interference (SSBI), which demands a receiver bandwidth equivalent to the baud rate while the coherent detection only requires the bandwidth of half baud rate. Moreover, the GS algorithm commonly requires hundreds of iterations to converge. To overcome these problems, a promising scheme called carrier-assisted differential detection (CADD) is recently proposed in [19]. Through the combination of three output photocurrents from the CADD receiver, the optical field of the complex-valued DSB signal can be retrieved without using a sharp-slope OBPF, and the required receiver bandwidth approaches half of the baud rate analogous to coherent detection. In [20], the CADD receiver is experimentally demonstrated. To further simplify the structure of the CADD receiver, a symmetric scheme without using the single-ended PD branch is proposed and numerically studied in [21]. In [22], the concept of the CADD is extended to a general selection of the transfer functions beyond the originally proposed delay interferometer-based CADD, and the performance is extensively investigated through numerical simulations. In [23], a subcarrier interleaved CADD receiver without the distortion of SSBI is demonstrated, whereas the electrical spectral efficiency (ESE) is halved due to the interleaved subcarrier loading.
The key characteristic of the CADD is the unique transfer function, which is only determined by the optical delay. To recover the complex-valued DSB signal, the transfer function is applied to the reconstructed signal and SSBI simultaneously. As a result, the spectrum of SSBI is reshaped by the transfer function. The SSBI in the frequency domain is suppressed when the magnitude of the transfer function is greater than 1, while it is dramatically amplified in the frequency region around the zero-magnitude frequencies of the transfer function. Hence, the delay value is deliberately selected to put the signal in the SSBI-suppression region. However, since the transfer function of the CADD is equivalent to that of a delay interferometer, the null point at zero frequency is inevitable. Thus, the SSBI is severely enhanced in the low-frequency region, which requires a guard band between the carrier and the signal. As such, a larger guard band demands a higher receiver bandwidth and implementation cost. A larger delay contributes to a reduced guard band, due to the sharp frequency response around the null points of the transfer function. However, as the delay increases, the 2nd null point moves closer to the zero frequency, limiting the available electrical bandwidth for transmission and the achievable capacity.
In this paper, we demonstrate that the required guard band in CADD can be reduced without sacrificing the available receiver electrical bandwidth by using our proposed parallel dual delay-based CADD (PDD-CADD), where an additional delay is placed parallel to the original delay in the conventional CADD receiver. In the PDD-CADD receiver, the transfer function has a sharper slope around the zero frequency, resulting in a narrower SSBI-enhanced frequency region. Meanwhile, the 2nd null point of the transfer function remains unchanged. Thus, the requirement on the guard band can be relaxed, without sacrificing the available electrical bandwidth. We first conduct numerical simulations to optimize the parallel delay value in the PDD-CADD receiver. Furthermore, a proof-of-concept experiment is performed to transmit a 100-Gb/s orthogonal frequency division multiplexing (OFDM) 16-ary quadrature amplitude modulation (16-QAM) signal over an 80-km single-mode fiber (SMF). Experimental results show that compared with the conventional CADD, the proposed PDD-CADD can reduce the required guard band by 60%, from 3 to about 1.2 GHz, under the 7% hard-decision forward error correction (HD-FEC) threshold of 3.8×10–3 in the transmission case. The PDD-CADD scheme enables a record ESE of 5.9 b/s/Hz for DD of single polarization complex-valued DSB signal without using a sharp-slope optical filter, to the best of our knowledge.
The rest of this paper is organized as follows. In Section II, the principle and the structure of the conventional CADD and the PDD-CADD are introduced. Section III describes the experimental setup and digital signal processing (DSP) algorithms. Section IV presents the experimental results and discussion. Finally, conclusions are drawn in Section V.
2. Principle of conventional CADD and PDD-CADD receivers
Figure 1(a) illustrates the structure of the conventional CADD receiver. We denote the received carrier-assisted signal as C + S, where C and S are the carrier and the complex-valued DSB signal, respectively. Correspondingly, the signal after an optical delay of τ is C + Sτ, where the additional common phase is neglected here for simplicity. In the conventional CADD receiver, one branch of the delayed signal is detected using a single-ended PD, while the other together with the received signal are input to a 90° optical hybrid followed by two BPDs. Considering the splitting ratio of the couplers and the hybrid, the detected three photocurrents can be expressed as:
Fig. 1. Structures of (a) the conventional CADD receiver, and (b) the proposed PDD-CADD receiver, respectively.
The reconstructed signal R consists of the carrier-signal beating term C · (S – Sτ) and the SSBI distortion S · Sτ* – |Sτ|2. We can obtain the desired linear term as:
Taking the Fourier transform of (3), the signal is recovered as follows: Here, Sf is the Fourier transform of S, and F{·} stands for Fourier transform. The transfer function of the conventional CADD receiver is HCADD = 1 – e–j2πfτ, which is a delay interferometer in essence.In the PDD-CADD, an additional optical delay is employed, which is placed parallel to the single delay in the conventional CADD receiver as shown in Fig. 1(b). The detected three photocurrents are given as:
Figure 2 plots the magnitude of the transfer functions for CADD and proposed PDD-CADD receivers. According to (4) and (8), the SSBI is reshaped by the transfer function: when the magnitude of the transfer function is greater than 1, SSBI is suppressed, otherwise it is enhanced. In particular, the SSBI is severely amplified at the magnitude zeros of the transfer function, e.g., at 0 GHz, ${\pm} $16.7 GHz, in the 60-ps CADD receiver, as shown in Fig. 2. Due to the inherent null point at 0 GHz of the transfer function, the SSBI enhancement is inevitable in the low-frequency region. Thus, a guard band is inserted between the carrier and the signal, which requires higher receiver bandwidth and implementation cost. As shown in Fig. 2, in the conventional CADD receiver, a larger optical delay contributes to a narrower required guard band. For example, by increasing the delay from 60 ps to 120 ps, the roll-off around zero frequency of the transfer function becomes sharper, thus a narrower guard band is sufficient to fit the signal in the SSBI-suppressed region. However, it can be observed that the 2nd null point frequency of the transfer function is halved simultaneously, which greatly limits the available passband for transmission systems. In this sense, the guard band is reduced but at the expense of a limited data rate. To relax the requirement on the guard band without sacrificing the achievable capacity, we propose the PDD-CADD receiver, in which an additional delay is placed parallel to the original delay. The structure and the transfer function of the PDD-CADD are presented in Fig. 1(b) and Fig. 2, respectively. The value of τ2 is set to 120 ps as an example. As shown in Fig. 2, compared with the conventional CADD with 60-ps delay, the transfer function of the PDD-CADD with 60-ps and 120-ps parallel delays has a sharper slope around the zero frequency. Meanwhile, the magnitude null at 8.3 GHz is eliminated compared to the 120-ps CADD. As such, the required guard band is reduced without sacrificing the available electrical bandwidth. Note that by loading data in another SSBI-suppressed frequency region, such as from 18.5 GHz to 31.3 GHz, the symbol rate and the capacity of the system can be increased. In addition, we can observe from Fig. 2 that the SSBI can be greatly suppressed in a few-GHz region for the conventional CADD receiver, compared to the PDD-CADD receiver. Thus, if entropy loading is applied by transmitting high-order modulation formats in this region, the conventional CADD receiver is expected to achieve a higher capacity than the PDD-CADD receiver with the same bandwidth. However, a thorough comparison should be made, which is beyond the scope of this work.
We numerically investigate the optimization of the parallel delay in the PDD-CADD receiver for detecting a 25-Gbaud OFDM 16-QAM signal. According to the optimized simulation results in [19], we set the carrier-to-signal power ratio (CSPR) to 8 dB and τ1 to 60 ps. Figure 3(a) presents the bit error ratio (BER) versus the value of the parallel delay τ2 under different guard bands. In this paper, the guard band is defined as the gap between the upper and lower sideband of the DSB signal. For example, the 1-GHz guard band indicates the frequency region of the gap is from –0.5 GHz to 0.5 GHz, thus the 25-GBaud 16-QAM signal occupies the bandwidths of [–13 GHz, –0.5 GHz] and [0.5 GHz, 13 GHz]. Since we aim to reduce the required guard band in the conventional CADD receiver, small guard band values are chosen in the optimization. As shown, 120-ps achieves the best BER performance among various guard band values, thus is used in the experiments. Moreover, the tolerance of the parallel delay τ1 with a 120-ps τ2 is depicted in Fig. 3(b).
3. Experimental setup and DSP algorithms
A proof-of-concept experiment is performed to detect the complex-valued DSB signal using the proposed PDD-CADD receiver. Figure 4(a) depicts the experimental setup. A 25-GBaud OFDM 16-QAM signal is generated from a 64-GSa/s arbitrary waveform generator (AWG) (Keysight M8195A). After being amplified by two electrical amplifiers (EAs), the generated signal drives a 22-GHz IQ modulator (IQM) with a null-point bias condition. A continuous-wave (CW) light from a 15-kHz-linewidth external cavity laser (ECL) is split into two paths. One branch is injected into the IQM, while the other serves as the optical carrier. After E/O conversion, the optical OFDM 16-QAM signal is combined with the optical carrier to form a complex-valued DSB signal. The CSPR is varied by adjusting a variable optical attenuator (VOA), and the polarization states between the two paths are carefully aligned up using polarization controllers (PCs). Figure 4(b) illustrates the optical spectrum of the generated 25-GBaud OFDM 16-QAM signal with a 2-GHz guard band, measured by an optical spectral analyzer (OSA) (APEX AP2040C) with a 1.12-pm resolution. As shown, the high-frequency attenuation in the spectrum is compensated by implementing pre-emphasis in the transmitter DSP. After being amplified to the optimum 6-dBm optical power by an erbium-doped fiber amplifier (EDFA), the complex-valued DSB signal is launched into an 80-km SMF. At the receiver side, the signal is boosted using another EDFA and then detected by a conventional CADD or a PDD-CADD. For the conventional CADD, the dual parallel delays are replaced with a single delay. A 90° optical hybrid is employed for differential detection, and the polarization states of the input signals are aligned by means of PCs. The optical signals are detected using three matched 43-GHz BPDs, one of which is used as a single PD. Then, the detected photocurrents are captured by a digital storage oscilloscope (DSO) (LeCroy 36Zi-A) operated at a sampling rate of 80 GSa/s.
Fig. 4. (a) Experimental setup. (b) Optical spectrum of the generated 25-GBaud 16-QAM signal with 2-GHz guard band.
Figure 5 presents the transceiver DSP algorithms. In the transmitter, the binary data is mapped to 16-QAM symbols and the synchronization and training sequences are added. The channel response is estimated using interleaved training sequence. Then, the signal is OFDM-modulated with a fast Fourier transform (IFFT) size of 4096, in which 2048 subcarriers are filled with 16-QAM symbols, and a 128-point cyclic prefix (CP) is employed. Pre-emphasis is implemented to compensate for the imperfect frequency response of the transmitter-side components. After being resampled to 64-GSa/s, the signals are clipped and sent to the AWG. At the receiver side, the signals are resampled to a sampling rate of 160 GSa/s and then synchronized. After amplitude normalization, equalization and SSBI cancellation are implemented to reconstruct the transmitted signal, followed by the symbol decision and BER calculation. The net data rate is 77.9 Gb/s considering the frame redundancy and 7% FEC overhead.
4. Experimental results and discussion
Figure 6 shows the BER versus guard band with different receiver structures in the optical back-to-back (OBTB) case. The optical delay is set to 60 ps in the conventional CADD. For the PDD-CADD, an additional 120-ps delay is placed parallel to the 60-ps delay. Due to the magnitude null point of the transfer function at zero frequency, SSBI is dramatically enhanced in the low-frequency region. Hence, a larger guard band contributes to a lower BER. It can be observed that when the guard band is increased from 1 to 5 GHz, the BER decreases by more than one order of magnitude. Meanwhile, it is anticipated that an excessive guard band results in a higher BER since the 2nd null point is moved into the signal spectrum. By using PDD-CADD, the required guard band to reach the 7% HD-FEC threshold is reduced from 2 to 1 GHz, relative to the conventional CADD, as shown in Fig. 6. The recovered constellations at the 2-GHz guard band with conventional CADD and PDD-CADD are depicted in the insets (i) and (ii), respectively.
Fig. 6. BER versus guard band with different receiver structures in the OBTB case. Insets (i) and (ii) are the recovered constellations at the 2-GHz guard band with conventional CADD and PDD-CADD, respectively.
In the transmission case, we first optimize the CSPR. The CSPR is defined as the ratio between the carrier power and the aggregates power of the upper and lower sidebands. Various CSPR values are obtained by adjusting the VOA in the carrier branch at the transmitter side. We calculate the CSPR by measuring the power of the signal and the carrier after the IQM and VOA, respectively. A high CSPR is normally preferred for a lower SSBI, whereas the effective signal power is sacrificed. As shown in Fig. 7(a), the CSPR of 14 dB provides the best performance and is used in the following measurements. The relatively high optimal CSPR is due to a large optical signal-to-noise ratio (OSNR) value of 41 dB in the experiment. For the large OSNR value, the major impairment in the system is SSBI distortion rather than noise. In this case, a high CSPR is required to suppress the SSBI. To reduce the CSPR, one can employ more effective SSBI cancellation algorithms, which will be studied in future work. Besides, the symmetric CADD scheme has been proved to be able to achieve lower optimal CSPR than the conventional asymmetric structure [21]. Figure 7(b) presents the BER versus iteration number of the SSBI cancellation algorithm at the 3-GHz guard band, with the PDD-CADD receiver. Due to the high CSPR value, the SSBI distortion to the desired signal is relatively small, thus only one iteration brings the performance improvement.
Fig. 7. (a) BER as a function of CSPR at the 3-GHz guard band. (b) BER as a function of iteration number of the SSBI cancellation algorithm at the 3-GHz guard band, with the proposed PDD-CADD receiver.
The BER versus guard band with different receiver structures after the 80-km transmission is plotted in Fig. 8, with the recovered constellations at the 3-GHz guard band using conventional CADD and PDD-CADD depicted in the insets (i) and (ii), respectively. After the 80-km transmission, the required guard band can be reduced from 3 to about 1.2 GHz by using PDD-CADD, considering the 7% HD-FEC threshold 3.8×10–3. In the transmission case, the system suffers Kerr nonlinearity, and the chromatic dispersion induces a higher peak-to-average power ratio (PAPR), increasing the quantization noise of the analog-to-digital converter (ADC). After the transfer function is applied, the quantization noise is dramatically enhanced in the low-frequency region of the reconstructed signal, which is the same as the SSBI. Since the received signal suffers more ADC quantization noise after the fiber transmission, the impairments in the low-frequency region become more severe for the reconstructed signal. Thus, the required guard bands to reach the threshold for both schemes are increased compared with that in the OBTB case.
Fig. 8. BER versus guard band with different receiver structures after the 80-km transmission. Insets (i) and (ii) are the recovered constellations at the 3-GHz guard band with conventional CADD and PDD-CADD, respectively.
Table 1 compares the ESE of our work with other DD systems of recovering complex-valued DSB signals. All the results in the table are based on the experimental demonstrations. As evidenced by the table, without using a sharp-roll-off optical filter, we achieve the highest ESE for DD of complex-valued DSB signal. Note that the dual-SSB scheme enables higher ESE by means of optical filter with a sharp slope, whereas it requires stable laser source thus increases the power consumption for wavelength stabilization.
Table 1. ESE Comparison of Complex-Valued DSB Signal DD Systems
5. Conclusion
In conclusion, we have proposed and demonstrated a PDD-CADD receiver to reduce the required guard band in the conventional CADD receiver. In the PDD-CADD receiver, an additional delay is placed in parallel to the single delay in the conventional CADD receiver. By this means, the transfer function has a sharper roll-off in low-frequency region, while the 2nd null frequency remains unchanged. Thus, the requirement on the guard band can be relaxed without sacrificing the available electrical bandwidth. The value of the additional delay is optimized by numerical simulations. In the experiment, a 100-Gb/s complex-valued DSB OFDM 16-QAM signal is transmitted over an 80-km SMF. By using PDD-CADD, the required guard band to reach the BER below the 7% HD-FEC threshold of 3.8×10–3 can be decreased from 2 to 1 GHz in the OBTB case, and from 3 to about 1.2 GHz after the fiber transmission. For the DD of single polarization complex-valued DSB signal without using a sharp-passband-edge OBPF, we achieve a record ESE of 5.9 b/s/Hz, to the best of our knowledge.
Funding
National Key Research and Development Program of China (2019YFB1803602); National Natural Science Foundation of China (61835008, 61860206001).
Disclosures
The authors declare no conflict 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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