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Abstract
High-order quadrature amplitude modulation (QAM) can effectively improve the capacity and spectral efficiency of coherent optical transmission systems. However, as the modulation order increases, the signal becomes less tolerant to noise and nonlinear effects during transmission, and the implementation cost also increases. We propose a single carrier (SC) and orthogonal frequency division multiplexing (OFDM) hybrid coherent optical transmission scheme based on a 1-bit bandpass (BP) delta-sigma modulation (DSM). The driving I-channel and Q-channel signals for the optical in-phase/quadrature (I/Q) modulator carry SC-modulated and OFDM-modulated transmitter data, respectively. Optical quadrature-phase-shift-keying (QPSK) modulation is realized by the 1-bit DSM quantizer and I/Q modulator, which can effectively suppress quantization noise and reduce the complexity of digital signal processing (DSP) and the performance requirements of optoelectronic devices. In addition, the hybrid transmission of SC and OFDM can balance the advantages of both to meet the variable channel conditions and complex application scenarios. High-fidelity transmission of SC 512QAM and OFDM 512QAM hybrid signals, in the form of a 60 Gbaud optical QPSK signal, over 60 km single-mode fiber-28 (SMF-28) is verified by offline experiments, and the bit error rates (BERs) of both SC 512QAM and OFDM 512QAM are below the hard-decision forward-error correction (HD-FEC) threshold of 3.8e-3.
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1. Introduction
With the rapid development of modern information networks and the large-scale emergence of new Internet services, people’s demands for the capacity and speed of communication systems are increasing. As the cornerstone of information networks, the realization technology of optical communication with ultra-high-speed, large-capacity, and long-distance transmission has become the critical point to support the implementation of global information development strategy. Higher-order quadrature amplitude modulation (QAM) techniques significantly enhance the capacity and spectral efficiency of optical network transmission [1–4]. However, as the modulation order increases, the Euclidean distance between the signal constellation points decreases, making the signal sensitive to noise and nonlinear effects during transmission over the fiber optic link [5,6]. More sophisticated modulation and demodulation techniques and digital signal processing (DSP) algorithms are required to ensure accurate data transmission and reception. Introducing delta-sigma modulation (DSM) into optical transmission systems can achieve substantial quantization signal-to-noise ratio (SNR) gains, thereby ensuring stable transmission of high-order QAM signals in optical fibers [7–11]. Based on oversampling and noise shaping, DSM can shift a portion of the quantization noise out of the signal band. A 1-bit DSM can convert any high-order QAM signal into an on-off keying (OOK) signal [9–13]. The transmitter (TX) only needs to use a low-resolution digital-to-analog converter (DAC), significantly reducing the performance requirements for optoelectronic devices [9]. The two OOK signals are optically modulated by the I/Q modulator into a QPSK signal for transmission over the fiber optic link, resulting in higher noise tolerance and reception sensitivity and making the design and implementation of the coherent receiver (RX) relatively easy to reduce the cost of the hardware as well as the complexity of the DSP algorithms.
In our scheme, the DSM technique enables the driving I-channel and Q-channel signals for the optical in-phase/quadrature (I/Q) modulator to carry single-carrier-modulated (SC-modulated) and orthogonal-frequency-division-multiplexing-modulated (OFDM-modulated) transmitter data, respectively. The hybrid transmission system based on our scheme offers enhanced flexibility, allowing for dynamic adjustment of the transmission strategy based on actual application needs and channel conditions, thereby optimizing overall performance. The main disadvantage of OFDM is the high peak-to-average power ratio (PAPR) [14,15]. Compared to OFDM, SC has a lower PAPR. Thus, the hybrid transmission of SC and OFDM reduces the overall PAPR of the system to a certain extent, which helps to reduce the difficulty and cost of the design of the power amplifiers and improve their efficiency. Moreover, it can simplify the RX DSP, reducing the system complexity and cost. OFDM achieves efficient spectrum utilization through the orthogonal arrangement of subcarriers [14,15]. Consequently, the hybrid transmission can improve the spectral efficiency of the overall system. The chrominance dispersion (CD) in the fiber can be effectively mitigated by employing OFDM, which involves dividing the high-speed data stream into multiple lower-speed sub-data streams and utilizing narrower subcarrier bandwidths. This is particularly crucial for long-distance fiber optic communications. In addition, OFDM allows for the flexible allocation and adjustment of bandwidth and power for each subcarrier, adapting to different channel conditions and service requirements, which is especially beneficial in multi-user optical communication systems [16–20]. In short, the hybrid transmission combining SC and OFDM enhances the system’s adaptability, flexibility, and robustness, providing an efficient communication solution adaptable to varying channel conditions and diverse application needs and meeting the evolving demands of fiber optic communication networks and the growing need for data transmission.
In this paper, we propose an SC and OFDM hybrid transmission scheme based on 1-bit bandpass (BP) DSM and experimentally demonstrate the transmission of 60 Gbaud DSM signals over 0-60 km single-mode fiber-28 (SMF-28). The RX DSP only adopts low-complexity traditional algorithms, effectively addressing the issues of high quantization noise and nonlinear damage of high-order QAM signals in coherent optical transmission systems. Through this approach, we successfully achieve the bit error rates (BERs) below the hard-decision forward-error correction (HD-FEC) threshold of 3.8e-3 for both SC 512QAM and OFDM 512QAM signals.
2. Principle
The 1-bit BP DSM technique mainly consists of oversampling, noise shaping, and BP filtering, the principle of which is shown in Fig. 1(a). First, at the TX, the original signal is oversampled at a rate much higher than the Nyquist sampling rate, which can reduce the impact of quantization noise. This is because at a higher sampling rate, noise can be dispersed across a wider frequency band, thereby diluting the quantization noise. Then, the signal is digitally up-converted from a baseband one into a radio frequency one. The noise shaping technique is then used to move the quantization noise from the in-band area of the signal to the out-of-band area [21]. This is a crucial step for DSM to change the spectral distribution of quantization noise. Through noise shaping, the quantization noise within the signal bandwidth is significantly attenuated, and the signal part is well preserved. At the RX, the signal is converted to a baseband signal by down conversion, and then it is downsampled and low-pass filtered by a decimation filter to remove most of the quantization noise in the out-of-band region, thus significantly improving the SNR and signal quality.
As shown in Fig. 1(b), a first-order BP DSM transfer function is generally expressed as
where $Y(z )$ is the output signal, $X(z )$ is the input signal, $E(z )$ is the quantization noise, $STF(z )$ is the signal transfer function, and $NTF(z )$ is the quantization noise transfer function. $STF(z )$ and $NTF(z )$ can be expressed as ${z^{ - 2}}$ and $1 - {z^{ - 2}}$, respectively [22]. The amplitude of $STF(z )$ is close to 1. In contrast, the amplitude of $NTF(z )$ is close to 0, which can eliminate in-band noise without causing signal attenuation, thereby greatly enhancing the quantization SNR.3. Experimental setup
As shown in Fig. 2, an SC and OFDM hybrid transmission offline experimental system based on 1-bit DSM is set up to investigate the validity and performance of the proposed scheme, and the DSP process of TX and RX are indicated. In the TX DSP, two pseudo-random binary sequences (PRBSs), I and Q, are generated and mapped to QAM symbols. I is modulated with SC modulation, and the QAM mapping is followed by RC shaping filtering and ×2 upsampling. Then, the signal I is then oversampled by an interpolating filter. The oversampled data is up-converted and fed into a 1-bit BP DSM quantizer to be quantized as OOK signals. The signal Q needs to be OFDM modulated before the raised cosine (RC) filter, with a total of 256 subcarriers, and the number of effective subcarriers carrying data can be changed. For the OFDM modulation, the signal Q is first subjected to a serial-parallel transform to be split into multiple low-speed data streams, then the discrete Fourier transformation-spread (DFT-spread) is implemented for the effective data subcarriers to reduce the PAPR of the OFDM signal, and finally the 256-point inverse fast Fourier transformation (IFFT) for all 256 subcarriers and parallel-serial transform is performed in series. In addition, the oversampling rate of signal I and signal Q during the interpolating filtering operation is set to 10 in the off-line experiment. The symbol rates of SC 512QAM and OFDM 512QAM are 6 Gbaud. And the bit rates of SC 512QAM and OFDM 512QAM are 54 Gbps and Ns/256 × 54 Gbps, respectively, where Ns is the number of effective subcarriers. The two generated OOK signals are fed into an AWG with a sampling rate of 120 G Sa/s to output drive signals, which drive the I/Q modulator to achieve optical QPSK modulation. An external cavity laser (ECL) with a central wavelength of 1550 nm is used as the optical source. The dual-polarization I/Q modulator is used in the experiment, and only one polarization input is used, but the output is a dual-polarized light, in which only the X-polarized state carries information, and the Y-polarized state does not carry information. In the process of optical signal transmission in SMF-28, due to polarization crosstalk, the Y-polarized state will also carry information, so it is still necessary to perform polarization demultiplexing at the receiver. Then, after SMF-28 transmission, a variable optical attenuator (VOA) is set up at the front end of the RX to control the received optical power (ROP). The wavelength of the coherent RX’s ECL is set to coincide with that of the TX, and coherent reception is performed. After coherent reception, the four electrical signals are sampled by a digital storage oscilloscope (DSO) at a sampling rate of 256 GSa/s. The sampled digital signals are then sent to the RX DSP module for further processing. In the RX DSP, the received signals are first resampled for processing due to the different sampling rates of the AWG and DSO. Then, IQ imbalance compensation, CD compensation, constant modulus algorithm (CMA) equalization, and carrier recovery are performed sequentially to recover the QPSK signal, in which the carrier recovery is realized by the fourth-power fast-Fourier-transformation (FFT) frequency offset estimation algorithm and Viterbi and Viterbi phase estimation (VVPE) algorithm in series. After QPSK hard decision and demodulation, the I-channel and Q-channel are separated. The XI and YI signals modulated by SC are successively performed with down conversion, decimation filter, and QAM demapping to perform the final BER calculation. For the OFDM modulated signals XQ and YQ, OFDM demodulation is required before QAM demapping. For the OFDM demodulation, serial-parallel transform, 256-point fast Fourier transformation (FFT) for all subcarriers, inverse discrete Fourier transformation (IDFT) for the effective data subcarriers, and parallel-serial transform are performed sequentially. Since only one polarized state signal is modulated at the TX, only the BER of the X-polarized state is calculated. It needs to be clarified that in the experiment, the number of CMA taps is set from 33 to 63, which increases with the transmission distance. And the data length for the BERs calculation is 462080.
4. Experimental results and discussions
Figure 3 shows the noise transfer function curves of BP DSM at different up-conversion frequencies of 21 GHz, 27 GHz, 30 GHz, 33 GHz, and 39 GHz, respectively. The up-conversion frequencies are normalized based on the AWG sampling frequency in Fig. 3. The maximum quantization SNR can be obtained when the up-conversion frequency is 30 GHz, which is 1/4 of the AWG sampling frequency at 120 GHz. This is because the quantization noise is distributed in the bandwidth range of 0 GHz to 60 GHz, and the up-conversion frequency of 30 GHz is in the center of this band, which makes the BP DSM move quantization noise out of the signal bandwidth uniformly to both sides, resulting in better noise shaping. The BER performance of the SC and OFDM hybrid transmission scheme at different up-conversion frequencies is measured to further explore the impact of the up-conversion frequency on system performance.
Fig. 3. Noise transfer function curves of BP DSM @ up-conversion frequency: (a) 21 GHz, (b) 27 GHz, (c) 30 GHz, (d) 33 GHz, (e) 39 GHz.
Figure 4(a) shows the BERs of QPSK, SC, and OFDM versus the up-conversion frequency under BTB conditions, and the red dashed line in the figure indicates the HD-FEC threshold of 3.8e-3. Both SC and OFDM are modulated with 512QAM, and the number of effective subcarriers of OFDM is 162. The result shows that the up-conversion frequency has a minimal impact on the BER of the QPSK signal, and the BER performance of QPSK is transparent to the SC and OFDM signals. However, the best BER performance for SC and OFDM is achieved at an up-conversion frequency of 30 GHz. It should be noted that at the 30 GHz up-conversion frequency, the OFDM does not exhibit any errors within a limited number of symbols. Then, the modulation format of the OFDM is changed to 1024QAM, and the up-conversion frequency of the SC 512QAM signal is fixed at 30 GHz to explore the relationship between the BER and the up-conversion frequency of the OFDM. As shown in Fig. 4(b), the BER performance of the OFDM is best at an up-conversion frequency of 30 GHz. Merely changing the up-conversion frequency of the OFDM does not affect the BER performance of the SC, indicating that SC and OFDM are independent and do not interfere with each other.
Fig. 4. (a) BERs of QPSK, SC 512QAM, and OFDM 512QAM versus (VS) up-conversion frequency, (b) BERs of SC 512QAM and OFDM 1024QAM VS up-conversion frequency.
Figure 5(a) shows the BERs versus the ROP for the SC 512QAM and OFDM 512QAM hybrid transmission schemes with 256 effective subcarriers in the scenarios of BTB, and the up-conversion frequency is fixed at 30 GHz. As the ROP increases, the BER of QPSK gradually decreases. For SC and OFDM, the BERs noticeably decline within the ROP range of −32 to −28dBm and become stable in the −26 to −24dBm range, reaching an error floor. This is due to the BP DSM’s inability to completely eliminate in-band quantization noise, especially for high-order QAM. The residual in-band quantization noise is a major factor limiting the performance of SC 512QAM and OFDM 512QAM, which no longer improve as the QPSK BER decreases. When the SC and OFDM use the same modulation format, and OFDM has 256 effective subcarriers, both BERs are similar under the same ROP. Figure 5(b) demonstrates the BERs versus the ROP for OFDM with different numbers of effective subcarriers in the BTB scenarios, and both SC and OFDM are modulated with 512QAM. The results show that in the ROP range of −32 to −28dBm, increasing the number of effective subcarriers does not significantly increase the BER, indicating that ROP is the main factor limiting system performance in this range. When the ROP exceeds −28dBm, as the number of effective subcarriers increases, the performance of OFDM 512QAM gradually deteriorates. With 256 effective subcarriers in OFDM, the BER can still be below the HD-FEC threshold. To further investigate the impact of QAM order on the BER performance of OFDM, SC is modulated with 512QAM, and the number of effective subcarriers for OFDM is fixed at 256. Under BTB conditions, the BERs of OFDM versus the ROP are plotted for different modulation orders of OFDM. As shown in Fig. 5(c), the higher the modulation order of OFDM, the worse the BER performance. When the QAM order is less than 1024, the BER of OFDM can reach the HD-FEC threshold.
Fig. 5. (a) BERs of QPSK, SC 512QAM, and OFDM 512QAM with 256 effective subcarriers VS ROP, (b) BERs of OFDM 512QAM with different numbers of effective subcarriers VS ROP, (c) BERs of OFDM with different modulation orders VS ROP.
Figure 6 shows the BERs versus ROP for SC 512QAM and OFDM 512QAM signals with 256 effective subcarriers at different transmission distances. The results indicate that within the ROP range of −26 to −24 dBm, SC 512QAM and OFDM 512QAM maintain a BER below the HD-FEC threshold for BTB and 20/40/60 km SMF-28 transmission. Furthermore, as the ROP rises, the BER of QPSK gradually decreases close to 0, and the effect of transmission distance on system performance is no longer obvious. Therefore, the BERs of SC 512QAM and OFDM 512QAM at different transmission distances are quite similar when the ROP is −24 dBm. In addition, the insets in Fig. 7(a) and Fig. 7(b) respectively show the recovered constellation diagrams of SC 512QAM and OFDM 512QAM after 60 km SMF-28 transmission at the ROP of −24 dBm.
Fig. 6. (a) BERs of SC 512QAM at different transmission distances VS ROP, (b) BERs of OFDM 512QAM at different transmission distances VS ROP.
5. Conclusion
In this paper, an SC and OFDM hybrid scheme based on 1-bit BP DSM for the coherent optical transmission system is proposed. The I-channel and Q-channel signals are modulated by SC and OFDM, respectively. The scheme achieves high-fidelity transmission of high-order QAM signals in the optical fiber link based on the significant quantization SNR gain provided by BP DSM. Offline experimental results show that SC 512QAM and OFDM 512QAM with 256 effective subcarriers can achieve 60 km transmission over SMF-28, and the BERs are lower than the HD-FEC threshold of 3.8e-3. Additionally, the SC and OFDM signals are independent of each other, and the BER performance of QPSK is transparent to both SC and OFDM signals. In summary, the proposed scheme effectively reduces hardware implementation costs and DSP complexity. Combining the advantages of SC and OFDM further enhances the system’s adaptability, flexibility, and robustness, providing an efficient solution for fiber optic communication networks.
Funding
National Key Research and Development Program of China (2023YFB2806100); National Natural Science Fund for Excellent Young Scientists Fund Program (Overseas) (3050013532305); National Natural Science Foundation of China (62305026).
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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