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Abstract
The six-generation mobile network (6G) based on millimeter-wave (mmWave) is expected to deliver more capacity and higher connection density compared with 5G. We demonstrate an ultra-dense wavelength division multiplexing (UDWDM) fiber-mmWave integration network based on non-orthogonal multiband carrier less amplitude and phase (NM-CAP) modulation to address the needs for dense access cells, high-spectral efficiency, and high data rate. We demonstrate a neural-network-based waveform to symbol converter (NNWSC), which can directly convert the received NM-CAP waveform into quadrature amplitude modulation (QAM) symbols to simultaneously handle the inter-symbol interference (ISI) and inter-channel interference (ICI), without the need for conventional matched filters and additional ISI and ICI equalizers. Experimental results show that this method is also effective for QAM constellations with probabilistic shaping. Since NNWSC simplifies the demodulation process of NM-CAP and avoids error accumulation caused by cascading filters and post-equalizers, NNWSC can reduce the computational complexity and provide good performance. Compared with the regular receiver with cascaded least mean square equalizer, matched filters, and ICI equalizer, NNWSC can reduce the computational complexity by 93%. The demonstrated spectrally efficient fiber-mmWave transmission is achieved at a total 414-Gbps net data rate with 24 PS-QAM NM-CAP sub-bands on 8 UDWDM channels with 25-GHz spacing.
© 2022 Optica Publishing Group under the terms of the Optica Open Access Publishing Agreement
1. Introduction
As emerging applications such as extended reality (XR) services (encompassing augmented, mixed, and virtual reality (AR/MR/VR)) increase, 5G will hardly be able to meet the demand for high-capacity wireless communications in the future [1]. The six-generation mobile network (6G) is expected to deliver 1000x times more capacity and 100x times higher connection density compared with 5G [2]. To achieve the capacity of up to 1 Tb/s, 6G radio-access-network (RAN) will revolutionize the spectrum to higher frequencies and broader bands (e.g., 73 GHz-140 GHz and 1 THz-3 THz) [3,4]. One of the key enablers for the stringent requirements in 6G RAN is the fiber-millimeter-wave integration network (FMWIN) [5]. Since the electrical signals modulated onto the millimeter-wave (mmWave) carrier are detected by a photodetector, FMWIN does not require any high-speed and high-complexity analog-to-digital converter (ADCs) or digital-to-analog converters (DACs). In this way, FMWIN simplifies antenna structures of remote radio units (RRUs) to enable high-speed, low-complexity transmission in 6G radio access networks (RANs) [6,7].
To achieve massive access in FMWIN, two of the key enablers are ultra-dense wavelength division multiplexing (UDWDM) and frequency division multiplexing (FDM), which provide wavelength-to-the-user and sub-band-to-the-user access, respectively [8–11]. One challenge with UDWDM is the susceptibility to crosstalk between adjacent wavelengths. As a spectrally efficient multiband modulation format, non-orthogonal multiband carrierless amplitude and phase (NM-CAP) can compress the total bandwidth to mitigate crosstalk between adjacent wavelengths [12,13]. The overall network architecture of NM-CAP based UDWDM FMWIN is shown in Fig. 1. Each wavelength (λ) is capable of transmitting multiple sub-bands. Each wavelength corresponds to one RRU and different sub-bands are allocated for different users. In practice, wavelengths and sub-bands can be assigned to users according to their specific requirements. Due to the bandwidth limitation of the mmWave system and the inter-wavelength crosstalk in UDWDM systems, non-orthogonal waveform, i.e., NM-CAP, will be very beneficial to spectrally efficient transmissions. However, both inter-symbol-interference (ISI) and inter-channel-interference (ICI) exist in the NM-CAP system. Therefore, advanced digital signal processing (DSP) algorithms are required to deal with the ISI and ICI [14–16]. In addition, considering the signal-to-noise ratio (SNR) which varies from sub-band to sub-band in a practical system, the maximum transmitted data rates of every sub-band are different. To enable the adaptive data rate of every sub-band closer to its channel capacity, constellation probabilistic shaping (PS) technology can be utilized separately for each sub-band [17,18].
Due to the overlap between adjacent sub-bands caused by compressing the bandwidth, significant ICI will be introduced if conventional matched filters are used to demodulate the received NM-CAP waveform. A complex independent component analysis (ICA) algorithm based on subcarrier component extraction (SCE) proposed by Wang et al. is used to cancel ICI [15,16]. However, there are three major limitations of the SCE-ICA ICI equalizer. The first is the high computational complexity. The second is the error accumulation effect. SCE algorithm is based on conventional matched filters. If there is ISI in the received signal caused by bandwidth limitations or multipath effects etc., an ISI equalizer should be used before matched filters and the SCE-ICA ICI equalizer. Cascading matched filters, ISI equalizer and ICI equalizer not only increases the computational complexity, but also makes the errors accumulate, thus reducing the system performance. The third is that the sources to be separated by ICA cannot all obey Gaussian distribution [19]. The probability distribution of high-order PS quadrature amplitude modulation (QAM) symbols is relatively close to Gaussian distribution, which makes it difficult for SCE-ICA to separate subcarrier components. Recently neural networks (NNs) have been applied in communication systems. Ye et al. demonstrated NNs for channel estimation and signal detection in orthogonal frequency division multiplexing (OFDM) systems [20]. The demonstrated NNs directly recover the transmitted symbols without estimating channel state information (CSI) explicitly. In [21], Xu et al. utilized NNs for interference cancellation in optical communication systems based on non-orthogonal spectrally efficient frequency division multiplexing (SEFDM) of multi-carrier signals. This work demonstrated the potential of NNs in non-orthogonal multi-carrier signal detection, however, only simulation results were presented. In [22], deep learning is used to blindly classify multi-carrier signals including their orthogonal and non-orthogonal varieties in the experimental systems both in line-of-sight and nonline-of-sight communication link scenarios.
In this paper, we demonstrate a UDWDM fiber-mmWave integration network based on non-orthogonal PS-QAM modulated multiband CAP to address the needs for 6G RAN dense access cells, high-spectral efficiency and high data rate. We demonstrate a neural-network-based waveform to symbol converter (NNWSC), which can directly convert the received NM-CAP waveform into PS-QAM symbols, without the need for conventional matched filters, additional ISI equalizers like the least mean square (LMS) equalizer and ICI equalizers like the SCE-ICA equalizer. Noting that NNWSC cancels the ISI and ICI simultaneously, it simplifies the demodulation process and provides much better performances. This paper is the extension of our previous OFC 2022 paper [14], in which 16QAM-based NM-CAP signals are successfully demonstrated based on the NNWSC. We extend the study and further investigate the performance under PS-QAMs with higher modulation formats and improved capacity. Finally, a spectrally efficient fiber-mmWave transmission is achieved at a total 414-Gbps net data rate with 24 PS-QAM NM-CAP sub-bands on 8 UDWDM channels with 25-GHz spacing based on the proposed method.
2. Principles
2.1 Principle of NNWSC based NM-CAP
The principle of the proposed NNWSC based NM-CAP is shown in Fig. 2. At the transmitter, the transmitted data after distribution matching (DM) and forward error correction (FEC) encoding is mapped into QAM symbols. The QAM symbols are then upsampled. The upsampling number should be large enough to ensure that there is no aliasing of the spectrum. Then the upsampled signals are separated into the in-phase (I) parts and the quadrature (Q) parts. The I/Q signals are filtered by pulse shaping filters (PSFs) and all added up as the transmitted digital signal. The I/Q PSFs of the nth sub-band are expressed as
where $g(t)$ is square root raised cosine (SRRC) filter, and ${\upsilon _n}$ is the center frequency of the nth sub-band. ${\upsilon _n}$ is represented as where $\alpha$ is the roll-off factor of the SRRC filter, $\beta$ is the sub-band spacing factor, and ${R_s}$ is the baud rate of every sub-band. When $\beta \ge 1$, all sub-bands are orthogonal and there are no overlaps between adjacent sub-bands; when $\beta < 1$, overlaps occur and sub-bands become non-orthogonal [12–13,15]. It’s noted that when $\beta < 0$, the sub-band frequency spacing is lower than ${R_s}$, so it becomes harder to mitigate the ICI caused by the overlap of adjacent sub-bands. The total bandwidth is where N is the number of sub-bands. If the I/Q signals of the nth sub-band are denoted as $s_I^n(t)$ and $s_Q^n(t)$, respectively, where t is the discrete time, then the transmitted digital signal is expressed asAt the receiver, the traditional multiband CAP receiver require an ISI equalizer operated on the received waveform and matched filters corresponding to each sub-band. For NM-CAP, an ICI equalizer like SCE-ICA is required. The cascade of matched filters, ISI equalizer and ICI equalizer not only increases the computational complexity, but also leads to error accumulation. NNWSC directly the received NM-CAP waveform into QAM symbols, mitigating ISI and ICI simultaneously.
The serial waveform data needs to be converted into parallel input of NNWSC first. The step of the serial to parallel conversion is the upsampling number s, which is to ensure that each input vector corresponds to the symbols of one sampling period. Suppose the received NM-CAP waveform is r(t). As shown in Fig. 2, the parallel input at t can be expressed as
Next, we compare the computational complexity of NNWSC and the receiver cascading LMS equalizer, matched filters and SCE-ICA equalizer. The computational complexity of NNWSC is K(l1l2+2Nl2), where K is the number of sampling periods, and l1, l2 and 2N are the input layer size, hidden layer size and output layer size of NNWSC, respectively. The complexity of matched filters is 2NKslm, where lm is the number of taps of matched filters. The complexity of LMS equalizer is Ksle, where le is the number of taps. The complexity of SCE-ICA is given by [15, Eq. (7) and Eq. (8)].
In this work, the number of sub-bands is 3, the upsampling number is 8, the taps number of the LMS equalizer is 81, the taps number of the matched filters is 65, the input size of the NNWSC is 129, and the number of the hidden layer nodes and output layer nodes is 6. The number of training epochs is different when the SNR of the received signal varies from low to high. When SNR is low, about 120 epochs are needed to train the NNWSC. When SNR is high, the NNWSC model can be converged after about 40 epochs. In general, K>>N (for example, in this work, K is 16384, and N is 3), so we can divide the total complexity by K to get the complexity per sampling period. We only calculate the complexity of SCE [15, Eq. (7)] and ignore the complexity of ICA [15, Eq. (8)]. The calculated results are shown in Table 1.
Table 1. Computational complexity per sampling period
As shown in Table 1, the computational complexity of NNWSC is lower than matched filters and the SCE-ICA equalizer. The main reason is that the sliding window size for the linear convolution calculation is 1, while the sliding window size for the NNWSC is the sampling number 8, which leads to the low computational complexity of NNWSC. Compared with the receiver cascading LMS equalizer, matched filters and SCE-ICA equalizer, NNWSC can reduce the computational complexity by 93%.
2.2 Principle of PS
Compared with conventional QAM modulation with equal probability distribution of symbols, PS-QAM changes the distribution probability of the transmitted symbols to get the proper entropy. Thus, the system can achieve an appropriate net data rate (NDR) while the normalized generalized mutual information (NGMI) reaches the FEC code rate threshold. The transmitted PS-QAM symbols obey Maxwell-Boltzmann distribution [24]
3. Experimental setup
The experimental setup of the UDWDM FMWIN is shown in Fig. 3. As Fig. 3(a) shows, 8 wavelengths with 25-GHz spacing are used to generate the UDWDM optical signal with 14.5-dBm output power. The 8 wavelengths are divided into 2 groups, 4 odd wavelengths and 4 even wavelengths with 50 GHz spacing. Thus, we can ensure that the adjacent wavelengths can be loaded different NM-CAP signals. The two groups of wavelengths are coupled as one by using two polarization-maintaining optical couplers (PM-OCs) before modulations. The two Mach-Zehnder modulators (MZMs) are utilized to modulate the two different 3-sub-band NM-CAP signals to the coupled optical carrier, respectively. The 3-sub-band NM-CAP signals are generated by a 4-output arbitrary waveform generator (AWG). The two branches of optical signals are coupled as one branch by a 3-dB optical coupler (OC) and then transmitted in a 10-km standard single mode fiber (SSMF). The optical signal after 10-km transmission is amplified by an EDFA to compensate for the coupling loss and fiber loss. At the receiver of the fiber link, a tunable optical filter (TOF) is used to filter the UDWDM optical signal to get a single wavelength. The measured optical spectrum of the UDWDM optical signal is shown in Fig. 3(b). The wavelengths are numbered as 1∼8 from left to right according to the optical spectrum. The measured optical spectrum of the 4th wavelength is shown in Fig. 3(c). At last, the filtered optical signal is detected by a photodetector (PD).
Fig. 3. The experimental setup (PM-OC: polarization-maintaining optical coupler; TOF: tunable optical filter; LO: local oscillator; PA: power amplifier; MFs: matched filters).
At the transmitter of the mmWave link as shown in Fig. 3(f), the electrical signal from PD is modulated to a 92-GHz mmWave local oscillator (LO) by a W-band mixer. The 92-GHz mmWave LO is generated by a ×6 active multiplier. The mmWave signal is amplified by a power amplifier (PA) and transmitted by a horn antenna in sequence. At the receiver of the mmWave link as shown in Fig. 3(e), the mmWave signal is down-converted to be baseband signal by the down-convertor RF mixer. The LOs used for up-conversion and down-conversion are the same. It’s noted that the experimental system is only a demonstration for testing the proposed NNWSC. In a practical system, the LOs are different, where pilot tones are needed to mitigate the phase noise [27]. The intermediate frequency (IF) range of the RF mixer is 12 GHz. The baseband signal is received in a real time oscilloscope (OSC) and offline processed by MATLAB.
In this work, we compare the performance two DSP receivers. One is the conventional receiver cascading the waveform-level LMS equalizer, the matched filters and the SCE-ICA equalizer, the other is the NNWSC. The tap number of the LMS equalizer is 81. The taps number of the pulse shaping filters and the matched filters is 65. The input size of the NNWSC is 129. The number of the hidden layer nodes and output layer nodes is 6. The training dataset and the test dataset for NNWSC both include 16384 NM-CAP symbol periods. It’s noted that the random number generator of the training dataset is different from that of the testing dataset to mitigate overfitting. The conventional algorithm only processes the test data to calculate NGMI and NDR, in order to ensure the fairness of the comparison with NNWSC.
4. Experimental results
In this work, we study the NDR of the system while the NGMI is above the threshold of 9/10 FEC code rate, i.e. 0.92. Before we test the NDR of the UDWDM FMWIN system, we test the NDR of single wavelength (SW) case. We mainly discuss the NDRs at different roll-off factors (α), sub-band spacing factors (β), the total baud rate of 3 sub-bands, and the received power. The magnitude frequency responses of pulse shaping filters at different α and β are shown in Fig. 4. As shown in Eq. (2), the total bandwidth gets wider as α or β increases. The wavelength spacing of adjacent wavelengths is 25 GHz, so the frequency of 12.5 GHz is marked in the figures. When the total bandwidth exceeds 12.5 GHz, the system performance degrades, as will be shown specifically in the experimental results later in the paper.
Fig. 4. The magnitude frequency response of pulse shaping filters: (a) α=0.3, β=0; (b) α=0.1, β=0; (c) α=0, β=0; (d) α=0.1, β=1; (e) α=0.1, β=0.2; (f) α=0.1, β=−0.4.
We firstly test the NDR of the SW FMWIN system. The fourth wavelength as shown in the optical spectrum in Fig. 3(b) is tested. The 3 NM-CAP sub-bands are numbered from lowest to highest center frequency. The baud rate of each sub-band is 4 Gbaud. The received power of the fiber link is −1dBm. The PS-QAM orders of the 3 sub-bands in the NNWSC case are all 64. The PS-QAM orders of the 3 sub-bands in the LMS + ICA case are all 32. The main factor affecting the NDR is the bandwidth limitation of the mmWave system. We only test back-to-back (BtB) transmission in this case.
Figure 5(a) shows the NDR per sub-band versus roll-off factor. Figure 4(b) shows the NGMIs, the entropies of transmitted symbols and the received constellations at 0.2 roll-off factor. The sub-band spacing factor β is 0. As mentioned in the principles, when β≥1, all sub-bands are orthogonal; when β<1, all sub-bands are non-orthogonal. All tested NGMI is above 0.92, which means the 9/10 FEC decoder can achieve error-free transmission. As shown in Eq. (2), when the roll-off factor becomes larger, the center frequencies of the second and the third sub-band become higher. Since the bandwidth limitation has the greatest impact on the third sub-band, the NDR of the third sub-band becomes lower when the roll-off factor becomes larger. In contrast, the NDRs of the first and the second sub-bands become larger when the roll-off factor is larger. This is because the performance of the SRRC filter gets better at larger roll-off factors. The fluctuation in the NDR of LMS + ICA sub-band 1 is different from the trend of the NNWSC sub-band 1. On the one hand, the SCE-ICA ICI equalizer is based on matched filters (MFs). The MFs of larger roll-off factors perform better, which leads to a performance improvement for SCE-ICA. So when the roll-off factor changes from 0.2 to 0.3, the NDR of the LMS + ICA sub-band 1 increases more than that of the NNWSC sub-band 1. On the other hand, When the performance of NNWSC is good enough, the main factor limiting the NDR is the SNR of the received signal, and it will be difficult to get a significant increase in NDR by adjusting other parameters such as the roll-off factor. On the whole, the NDRs of 3 sub-bands in the NNWSC case are all higher than that in the LMS + ICA case, respectively.
Fig. 5. The NDR per sub-band in the SW BtB case: (a) the relationship between NDR per sub-band and roll-off factor; (b) the NGMIs, the entropies of transmitted symbols and the received constellations at 0.2 roll-off factor.
Figure 6(a) shows the NDR per sub-band versus sub-band spacing factor β. Figure 5(b) shows the NGMIs, the entropies of transmitted symbols and the received constellations at 0.5 sub-band spacing factor. The roll-off factor is 0.3. As mentioned in the principles, when β≥1, all sub-bands are orthogonal; when β<1, all sub-bands are non-orthogonal. All tested NGMI is above 0.92. As β approaches 1, the overlap between the adjacent sub-bands becomes less, so the NDRs of the first and second sub-bands gradually increase. The center frequency of the last sub-band increases with β, which makes the distortion caused by the bandwidth limitation to the third sub-band more and more serious. As a result, the NDR of the third sub-band decreases a lot with β, leading to the reduction of the total NDR of the 3 sub-bands. When β<0, too much overlap between adjacent sub-bands makes it difficult for both NNWSC and ICA equalizer to cancel ICI. The NDR of the third sub-band is highest at β=0. The total NDR of the 3 sub-bands is highest at β=0.2. The NDRs of 3 sub-bands in the NNWSC case are all higher than that in the LMS + ICA case, respectively.
Fig. 6. The NDR per sub-band in the SW BtB case: (a) the relationship between NDR per sub-band and sub-band spacing factor; (b) the NGMIs, the entropies of transmitted symbols and the received constellations at 0.5 sub-band spacing factor.
The above results fully demonstrate that for bandwidth-limited PS-QAM FMWIN systems, the bandwidth compression of NM-CAP can lead to an overall system performance improvement; the NNWSC outperforms the conventional receiver cascading the LMS equalizer, matched filters and the SCE-ICA equalizer.
Next, we test the NDR of the UDWDM FMWIN system. The baud rate of each sub-band is 4 Gbaud. The PS-QAM orders of the 3 sub-bands in the NNWSC case are 64, 64, and 32 respectively. The PS-QAM orders of the 3 sub-bands in the LMS + ICA case are all 32. Compared with the single wavelength case, the main factors affecting the NDR are the bandwidth limitation of the mmWave system and the adjacent wavelength crosstalk of the UDWDM system. We test both BtB and 10-km transmission in this case. We firstly show the NDRs per sub-band of BtB transmission in the fourth wavelength.
Figure 7(a) shows the NDR per sub-band versus roll-off factor. Figure 6(b) shows the NGMIs, the entropies of transmitted symbols and the received constellations at 0.15 roll-off factor. The received power of the fiber link is −1 dBm. The sub-band spacing factor β is 0. All tested NGMI is above 0.92, which means the 9/10 FEC decoder can achieve error-free transmission. Due to the adjacent wavelength crosstalk, the third sub-band suffer from more serious distortion compared with the single wavelength case. Thus, the PS-QAM order of the third sub-band is 32 to ensure the NGMI is higher than 0.92. The tested NDR of the third sub-band is lower than that in the single wavelength case. Since the performance of the SRRC filter gets better at larger roll-off factors, the NDRs of the first and the second sub-bands become larger when the roll-off factor is larger. However, as the roll-off factor increases, the center frequency of the third sub-band increases, which leads to more severe crosstalk from the adjacent wavelength and distortion caused by bandwidth limitation to the third sub-band. As a result, the NDR of the third sub-band decreases as the roll-off factor increases from 0 to 0.15. The NDRs of 3 sub-bands in the NNWSC case are all higher than that in the LMS + ICA case, respectively.
Fig. 7. The NDR per sub-band in the WDM BtB case: (a) the relationship between NDR per sub-band and roll-off factor; (b) the NGMIs, the entropies of transmitted symbols and the received constellations at 0.15 roll-off factor.
Figure 8(a) shows the NDR per sub-band versus sub-band spacing factor. Figure 8(b) shows the NGMIs, the entropies of transmitted symbols and the received constellations at 0.4 sub-band spacing factor. The received power of the fiber link is −1 dBm. The roll-off factor α is 0.1. All tested NGMI is above 0.92. As β approaches 1, the overlap between the adjacent sub-bands becomes less, so the NDRs of the first and second sub-bands increase from −0.4 to 0.2. When the sub-band spacing factor increases from 0.2 to 1, the NDRs of the first and the second sub-bands are almost virtually unchanged. The center frequency of the last sub-band increases with β, which makes the distortion to the third sub-band more and more serious. The distortion is caused by both the crosstalk from the adjacent wavelength and the bandwidth limitation of the mmWave system. As a result, the NDR of the third sub-band decreases a lot with β, leading to the reduction of the total NDR of the 3 sub-bands. When β<0, too much overlap between adjacent sub-bands makes it difficult for both NNWSC and ICA equalizer to cancel ICI. The NDRs of the 3 sub-bands all decrease as β decreases from 0 to −0.4. The NDR of the third sub-band is highest at β=0. The total NDR of the 3 sub-bands is highest at β=0.2. The NDRs of 3 sub-bands in the NNWSC case are all higher than that in the LMS + ICA case, respectively.
Fig. 8. The NDR per sub-band in the WDM BtB case: (a) the relationship between NDR per sub-band and sub-band spacing factor; (b) the NGMIs, the entropies of transmitted symbols and the received constellations at 0.4 sub-band spacing factor.
Next, we show the total NDR of the three sub-bands in the NNWSC based FMWIN system. Figure 9(a) shows the NDR of the three sub-bands versus the roll-off factor when only NNWSC is employed. The received power of the fiber link is −1 dBm, −1 dBm, and 1 dBm in the SW BtB case, the WDM BtB case, and the WDM 10 km case, respectively. The sub-band spacing factor β is 0. The baud rate of each sub-band is 4 Gbaud. Due to the dispersion effect of the fiber, the performance of the WDM 10 km case is worse than that of the WDM BtB case. The total NDR of the WDM 10 km case is about 4 Gbps lower than that of the WDM BtB case. Compared with the WDM BtB case, there is no crosstalk from adjacent wavelengths in the SW BtB case. As a result, when the roll-off factor increases from 0 to 0.3, the NDR of the SW BtB case keeps increasing, which is different from the WDM cases. The highest NDR of the SW BtB case, the WDM BtB case and the WDM 10 km case is achieved when the roll-off factor is 0.3, 0.1, 0.1, respectively. Figure 9(b) shows the NDR of the three sub-bands versus sub-band spacing factor when only NNWSC is employed. The received power of the fiber link is −1 dBm, −1 dBm, and 1 dBm in the SW BtB case, the WDM BtB case, and the WDM 10 km case, respectively. The roll-off factor is 0.3, 0.1 and 0.1 in the SW BtB case, the WDM BtB case, and the WDM 10 km case, respectively. If the sub-band spacing factor is too low, it’s difficult for NNWSC to mitigate the ICI caused by overlaps. If the sub-band spacing factor is too high, the center frequency of the third sub-band is high, which makes the third sub-band signal seriously distorted by the crosstalk from the adjacent wavelengths and the bandwidth limitation of the mmWave system. It’s noted that the roll-off factor of the SW case is larger than that of the WDM cases, so the overlap of adjacent sub-bands is larger than that of the WDM cases at the same sub-band spacing factor. As a result, when the sub-band spacing factor is less than −0.15, the NDR of the SW case is lower than that of the WDM cases. When the sub-band spacing factor is larger than −0.15, the NDR of the SW case is higher than that of the WDM cases because there is no crosstalk from the adjacent wavelengths in the SW case. The highest NDRs of the three cases are achieved in the sub-band spacing factor range from 0 to 0.4.
Fig. 9. The total NDR when only NNWSC is employed: (a) the relationship between total NDR of 3 sub-bands and roll-off factor; (b) the relationship between total NDR of 3 sub-bands and sub-band spacing factor.
Figure 10(a) shows the total NDR of 3 sub-bands versus the received power when only NNWSC is employed. The roll-off factor is 0.3, 0.1 and 0.1 in the SW BtB case, the WDM BtB case, and the WDM 10 km case, respectively. The sub-band spacing factor is 0.2. The baud rate of each sub-band is 4 Gbaud. The NDRs in the SW BtB case and the WDM BtB case are both higher than the NDR in the WDM 10 km case at the same received power. Figure 10(b) shows the total NDR of 3 sub-bands versus the total baud rate when only NNWSC is employed. The roll-off factor is 0.3, 0.1 and 0.1 in the SW BtB case, the WDM BtB case, and the WDM 10 km case, respectively. The sub-band spacing factor is 0.2. The received power of the fiber link is −1 dBm, −1 dBm, and 1 dBm in the SW BtB case, the WDM BtB case, and the WDM 10 km case, respectively. Since there is no crosstalk from the adjacent wavelengths in the SW case, the total bandwidth can be larger compared with the WDM cases. The highest total NDR of the SW BtB case achieved at 13 Gbaud. When the total baud rate is larger than 13 Gbaud, the signal of the third sub-band is distorted seriously by the bandwidth limitation, so the total NDR becomes lower. As for the WDM cases, the highest total NDR is achieved at 12 Gbaud. If the total baud rate is larger than 12 Gbaud, the signal of the third sub-band suffers crosstalk from the adjacent wavelengths, so the total NDR becomes lower.
Fig. 10. The total NDR when only NNWSC is employed: (a) the relationship between total NDR of 3 sub-bands and received power; (b) the relationship between total NDR of 3 sub-bands and total baud rate of 3 sub-bands.
Figure 11(a) and Fig. 11(b) show the electrical spectrum of the received NM-CAP signals. In the cases of α=0, β=0 and α=0.1, β=−0.4, the total bandwidth is narrower than 12.5 GHz, so the crosstalk from the adjacent wavelength is out of the 3 sub-bands. As α and β increase, the crosstalk from the adjacent wavelength is mixed in the third sub-band when the total bandwidth is wider than 12.5 GHz. In the case of α=0.1, as β decreases, the overlap between sub-bands gets more, and the total bandwidth is narrower. When β<0, The overlaps between the adjacent sub-bands cause the spectrum to bulge and the system performance will drop drastically. The bulge region in the case of α=0.1, β=−0.4 is marked in Fig. 11(b). In the case of α=0.1, β=1, the spectrum jitter of the third sub-band is relevant large as a result of the combined effect of the adjacent wavelength crosstalk and bandwidth limitation.
Figure 12 shows the measured NDRs of all 8 UDWDM wavelengths. The length of the transmitted fiber is 10 km, the roll-off factor is 0.1, and the sub-band spacing factor is 0.2. The baud rate of each sub-band and the received power are 4 Gbaud and 1 dBm, respectively. The left y-axis represents the NDRs per sub-band shown as 8 × 3 bars, and the right y-axis represents the total NDRs per wavelength shown as 8 square solid points. In the experimental system, the accuracy of the TOF is limited. In some wavelength ranges, the center wavelength and the bandwidth of the TOF slightly deviate from the ideal value. As a result, the total NDR of the wavelength index 7 is slightly lower than that of other wavelengths. The sum of the NDRs of 8 wavelengths is 414 Gbps.
5. Conclusion
In this paper, we have demonstrated an UDWDM FMWIN system based on non-orthogonal multiband carrierless amplitude and phase (NM-CAP) modulation. To deal with the ISI and ICI impairments, we have also proposed and demonstrated the NNWSC, which can directly convert the received NM-CAP waveform into QAM symbols, without the need for matched filters, additional ISI equalizers and ICI equalizers. NNWSC learns a group of filters that can down-convert the NM-CAP sub-bands and mitigate ISI and ICI simultaneously. Since NNWSC simplifies the demodulation process of NM-CAP and avoids error accumulation caused by cascading filters and post-equalizers, NNWSC can reduce the computational complexity and provide better performance. The effectiveness of proposed method on PS-QAM in NM-CAP signals is also verified. Based on proposed method, we have demonstrated a spectrally efficient fiber-mmWave transmission with 8 UDWDM channels at 25-GHz spacing. Each wavelength is loaded with 3 PS-QAM NM-CAP sub-bands. A total 414-Gbps net data rate with 24 sub-bands is achieved. In addition, NNWSC can reduce the computational complexity by 93% compared with the receiver cascading LMS equalizer, matched filters and SCE-ICA equalizer.
Funding
The Major Key Project of PCL; Natural Science Foundation of Shanghai (21ZR1408700); National Natural Science Foundation of China (61925104, 62031011, 62171137).
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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