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Abstract
D-band fiber-wireless technique that overcomes the bandwidth bottleneck of electrical devices has been popularized, but long-range D-band wireless transmission is still limited by the large absorption loss. So, the exploration of m-QAM formats is essential for the D-band long distance wireless transmission due to their different spectrum efficiency and SNR requirement. Moreover, nonlinearity in photonics-aided millimeter-wave (mm-wave) system is also a significant problem caused by fiber, photoelectrical devices and power amplifiers. So it is critical to employ a machine learning-based nonlinear compensation algorithm especially for long-distance D-band wireless delivery. A novel Gate Recurrent Unit (GRU) algorithm with a complex QAM input is proposed to further improve the receiver sensitivity of coherent D-band receiver, which effectively preserves the relative relationship between I/Q components of QAM signals and has memory capabilities with a better precision. We mainly discuss three learners with a complex QAM input, including complex-valued neural network (CVNN), single-lane Long Short-Term Memory (SL-LSTM) and single-lane Gate Recurrent Unit (SL-GRU). Thanks to these adaptive deep learning methods, we successfully realize 135 GHz 4Gbaud QPSK and PS-64QAM signal wireless transmission over 4.6 km, respectively. Considering the aspects of transmission capacity and recovery precision, CVNN equalizer is suitable for QPSK recovery, SL-GRU would be the best choice for PS-64QAM over D-band long range wireless transmission link up to km magnitude. The effective data rate can be achieved up to 17.6 Gbit/s. Therefore, we believe that the combination of high-order modulation and NN supervised algorithms with a complex input has an application prospect for the future 6 G mobile communication.
© 2023 Optica Publishing Group under the terms of the Optica Open Access Publishing Agreement
1. Introduction
As the next decade unfolds, 6 G is on the agenda, technologies from big data to artificial intelligence are booming, and various mobile applications are constantly emerging. With the emerging demand for a range of image-rich services and real-time joint communication and sensing applications, the wireless data traffic is continuously growing. Photonic technology for handling broadband microwave, millimeter wave and THz wireless signal generation has been regarded as a solution for the future data-hungry mobile communication [1–8]. D-Band ranges from 110 GHz to 170 GHz in the electromagnetic spectrum, corresponding to the recommended frequency band of operation of the WR6 and WR7 waveguides. These frequencies are equivalent to wavelengths between 2.7 mm and 1.8 mm. Numerous photonics-based methods to D-band (110-170 GHz) millimeter wave (MMW) signal generation demonstrated thus far include schemes using optical frequency comb [9,10], optical heterodyne [11,12] and so on. Yet there are several technical issues, i.e., the rapid attenuation of D-band in air space holds back the high-speed wireless transmission, which usually employs high-order QAM formats to further improve the spectrum efficiency [13,14]. And it faces a fundamental signal-to-noise ratio (SNR) limitation especially in D-band long-distance transmission channel.
While for long-range high-capacity D-band PS-QAM wireless transmission up to km and tens of Gbit/s scale, the major challenges are concluded from the following four aspects. 1) SNR is still limited because of the lack of high-gain silicon antennas [15], photodiodes [16] and large-power electrical amplifiers [17] in high frequency band above 100 GHz. 2) The high demands on both the radio frequency (RF) resource into the mixer and digital oscilloscope (DSO) for D-band large capacity transmission are put forward, which means that the generated intermediate frequency (IF) frequency fIF should be larger than the baud rate B, and the sum of fIF and B should be within DSO bandwidth range. 3) The main source of nonlinearity is originated from four aspects as follows: a) the large optical power from fiber; b) optoelectronic devices including modulators and photodiodes (PD); c) electrical amplifier (EA) and high-power amplifier (HPA) in wireless channel; d) the nonlinear impairments from mixers during down conversion. CMA, known as a linear and decision-feedback equalizer, uses tap delay line filters to equalize a modulated signal and remove inter-symbol interference (ISI). However, its higher residual mean square error (MSE) is a major challenge for equalizing nonlinear channels in low SNR conditions.
Furthermore, the advanced DSP for high order QAM signals is a critical part of 6 G high speed data transfer solutions. Among which, different approaches based on deep neural network (DNN) [18,19], convolutional neural network (CNN) [20,21], recurrent neural network (RNN) such as long short-term memory (LSTM) network [22,23] and Gate Recurrent Unit (GRU) [24] have been widely used to mitigate the nonlinear distortion in mm-wave ROF systems. But these methods often deal one QAM symbol with two separated real-valued I and Q data, respectively, regardless of the phase information between them. Therefore, it is meaningful to investigate a single neural network processing both I and Q components together.
In this paper, we experimentally realize photonics-aided D-band m-QAM mm-wave transmission over 4.6 km wireless distance. We transmit QPSK and PS-64QAM signals, respectively and receive them by using different machine learning (ML) algorithms. Their performance is evaluated and compared in terms of computation complexity and BER accuracy. The results show that 4 Gbaud QPSK signal is successfully transmitted with a BER below HD-FEC of 3.8 × 10−3 with the help of complex-valued neural network (CVNN) equalizer. In order to further increase the data rate, the BER of 4Gbaud PS-64QAM can be decreased to SD-FEC with 25% overhead only by single-lane GRU classification algorithm. Therefore, we can achieve a net rate of 17.6 Gbit/s D-band ROF delivery over 4.6 km air free wireless distance.
2. Principle of deep learning algorithms for complex m-QAM data input
Generally, both I and Q parts are divided. The separated real and imaginary components of the complex m-QAM signal are trained via two real-valued NN classifiers, respectively. But this problem is becoming increasingly important where the complex nature of the m-QAM signal cannot be ignored especially sensitive to noises. To solve this problem, we present a complex-valued network. First, the complex training set X is fed into fully connected complex-valued neural network (CVNN) shown in Fig. 1. We employ complex active function ℂReLU [25] in Eq. (1) to accurately model the non-linearity of complex channel.
Fig. 1. The schematic structure complex valued NN (a) equalizer with MSE loss function, (b) classifier with a cross entropy loss function.
2.1 Complex-valued neural network (CVNN)
As we know, there are a multitude of common loss functions in deep neural network such as mean square error (MSE) loss [26], cross-entropy (CE) loss [27], L1 loss [28], hinge loss [29] and so on. One of which, the loss function deployed in nonlinear equalization (NLE) framework is mean square error (MSE) loss and given as,
Where ${T_n} \in {{\mathbb C}^N}$ is the target complex signal, and ${O_n} \in {{\mathbb C}^N}$ is the output complex value from CVNN equalizer in Fig. 1(a).Besides, CE has a superiority in the term of convergence speed and is often used as a reasonable loss function for classification tasks [30,31]. Actually, m-QAM$(Y(n) \in [1,2,3\ldots M])$ equalization also can be regarded as multi-classification in Fig. 1(b). For example, to solve 64-QAM classification ${[p_0^t,p_1^t,p_2^t,p_3^t\ldots p_{63}^t]^T}(t = 1,2,\ldots P)$(CF) problem, the softmax function is a generalization of the logistic function that maps a length-T signal series of real values to a length-64 probability vector. In this manner, the sum of the output vector equals to 1, namely, $\sum {(p_0^t,p_1^t,p_2^t,p_3^t\ldots p_{63}^t)} = 1$. Specially, the probability of the t-th symbol is given as below,
The given result from Eq. (5) is the gradient updating according to back-propagation algorithm, so that the connected weight vector can be iteratively updated until the desired epoch or error value is reached.
In the term of complexity, MSE is superior to CE because there is only one neuron unit in the output layer of CVNN NLE, while there are M units in the output softmax layer of CVNN CE. In the term of precision, on one hand, CE loss weight updates faster than MSE. On the other hand, MSE is a non-convex optimization while cross entropy is a convex one. So, CE avoids falling into local optimal solution and is more convenient especially for the multi-classification optimization. Thus, we should consider in the two aspects of complexity and training precision to select the optimal loss function.
2.2 Single-lane LSTM (SL-LSTM) classifier
The principle of I-and Q-component joint long-short term memory (SL-LSTM) in Fig. 2 is demonstrated as follows:
Here, ${W^i}/{U^i}$, ${W^f}/{U^f}$, ${W^o}/{U^o}$, and $W/U$ are the weight matrices for the input gate, forget gate, output gate and input. Because the activation function ‘tanh’ lacks complex feature, we transform the input complex QAM data (${I_j} + i\ast {Q_j}$) into a real sequence ${x^t}$ of ${I_1},{Q_1},{I_2},{Q_2},\ldots {I_n},{Q_n}$ to restore the relationship between the real and imaginary parts. ${x^t}$ and ${h^t}$ denote the input data and hidden state of the LSTM at the time step t. Meanwhile, LSTM consists of three gate structures: input gate ${i^t}$, forget gate ${f^t}$, and output gate ${o^t}$. These gate mechanisms extract the valid information including long-term and short-term dependency information from the input data, which is the key to remove the inter symbol interference (ISI).
2.3 Single-lane GRU (SL-GRU) classifier
Gated Recurrent Units (GRUs) is simplified by Chung et al. [24] according to LSTM, in which the hidden state is in combination with cell states as a single state. So, the total amount of gates in GRU is half of that of gates in LSTM, which implies that GRU needs the less training time with an improved performance. Furthermore, similar to LSTM employing ‘tanh’ function, we also change the input transforms the complex QAM matrix ${[{{I_j},{Q_j}} ]^T}$ into a single-way real sequence ${x^t}$ of ${I_1},{Q_1},{I_2},{Q_2},\ldots {I_n},{Q_n}$ to restore the phase information. The principle of I-and Q-component joint gate recurrent unit (I/Q joint GRU) in Fig. 3 is demonstrated as follows:
Here, ${W^z}/{U^z}$, ${W^r}/{U^r}$ and $W/U$ are the weight matrices for the update gate, reset gate, and input gate, respectively. ${x^t}$ and ${h^t}$ represent the input hidden state of the GRU at the time step t. As for the operation, o denotes the Hadamard product between two matrices or vectors. Compared with the conventional recurrent neural network (RNN), the GRU consists of two crucial parts to improve performance: reset gate ${r^t}$ and update gate ${z^t}$. In the reset gate, the hidden state of the last time step ${h^{t - 1}}$ is multiplied by the weight matrix ${U^r}$. The input data ${x^t}$ is also multiplied by another weight matrix ${U^r}$. These two products are added and then activated by the ‘Sigmoid’ function to compress the results between 0 and 1. Then, the Hadamard product of the reset gate ${r^t}$ and hidden state ${h^{t - 1}}$ filters the legacy information passed from the last time step. After the reset gate, the new memory information ${\tilde{h}^t}$ is calculated.
The structure of the update gate is same with the reset gate employing different weight matrices. It is crucial because it decides the amount of the information transmitted to the next time step. Finally, the hidden state of current time step is calculated and transferred to the next time step. Overall, the sophisticated structure of GRU retains the valid information and abandons the useless information to avoid the gradient explosion and disappearance.
3. Experimental setup
The experimental setup of illustrated photonics-aided mm-wave communication through 4.6 km free-space link is presented in Fig. 4. It is conducted on a sunny day in winter with a temperature of 3°C and a humidity of 25% at Fudan University. The transmit-side (Tx-side) is located at Guanghua Building with a height of 142 m on Handan campus, and the receiver-side (Rx-side) is located at Wuli Building with a height of 24 m on Jiangwan campus.
Fig. 4. Experiment setup and schematic diagram of 135 GHz fiber-wireless system over 4.6 km free space distance.
M-QAM modulation formats such as QPSK PS-16QAM and PS-64QAM generated by AWG (Tektronix 7122C) are used to drive I and Q branch of the I/Q modulator. It is worth noting that the probabilistic amplitude shaping (PAS) scheme is employed for I and Q branch, respectively. Constant composition distribution matcher (CCDM) is combined with DVB-S2 LDPC, which supports bit-interleaved coded modulation (BICM). The information entropy of the transmitted PS-64QAM signal is adjusted as 5.6 bit/symbol. Both ECLs we used has a Linewidth < 10KHz. The optical signal from ECL2 at 1551.37 nm is modulated by I/Q modulator and amplified by PM-EDFA. ECL1 operating as a local oscillator (LO) has a wavelength of 1550.29 nm, and is then combined with ECL2 by a polarization-maintaining optical coupler (PM-OC). The optical spectrum(with a resolution of 0.01 nm) after PM-OC is given in Fig. 5, and the frequency between them is 135 GHz. The combined optical beam is optimized by an attenuator (ATT) and passes through a 100 m SMF-28, finally beats in UTC-PD and generates a sub-THz (∼135 GHz, D-band, 3 dB bandwidth of 60 GHz) signal. After the two-stage amplification (LNA with 20 dB gain & PA with 14 dB gain), the D-band mm-wave signal is transmitted from the HA, and travels over 4.6 km in the free-space link. Here, HA has a gain of 25 dBi and has a 3 dB Beamwidth of 9 deg.
In addition, Lens1 (Diameter of 10 cm) and Lens2 (Diameter of 60 cm) are placed at the receiving end and the transmitting end, respectively. Lens 1 has a focal length of 10 cm and Lens 2 has a focal length of 60 cm. At the receiving end, after the signal is detected by the HA identical to the one at transmit-side, it is first amplified by a low noise amplifier (LNA) with a gain of 30 dB, then mixed with a 131.4 GHz (10.95 × 12 = 131.4 GHz) signal in a mixer and generate a 3.6 GHz (135-10.95 × 12 = 3.6 GHz) IF signal, and is amplified by an EA with a gain of 26 dB and final captured by 50 GSa/s OSC. The end-to-end block diagram of the digital signal processing blocks is shown in Fig. 6. The received signal is firstly down converted into the baseband, and then processed via resampling, CMA, frequency offset estimation (FOE), carrier phase recovery (CPR), Gram-Schmidt orthogonalization process (GSOP), DD-LMS linear equalization. GSOP is mainly used to compensate for the I/Q amplitude and phase imbalance introduced by the I/Q modulator at the Tx. DD-LMS equalization based on stochastic gradient descent method is used to eliminate the phase noise and converge each constellation points [32]. Finally, the nonlinearity is equalized by machine learning (ML) algorithms. Here, ML includes nonlinear learning networks with a complex input (i.e., CVNN, SL-GRU, SL-LSTM).
Fig. 6. End-to-end block diagram of the digital signal processing blocks at receiver of 135 GHz fiber-wireless system over 4.6 km free space distance.
We give the electrical spectrum of IF signal captured by OSC when the baud rate ranges from 2 Gbaud to 5 Gbaud in Fig. 7. Since the IF is set to 3.6 GHz, the frequency overlapping occurs when the baud rate is 5 Gbaud in Fig. 7(d). Thus, the signal quality drops sharply when the baud rate is larger than 5 Gbaud.
Fig. 7. The electric spectrum of IF signals captured by OSC at (a) 2 Gbaud, (b) 3 Gbaud, (c) 4 Gbaud, (d) 5 Gbaud.
4. Experimental results and discussions
4.1 QPSK signal recovery with CVNN NLE
For the recovery of 4Gbaud QPSK signal at 135 GHz, the traditional DSP processing is implemented in Fig. 8. First, the IF signal is down converted to the baseband and resampled. We use CMA, then FOE and CPR. After that, we use GSOP for orthogonal imbalance compensation and DD-LMS for the blind equalization. Finally, we use Volterra nonlinear equalizer (NLE), real-valued DNN (RVNN) NLE, complex-valued DNN (CVNN) NLE and classifier (CF) to perform nonlinear compensation and decision. Here, both the first order taps and the second order taps are 201 in Volterra NLE. Both RVNN and CVNN equalizers have the same structure [261-420-320-1] composed of 301 cells n0 in the input layer, 420 cells n1 in the first hidden layer, 260 cells n2 in the second hidden layer and only one cell n3 in the output layer, but CVNN classifier (CF) has a different output number of neurons as 4 since QPSK recovery can be regarded as 4 classification issue.
Fig. 8. Constellation diagrams of 4Gbaud QPSK after (a) resample; (b) CMA; (c) FOE; (d) CPR; (e) GSOP; (f) DD-LMS.
Our input network has a training set sequence length with a range from 5000 to 25000, and the testing length is 5000. Our training and test sets are independent. In addition, the training dataset is randomly shuffled before being fed into the DNN network to enhance the generalization properties.
We discuss the performance of 5 Gbaud QPSK signals using NLE/CF under different receiving optical power in Fig. 9(a). It can be seen that CVNN achieve better receiving sensitivity of 1.5 dBm than RVNN. It means that CVNN performs better because of the phase restoration. That’s why we mainly discuss complex-valued deep learning networks such as CVNN, SL-LSTM and SL-GRU in our paper. For the further discussion of higher-order QAM such as PS-64QAM, the received optical power is fixed as 9 dBm in order to satisfy the requirement of large SNR. The performance of 4Gbaud QPSK signals versus the training size is shown in Fig. 9(b). It can be seen that BER decreases with the training size. BER drops to HD-FEC 3.8 × 10−3 with a training size of 11000, while cannot be further decreased when the size is larger than 20000. Considered in the aspect of complexity, the total length of the received I/Q pattern sequence is 30000, one of which 11000 is used for the training set and 5000 for the test set.
Fig. 9. (a) BER curves versus the optical power into UTC-PD by using deep learning learners. (b) The relationship between the training sequence length of CVNN NLE and the BER at 5 Gbaud with an optical power of 9 dbm.
We also calculated the BER under different baud rates when the optical power into UTC-PD is 9 dBm and the training length is 11000 in Fig. 10(a). 4 Gbaud QPSK signal compensated by RVNN NLE, CVNN NLE and CF can reach the BER of HD-FEC 3.8 × 10−3, which is consistent with the constellation comparison in Figs. 10(b)-(d). Considered in the term of complexity, CVNN NLE has less computation burden than the other two learners in Table 1. Therefore, in our opinion, the best option is CVNN NLE for 135 GHz QPSK delivery over 4.6 km.
Fig. 10. (a) BER curves versus the baud rate when the optical power into UTC-PD is 9 dBm by using deep learning learners. Constellation diagrams of 4 Gbaud QPSK after (b) Volterra nonlinear equalizer; (c) real-valued DNN equalizer; (d) complex-valued DNN equalizer.
Table 1. Parameters and performance of deep learning methods for qpsk
4.2 PS-64QAM signal recovery with SL-GRU classifier
We also give the density distribution of PS-64QAM constellation diagrams after resample, CMA, FOE, CPR, GSOP, and DD-LMS are given as Insets (i)-(vi) in Fig. 11.
Fig. 11. The density distribution of constellation diagrams for 4 Gbaud PS-64QAM after (i) resample; (ii) CMA; (iii) FOE; (iv) CPR; (v) GSOP, and (vi) DD-LMS.
As the constellation diagram shown in Fig. 12(a), PS-64QAM has 9 reference circles, namely, ring1∼ring9. According to PS scheme, there are fewer points in outer rings (i.e., rings 6∼9) while more points in inner rings (i.e., rings 1∼5), as the green bars shown in Fig. 12(b). At the same time, the points in outer rings 6∼9 are easily affected by the noises, and the error rate is close to 100% when the baud rate is 3 Gbaud, as the blue bars shown in Fig. 12(b).
Fig. 12. (a) BER of PS-64QAM signal versus baud rate with different equalizers when ROP is 7 dBm. (b) Distribution and error ratio of each amplitude of 2-Gbaud PS-64QAM signal after DD-LMS. (c) BER for PS-64QAM with different algorithms.
We compare a linear 21-tap CMMA equalizer combined with a 223-tap DD-LMS and three kinds of training networks with a complex-valued input including CVNN, SL-LSTM and SL-GRU in Fig. 12(c). The structure of CVNN is [361-360-64] with a softmax output layer. SL-LSTM classifier has an input data size of L = 401, features of F = 2 in the input layer, hidden size of H = 400, the fully connected hidden size of Hfc =320 and an output size of M = 64. SL-GRU classifier has an input data size of L = 257, features of F = 2 in the input layer, hidden size of H = 125, the fully connected hidden size of Hfc =300 and an output size of M = 64. The result shows that BER of 4-Gbaud PS-64QAM signal can be achieved below the SD-FEC threshold of 4.2 × 10−2 at 25% SD-FEC threshold [33] by using SL-GRU.
4.3 Performance evaluation for D-band m-QAM transmission
In summary, we choose the optimal nonlinear equalization scheme when different modulation formats are used for D-band mm-wave transmission over 4.6 km. When taking the HD-FEC threshold into account, CVNN NLE can be employed as the optimum option for QPSK to transmit signals at a 4-Gbaud rate. Thanks to the SL-GRU, 4Gbaud PS-64QAM can reach a SD-FEC threshold of 4.2 × 10−2 with 25% overhead. The highest line bit rate is 5.6 × 4 = 22.4 Gbps, and the net bit rate is [5.6-6 × (1-4/5)] × 4 = 17.6 Gbit/s. Due to the severe frequency overlap of 5 Gbaud signals, neither linear nor nonlinear equalizers can effectively compensate for the serious bandwidth limitation issue. As shown in Table 2, we compare the performance of QPSKand PS-64QAM signals, it can be concluded that the achievable efficient rate of PS-64QAM is higher up to 17.6 Gbit/s by employing GRU classifier with a complex input. As seen in Table 3, the results show that the data rate in our presented work is higher.
Table 2. Parameters and performance of deep learning methods for m-qama
Table 3. Reported D-band ROF transmission results
5. Conclusions
In this paper, 135 GHz fiber-wireless transmission using QPSK and PS-64QAM over 4.6 km wireless link is experimentally demonstrated. The performance between these three m-QAM formats is evaluated by employing complex-valued NN, SL-LSTM, SL-GRU, respectively. Compared with RVNN, these deep learning methods realize phase information restoration and BER performance improvement. Although PS-64QAM is employed to increase the spectrum efficiency, it is easily affected by the nonlinear noises. SL-GRU classifier would be the best choice for PS-64QAM over D-band long range wireless transmission link up to km magnitude since it largely can improve the BER decision accuracy. Thanks to the ML paradigms, we can achieve 8 Gbit/s QPSK and 17.6 Gbit/s PS-64QAM mm-wave transmission at 135 GHz over 4.6 km. Therefore, we believe that the combination of high-order modulation and NN supervised algorithms has an application prospect for the future 6 G mobile communication.
Funding
National Natural Science Foundation of China (61821001, 62127802).
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.
References
1. Z. Tang and S. Pan, “A Full-Duplex Radio-Over-Fiber Link Based on a Dual-Polarization Mach–Zehnder Modulator,” IEEE Photon. Technol. Lett. 28(8), 852–855 (2016). [CrossRef]
2. T. Nagatsuma, T. Takada, H. J. Song, K. Ajito, N. Kukutsu, and Y. Kado, “Millimeter- and THz-wave photonics towards 100-Gbit/s wireless transmission,” in Proc. 2010 23rd Annual Meeting of the IEEE Photonics Society, Denver, CO, USA, 2010, 108–109.
3. X. Li, J. Xiao, and J. Yu, “W-Band Vector Millimeter-Wave Signal Generation Based on Phase Modulator With Photonic Frequency Quadrupling and Precoding,” J. Lightwave Technol. 35(13), 2548–2558 (2017). [CrossRef]
4. Z. Wang, Y. Xiao, S. Wang, S. Yanyuan, B. Wang, Y. Chen, Z. Zhou, J. He, and L. Yang, “Probabilistic shaping based constellation encryption for physical layer security in OFDM RoF system,” Opt. Express 29(12), 17890–17901 (2021). [CrossRef]
5. X. Li, J. Yu, and G. K. Chang, “Photonics-aided millimeter-wave technologies for extreme mobile broadband communications in 5 G,” J. Lightwave Technol. 38(2), 366–378 (2020). [CrossRef]
6. V. Pistore, H. Nong, P. B. Vigneron, K. Garrasi, S. Houver, L. Li, A. G. Davies, E. H. Linfield, J. Tignon, J. Mangeney, R. Colombelli, M. S. Vitiello, and S. S. Dhillon, “Millimeter wave photonics with terahertz semiconductor lasers,” Nat. Commun. 12(1), 1427 (2021). [CrossRef]
7. T. Nagatsuma, “Photonic Generation of Millimeter Waves and Its Applications,” inProc. Optical Fiber Communication Conf. (OFC), Los Angeles, CA, USA, 2012, pp.OM2B.7. doi:10.1364/OFC.2012.OM2B.7.
8. W. Zhou and C. Qin, “Simultaneous generation of 40, 80 and 120 GHz optical millimeter-wave from one Mach-Zehnder modulator and demonstration of millimeter-wave transmission and down-conversion,” Opt. Commun. 398, 101–106 (2017). [CrossRef]
9. W. Zhou, X. Li, and J. Yu, “Pre-coding assisted generation of a frequency quadrupled optical vector D-band millimeter wave with one Mach-Zehnder modulator,” Opt. Express 25(22), 26483–26491 (2017). [CrossRef]
10. D. Sun, Y. Dong, L. Yi, S. Wang, H. Shi, Z. Xia, W. Xie, and W. Hu, “Photonic generation of millimeter and terahertz waves with high phase stability,” Opt. Lett. 39(6), 1493–1496 (2014). [CrossRef]
11. X. Li and J. Yu, “Over 100 Gb/s Ultrabroadband MIMO Wireless Signal Delivery System at the D-Band,” IEEE Photonics J. 8(5), 1–10 (2016). [CrossRef]
12. X. Li, J. Yu, L. Zhao, K. Wang, C. Wang, M. Zhao, W. Zhou, and J. Xiao, “1-Tb/s Photonics-aided Vector Millimeter-Wave Signal Wireless Delivery at D-Band,” Optical Fiber Communication Conference 2018, San Diego, CA, USA), TH4D.1. doi:10.1364/OFC.2018.Th4D.1.
13. P. J. Artz and F. Gerfers, “6 G D-Band Receiver Model with High Spectral Efficiency Enabling Global System Optimization,” 2022 IEEE 65th International Midwest Symposium on Circuits and Systems (MWSCAS), Fukuoka, Japan, pp.1–4.
14. J. L. Gonzalez Jimenez, B. Martineau, A. Hamani, A. Siligaris, F. Foglia Manzillo, F. Hameau, and C. Dehos, “A 56.32 Gb/s 16-QAM Link over Dielectric Fiber using a D-band Channel Bonding Transceiver,” 2021 51st European Microwave Conference (EuMC), London, UK, 197–200.
15. A. Gomez-Torrent, M. Garcia-Vigueras, L. L. Coq, A. Mahmoud, and J. Oberhammer, “A low-profile and high-gain frequency beam steering sub-THz antenna enabled by silicon micromachining,” IEEE Trans. Antennas Propagat. 68(2), 672–682 (2020). [CrossRef]
16. E. Chao, B. Xiong, C. Sun, Z. Hao, J. Wang, L. Wang, Y. Han, H. Li, J. Yu, and Y. Luo, “D-Band MUTC Photodiodes With Flat Frequency Response,” IEEE J. Select. Topics Quantum Electron. 28(2: Optical Detectors), 1–8 (2022). [CrossRef]
17. M. K. Ali, G. Panic, and D. Kissinger, “A Broadband Low-Noise Amplifier for D-Band Communications in SiGe BiCMOS Technology,” 2022 14th German Microwave Conference (GeMiC), Ulm, Germany, 92–95.
18. T. Xu, T. Xu, and I. Darwazeh, “Deep Learning for Interference Cancellation in Non-Orthogonal Signal Based Optical Communication Systems,” inProc. 2018 Progress in Electromagnetics Research Symposium (PIERS-Toyama), Toyama, Japan, 2018), 1–8.
19. P. P. Shinde and S. Shah, “A review of machine learning and deep learning applications,” inProc. 2018 Fourth International Conference on Computing Communication Control and Automation (ICCUBEA), Pune, India, 2018), 1–6.
20. L. Li, H. Hou, and W. Meng, “Convolutional-Neural-Network-Based Detection Algorithm for Uplink Multiuser Massive MIMO Systems,” IEEE Access 8, 64250–64265 (2020). [CrossRef]
21. F. Tang, Z. M. Fadlullah, B. Mao, and N. Kato, “An intelligent traffic load prediction-based adaptive channel assignment algorithm in sdniot: A deep learning approach,” IEEE Internet Things J. 5(6), 5141–5154 (2018). [CrossRef]
22. X. Dai, X. Li, M. Luo, Q. You, and S. Yu, “LSTM networks enabled nonlinear equalization in 50-Gb/s PAM-4 transmission links,” Appl. Opt. 58(22), 6079–6084 (2019). [CrossRef]
23. X. Liu, Y. Wang, X. Wang, H. Xu, C. Li, and X. Xin, “Bi-directional gated recurrent unit neural network based nonlinear equalizer for coherent optical communication system,” Opt. Express 29(4), 5923–5933 (2021). [CrossRef]
24. J. Chung, C. Gulcehre, K. Cho, and Y. Bengio, “Empirical evaluation of gated recurrent neural networks on sequence modeling,” arXiv, arXiv:1412.3555 (2014). [CrossRef]
25. W. Zhou, J. Shi, K. Wang, C. Wang, Y. Wang, M. Kong, F. Wang, C. Liu, and J. Ding, “Comparison of Real- and Complex-Valued NN Equalizers for Photonics-Aided 90-Gbps D-band PAM-4 Coherent Detection,” J. Lightw. Technol. 39(21), 6858–6868 (2021). [CrossRef]
26. C. Yang, F. Yang, and Z. Wang, “Iterative Minimum Mean Square Error Equalization for Optical Fiber Communication Systems,” IEEE Photon. Technol. Lett. 19(19), 1571–1573 (2007). [CrossRef]
27. D. B. Pieter Tjerk, D. P. Kroese, S. Mannor, and R. Rubinstein, “A tutorial on the cross-entropy method,” Annals of Operations Research 134(1), 19–67 (2005). [CrossRef]
28. N. Zhang, X. Xue, X. Xia, W. Jiang, and J. Zhou, “Robust T-S Fuzzy Model Identification Approach Based on FCRM Algorithm and L1-Norm Loss Function,” IEEE Access 8, 33792–33805 (2020). [CrossRef]
29. K. Duan and S. Keerthi, “Which is the best multiclass svm method? an empirical study,” in International workshop on multiple classififier systems, 2005, 278–285.
30. K. Zhang, X. Wang, Y. Guo, Z. Zhao, and Z. Ma, “Competing Ratio Loss for Multi-class image Classification,” inProc. 2019 IEEE Visual Communications and Image Processing (VCIP), Sydney, NSW, Australia, 2019, 1–4.
31. N. C. Kurian, P. S. Meshram, A. Patil, S. Patel, and A. Sethi, “Sample Specific Generalized Cross Entropy for Robust Histology Image Classification,” inProc. 2021 IEEE 18th International Symposium on Biomedical Imaging (ISBI), Nice, France, 2021, 1934–1938.
32. X. Li, J. Yu, Y. Xu, X. Pan, F. Wang, Z. Li, B. Liu, L. Zhang, X. Xin, and G. Chang, “60-Gbps W-Band 64QAM RoF System with T-spaced DD-LMS Equalization,” in Optical Fiber Communication Conference, 2017, p. M3E.2.
33. K. Onohara, K. Sugihara, T. Konishi, Y. Miyata, Y. Inoue, T. Kametani, S. Sugihara, K. Kubo, K. Yoshida, and H. Mizuochi, “Soft-decision-based forward error correction for 100 Gb/s transport systems,” IEEE J. Select. Topics Quantum Electron. 16(5), 1258–1267 (2010). [CrossRef]
34. J. C. Patra, R. N. Pal, R. Baliarsingh, and G. Panda, “Nonlinear channel equalization for QAM signal constellation using artificial neural networks,” IEEE Trans. Syst., Man, Cybern. B 29(2), 262–271 (1999). [CrossRef]
35. K. Wang, C. Wang, W. Li, Y. Wang, J. Ding, C. Liu, M. Kong, F. Wang, W. Zhou, F. Zhao, and J. Yu, “Complex-valued 2D-CNN Equalization for OFDM Signals in a Photonics-aided MMW Communication System at the D-band,” J. Lightwave Technol. 40(9), 2791–2798 (2022). [CrossRef]
36. F. Wang, Y. Wang, W. Li, B. Zhu, J. Ding, K. Wang, C. Liu, C. Wang, M. Kong, L. Zhao, W. Zhou, F. Zhao, and J. Yu, “Echo State Network Based Nonlinear Equalization for 4.6 km 135 GHz D-Band Wireless Transmission,” J. Lightwave Technol. 41(5), 1278–1285 (2023). [CrossRef]
