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Abstract
Fiber-wireless integration has been widely studied as a key technology to support radio access networks in sixth-generation wireless communication, empowered by artificial intelligence. In this study, we propose and demonstrate a deep-learning-based end-to-end (E2E) multi-user communication framework for a fiber-mmWave (MMW) integrated system, where artificial neural networks (ANN) are trained and optimized as transmitters, ANN-based channel models (ACM), and receivers. By connecting the computation graphs of multiple transmitters and receivers, we jointly optimize the transmission of multiple users in the E2E framework to support multi-user access in one fiber-MMW channel. To ensure that the framework matches the fiber-MMW channel, we employ a two-step transfer learning technique to train the ACM. In a 46.2 Gbit/s 10-km fiber-MMW transmission experiment, compared with the single-carrier QAM, the E2E framework achieves over 3.5 dB receiver sensitivity gain in the single-user case and 1.5 dB gain in the three-user case under the 7% hard-decision forward error correction threshold.
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1. Introduction
With the increasing availability of fifth-generation mobile communication technology, research on sixth-generation (6G) mobile communication technology in both academia and industry has accelerated. The reliability and capacity requirements to cope with upcoming applications, including augmented reality, virtual reality, intelligent sensors, and digital twins, have driven the evolution of the physical layer [1]. Fiber-wireless integration has emerged as a key technology to support radio access networks (RAN) in 6G because of its smooth media conversion between wireless and optical signals, flexible multichannel aggregations, broad service coverage, and low latency [2]. Further, artificial intelligence (AI) has become crucial in designing and optimizing 6G architecture, protocols, and operations; 6G is expected to offer ubiquitous AI services from the network's core to end devices [3]. With AI becoming a new paradigm for the design and optimization of 6G, the RAN will realize autonomous and self-optimization, and E2E is a primary application of AI [4–6].
For the conventional block-structured communication systems, data-driven AI approaches have achieved remarkable results by optimizing independent blocks, such as coding [7] [8], detection [9] [10], channel decoding [11], channel estimation [12], and equalization [13–15]. However, these individually optimized blocks do not guarantee the global optima of communication systems [16]. Aside from optimizing the communication blocks, [16] proposed a learning-based E2E optimization scheme in which the entire communication system was interpreted into an autoencoder (AE). The transmitter and receiver are represented by two artificial neural networks (ANNs), between which is a surrogate channel layer simulating the states and responses of the hardware and channel combinations. With deep learning algorithms, the AE can self-optimize to combat channel impairments in the E2E feedback loop between the transmitter and receiver. Several previous works have validated this intelligent E2E optimization technique to achieve global enhancement in wireless systems [17,18] and optical fiber systems [19–21]. In [17], an autoencoder was trained using a two-step transfer learning technique to perform similarly to a practical baseline. By utilizing the reinforcement learning method over the actual channel, the improved E2E wireless system achieved a performance gain of approximately 1.3 dB over a 256-QAM baseline while retaining the same communication rate [18]. The results in [17] and [18] demonstrate the importance of an accurate channel model in actual communication experiments. In optical fiber communications, researchers attempted to embed the fiber channel model into an AE and optimize the shape of the geometric constellation to resist fiber nonlinearities [19]. In [20], both modulation and demodulation were realized in an intelligent E2E framework for a short-distance optical fiber system. To compensate for fiber chromatic dispersion and other channel memory, the same team applied a bidirectional deep recurrent neural network in the E2E optimization scheme [21]. In [22], the study considered a more complicated long-haul fiber channel where both dispersion and nonlinearity existed. With the gradient estimation method, the optimized transmitter improved the E2E geometric constellation shaping scheme by a 0.25 dB Q-factor at 1200 km transmission compared with the square QAM signal.
However, the previous works only considered deep-learning-based E2E communication for single-user cases in wireless or fiber systems. The E2E fiber-wireless integrated communication system, as shown in Fig. 1, needs to be investigated, which has great potential for realizing the vision of autonomous and self-optimizing RAN in 6G. The impacts of fiber-wireless integration on the signal, such as photoelectric conversion loss, nonlinear impairment, or local oscillator (LO) leakage, should be fully considered when constructing the E2E fiber-wireless integrated system. This imposes significant pressure on the data-driven channel model, which should simulate the states, behaviors, and rules for the hardware and channel combinations. Moreover, a practical E2E communication system should support the transmission of multi-user information in a single link.
This work focuses on constructing a deep-learning-based E2E optimization framework for the fiber-mmWave (MMW) integrated multi-user communication system. We first use the real data collected from a fiber-MMW integrated platform to train the ANN-based channel model. Filters and transfer learning techniques are used to improve the accuracy of the channel model. Subsequently, the trained channel model bridges the gap between the transceiver ANNs and realizes gradient backpropagation. The connected transmitter, channel model, and receiver ANNs create an AE network. By connecting the computation graph of multi-transceivers, we can jointly train a multi-user E2E framework in the AE network. The trained transceiver ANNs are deployed in the fiber-MMW integrated system and realize deep-learning-based E2E multi-user communication. An experimental study of a 46.2 Gbit/s 10-km fiber-MMW integrated system is conducted to evaluate the performance of the proposed E2E framework. Compared with the single-carrier quadrature amplitude modulation (SC-QAM), the E2E framework achieves over 3.5 dB sensitivity gain in the single-user case and 1.5 dB sensitivity gain in the three-user case under the 7% hard-decision forward error correction (HD-FEC) threshold (3.8E-3).
The rest of the manuscript is organized as follows: Section 2 introduces the channel modeling strategy. Section 3 discusses the deep-learning-based E2E framework for the fiber-MMW integrated multi-user communication system. In Section 4, we first introduce the experimental fiber-MMW integrated platform and then evaluate the performance of the E2E framework and SC-QAM scheme. The paper is summarized in Section 5.
2. Channel modeling strategy
The deep-learning-based E2E system is trained to optimize the transmitter and receiver. However, a real channel cannot propagate the gradient between the transceiver ANNs, which prevents the weight-updating process of the transceiver neural network. We utilize a data-driven ANN-based channel model (ACM) to simulate the channel response and connect the computation graph between the transceiver chain to allow gradient back propagation (BP). The structure of the ACM is motivated by the two tributaries of the ANN channel emulator proposed in [23]. The ACM uses two tributaries to respectively learn the linear and nonlinear channel effects. The transfer function of the ACM can be expressed as
Besides the ACM structure, the training data also determines the channel modeling accuracy. As Fig. 2 shows, the ACM should emulate the main impairments in a real fiber-MMW integrated channel including frequency fading, bandwidth limitation, additive noise, channel memory, and nonlinear distortions. After these channel effects, the transmitted (Tx) signal is transformed into the received (Rx) spectrum in Fig. 1. The red area in the Rx spectrum denotes the low signal-to-noise ratio (SNR) frequency components induced by bandwidth limitation and noise. When utilizing the Rx data to train the ACM, the noisy high-frequency components disrupt the weights updating direction, causing the ACM to distribute the prediction error across all frequency components. To mitigate the influence of noise, an ideal low pass filter (ILPF) is used to filter the low SNR frequency components when training the ACM. The randomly generated transmitted data and corresponding received data after the ILPF (Rx’) are chosen as the initial Tx and Rx’ data to train the ACM. The trained ACM is then embedded into our deep AE network, with a fixed weight. In the training process of AE, the fixed-weight ACM applies the learned channel effect to the transmitted signal and outputs the signal for the receiver ANN. The weights of the transmitter (T-ANN) and R-ANN are updated to combat the channel effect from the ACM.
Fig. 2. Schematic of channel modeling strategy. The Tx and Rx data are repetitively collected from a fiber-MMW channel to retrain the ACM.
3. Deep-learning-based E2E framework
We interpret the entire fiber-MMW communication system as a deep-learning-based E2E framework. Before deploying into the real communication system, the T-ANN and R-ANN should be trained within an AE network to address the channel impairments generated by the ACM. The T-ANN, ACM, and R-ANN consist of the main parts of the AE network. During the training of the AE, the gradients propagate from the R-ANN to T-ANN through the trained ACM. The well-trained T-ANN and R-ANN are then deployed in the real fiber-MMW integrated system to build the E2E communication system. This section describes the single-and multi-user deep-learning-based E2E frameworks, as well as the training detail for each module.
3.1 E2E framework for single user
In the training phase, the structure of the single-user E2E framework is the AE network illustrated in Fig. 3. We first convert the random integer symbol m ∈{1, …, M} into an M × 1 one-hot vector s. In s, the mth element is equal to 1, whereas the other elements are equal to 0. In this work, we adopt the one-hot encoding to train our AE network as an ad hoc approach. The one-hot encoding is the standard way of representing categorical values and facilitates the minimization of the symbol error rate [20]. The one-hot encoding also has a simple encoding form that avoids imposing undesired ordering of the messages compared to an integer encoding [20]. However, the one-hot vector cannot lead to the best bit-level performance since a symbol error may not result in a single-bit error. Solutions based on bit-level autoencoder networks, such as adopting the bit-level labeling and bit-level loss functions, will be studied in our future work for potentially better bit-level performance. The T-ANN learns to represent the one-hot vector using a data sequence. The T-ANN has two hidden layers both with 4M neurons. We use nK to represent the output dimension of the T-ANN for the K-user E2E Framework. For the single-user case, n1 neurons in the output layer generate the data sequence for transmission. We choose tanh as the activation function in the hidden and output layers to generate encoded sequences ranging from -1 to 1. Thus, the M × 1 one-hot vector is encoded into an n1 × 1 data sequence, each carrying log2(M) bits of information. Considering the output dimension n1 determines the oversampling rate of the signal, both M and n1 influence the data rate of the E2E system. Because the channel memory causes ISI between adjacent samples, we feed the ACM multiple transmitted sequences to simulate real transmission [20]. In Fig. 3, s1, sN + 1, and s2N + 1 denote the inputs of the 1st, N + 1, and 2N + 1 T-ANN. The outputs of the 2N + 1 neighbor T-ANNs are connected in series by the flatten layer to form a sequence of (2N + 1)·n1 samples. These 2N + 1 T-ANNs have the same hyperparameters. The (2N + 1)·n1 samples go through an ILPF layer. The cut-off frequency of the ILPF equals that of the fiber-MWW channel. The low pass filtering effect forces the T-ANN to encode most of the information onto the in-band frequency component during the training process [20]. The library TensorFlow provides the Fast-Fourier transform (FFT) and Inverse Fast-Fourier transform (IFFT) required in the ILPF layer. The filtered samples are then input to the ACM to address the simulated channel impairments.
Fig. 3. Structures of deep-learning-based single-user E2E framework in the training phase. s1, sN + 1, and s2N + 1 are the input of the 1st, N + 1, and 2N + 1 T-ANN. The R-ANN learns to recover the information ${\tilde{{\boldsymbol s}}_{N + 1}}$ corresponding to the input of the N + 1 T-ANN.
On the receiver side, the ACM outputs the received signal for the R-ANN to recover the information from the N + 1 T-ANN. Additionally, the R-ANN has two hidden layers both with 4M neurons with tanh activation functions. The R-ANN gives the approximation ${\tilde{{\boldsymbol s}}_{N + 1}}$ with the soft-max function at the output layer. The approximation ${\tilde{{\boldsymbol s}}_{N + 1}}$ is a probability vector in which the largest probability item is expected to have the same index as the “1” item in the corresponding one-hot input ${{\boldsymbol s}_{N + 1}}$, which is the input of the N + 1 T-ANN. The cross-entropy is calculated at the end of the AE to measure the difference between ${\tilde{{\boldsymbol s}}_{N + 1}}$ and ${{\boldsymbol s}_{N + 1}}$, which is defined as
3.2 E2E framework for multi-user
As illustrated in Fig. 4, the structure of the multi-user E2E framework in the training phase is also an AE network. For the ith user, [s](i) = [s1, …, s2N + 1](i) denotes the inputs of the 2N + 1 T-ANNs, whereas ${\tilde{{\boldsymbol s}}^{(i)}}_{N + 1}$ denotes the recovered vector corresponding to the input of the N + 1 T-ANNs. Here, we discuss the situation where three users communicate simultaneously. The output dimension of the T-ANN for the three-user case is n3. At the transmitter side, the encoded data of each user contains (2N + 1)·n3 samples generated by the 2N + 1 adjacent T-ANNs. The encoded data of the three users are added in order and normalized in the sum layer. The summed result is then reshaped into a single transmitted sequence in the flattened layer. The transmitted sequence is filtered by the ILPF layer and ACM to generate the received signal, which is finally processed by the R-ANN of each user to reconstruct the one-hot input of the N + 1 T-ANNs. The cross-entropy loss for each user is calculated with (5) and the gradient of the loss is used to update the weights of the T-ANN and R-ANN. The multi-user E2E framework utilizes a sum layer to merge the transmitted signals from multiple users. Therefore, the computation graphs of the multiple users are connected to the same node between the transceiver chain, which enables the joint optimization of the three users in one single BP path.
Fig. 4. Structures of the deep-learning-based multi-user E2E framework in the training phase. For the ith user, [s](i) denotes the inputs of 2N + 1 T-ANNs, $\tilde{s}_{N + 1}^{(i )}$ denotes the recovered vector corresponding to the input of the N + 1 T-ANN.
Owing to the structure in Fig. 4, the T-ANN is trained to encode the information of three users into three orthogonal bases so that the R-ANN of each user can extract independent information from the same received signal. Simultaneously, there is a unique matched filter within the R-ANN of each user which can filter out the signal component from other users. The T-ANNs from the three users learn to jointly optimize their weights so that the encoded signal for each user is independent of the others. Figure 5 shows the confusion matrixes of the R-ANNs in the three-user E2E framework. In each confusion matrix, the column is the probability vector ${\tilde{{\boldsymbol s}}^{(i)}}_{N + 1}$ approximated by the R-ANN and the horizontal axis represents the Tx symbols. Figure 5 (i)-(iii) gives the results if we use the three trained R-ANNs to recover the data sequences encoded by the T-ANN of the first user (U1). Only the R-ANN of U1 can accurately recover the encoded sequences with high probabilities while the other two R-ANNs output chaotic probability vectors all with low probability items. A similar phenomenon also occurs in the series of Fig. 5 (iv)-(vi) and Fig. 5 (vii)-(ix) when we fix the T-ANN source and test different R-ANNs on the encoded sequences. This phenomenon supports the claim that T-ANN and R-ANN have the potential to construct the orthogonality between different users in the three-user E2E framework.
The AE network structure used for training the deep-learning-based E2E framework is summarized in Table 1. The number of hidden neurons in the transceiver and ACM follow the empirical configuration in [20] to be proportional to M and nK, respectively. To consider ISI in the AE network, (2N + 1) encoded sequences of the T-ANN are connected to the ACM input. The two tributaries ACM generates channel impairments on its input signal and feeds l samples of the distorted signal to the R-ANN for decoding. The structure of the multi-user E2E framework in Fig. 4 is similar to that of the single-user E2E framework in Fig. 3. But the output dimension of the T-ANN for the K-user case is K times that of the single-user case, i.e., n3 = 3n1. Since the overall capacity of the E2E framework is determined by the channel, the capacity of the one-user case is K times the capacity of each user in the K-user case. With the emergence of more users, it is necessary to increase the output dimension of T-ANN or decrease the value of M (the bits of information of each encoded data sequence) to ensure that the trained T-ANN and R-ANN of each user can achieve independent encoding and decoding without affecting the other users. Notably, in this work, we experimentally validated the deep-learning-based multi-user E2E framework in the three-user case as proof of concept. In theory, the number of supported users can be extended by increasing the output dimension of the T-ANN and the number of the T-ANN and R-ANN pairs when training in the AE network. However, as the user number increases, the input and output lengths of the ACM should also increase to connect to the T-ANN and R-ANN. The ACM cannot guarantee prediction accuracy when predicting a longer received signal. The prediction error causes the trained E2E framework to mismatch with the real channel and reduces the performance of the E2E communication. Training the high-accuracy data-driven channel model with a limited amount of data and model scale is still difficult and needs to be further investigated. The inaccurate ACM limits the number of supported users in the experimental system.
Table 1. The AE network structure for the K-user E2E framework
3.3 Network retraining
The training of AE aims to empower the T-ANN and R-ANN to encode the transmitted information into the signal robust to interference and decode the received signal with high accuracy, respectively. To do this, the AE network should embed an accurate ACM so that the AE can check the true deviation of its output and make rectification on its weights in the training process, making the T-ANN and R-ANN robust to the impairment and interference from a real channel. We apply a two-step retraining (TSRT) method to improve the accuracy and robustness.
The initial ACM only learns the coarse channel response of the fiber-MMW integrated system from the randomly generated Tx and the corresponding Rx’ data. The T-ANN encoded signal has a different distribution from the random Tx data used for training the initial ACM. Therefore, the initial ACM cannot accurately reflect the channel effects on the encoded signal, which causes sub-optimal parameters in the T-ANN and R-ANN [18]. Updating the weight of the ACM iteratively is necessary to guarantee a more precise prediction and thus a better performance of the E2E system. We utilize the TSRT technique in the training process of the ACM and AE. In the first step, the initial ACM is trained using the randomly generated Tx data and the corresponding ILPF-filtered Rx’ data. After training the AE with the initial ACM, we transmit the encoded signal of the T-ANN in the fiber-MMW integrated channel and obtain the received signal. In the second step, the encoded signal together with the received signal after ILPF serve as the new Tx and Rx’ data in the training process of Fig. 2. The initial ACM is retrained using the new Tx and Rx’ data, improving the prediction accuracy of the channel effects on the encoded signal. Subsequently, we restart the weight updating of the previously trained AE with the retrained ACM. Although the weight updating of T-ANN results in a new encoded signal, adjusting the encoded signal is a fine-tuned process. The retrained ACM still predicts the channel response of the newly encoded signal more accurately than the initial ACM. Owing to the use of TSRT, the retrained ACM facilitates the production of more robust T-ANN and R-ANN that achieve a more accurate compensation and performance gain in the E2E fiber-MMW integrated communication experiments.
The TSRT process of our E2E frameworks is conducted by the Adam optimizer [26]. In Fig. 3 and Fig. 4, the training symbol sequence of each user contains 16384 symbols, which is a pseudo-random bit sequence (PRBS) generated by the Mersenne twister algorithm with different seeds. The initial training data of the ACM is also a random sequence containing 16384 samples ranging from –1 to 1. In each step, we train the ACM and AE with a batch size of 256 for 60 epochs, which is enough for the model to reach convergence. In the deployment phase, the symbol sequence of each user is generated with a different seed to prevent the R-ANN from recognizing the pattern of one specific PRBS.
4. Experiment and results
In this section, we provide the details of the deep-learning-based E2E framework in our test bed and experimentally validate the performance of the proposed E2E framework in a fiber-MMW integrated platform.
4.1 Experimental setup
The experimental setup of our deep-learning-based E2E fiber-MMW integrated communication system is shown in Fig. 6(a). In the deployment phase, the trained T-ANN and R-ANN are separately applied in the transmitter and receiver of the system. On the transmitter side, one-hot vectors are used for the random symbol sequence coding and fed into the T-ANN to generate the encoded baseband signal offline first. Different seeds of PRBS are used in this deployment phase to avoid overfitting. After a parallel to serial conversion, frequency-domain signal processing is applied. As shown in Fig. 6(a), after FFT process, the signals are filtered by a notch filter to remove the harmonics (HMNF), an ILPF to remove the high-frequency noise, and finally transformed back into the time domain to obtain the transmitted signal. The transmitted signal is generated through a 120 GSa/s DAC and amplified by the electrical amplifier (EA) before the optical signal modulation by using a Mach-Zehnder modulator (MZM). 10-km single-mode fiber (SMF) is applied for fronthaul transmission before the receiver-side photodiode (PD). Figure 6(b) shows the optical spectrum of the transmitted signal. Then, the intermediate frequency (IF) signal is up-converted into an MMW signal with the 88.8 GHz local oscillator (LO) generated by a 6x frequency multiplier from a 14.8 GHz source and boost-amplified by a W-band power amplifier (PA). A pair of horn antennas are employed for wireless transmission. As a proof-of-concept, 1-m wireless transmission is applied. The down-conversion at the user side is carried out by a second mixer. The received IF signal is then captured by an oscilloscope for further offline DSP. Figure 6(c) shows the electrical spectrum of the received signal, in which we can find the frequency leakage from the frequency multiplier at 14.8 GHz. The received signal is filtered by an ILPF in the frequency domain, serial-to-parallel converted, and sent to the R-ANN for decoding. To compensate for the imperfect channel modeling of the ACM, we employ 30% of the Rx’ and Tx data to fine-tune the receiver ANN. The remaining 70% of the data is used to evaluate the performance of fine-tuned R-ANNs. The outputs of R-ANNs are converted to binary vectors before the BER performance evaluation.
Fig. 6. (a) Experimental setup of the deep-learning-based E2E framework; (b) optical spectrum of the transmitted signal; (c) electrical spectrum of the transmitted and received signals.
We apply the SC-QAM scheme as the baseline for performance comparisons with the E2E framework. In our baseline scheme, the 32-QAM symbol is generated and pulse-shaped by a square-root raised-cosine (RRC) filter with a roll-off of 0.3 and 13 samples per symbol to form the transmitted signal. The data rate of the SC-QAM signal is also 46.2 Gbit/s. After propagating through a back-to-back (BtB) and 1-meter MMW channel, the received signal is processed by a third-order Volterra nonlinear equalizer (VNE) to mitigate the linear and nonlinear distortions [27]. The equalized signal is filtered by a matching RRC filter and down-sampled to get the recovered symbols.
4.2 Modeling the channel
Before optimizing the E2E framework, we should first obtain an accurate channel model, namely, the data-driven differentiable ACM. The ACM is trained with experimental data collected from the fiber-MMW integrated platform shown in Fig. 6(a). Figure 7 provides the grid search results when adjusting the input and output length of ACM. The ACM has a lower prediction error when its input and output lengths are chosen from the circled-out optimal range. According to the network configuration in Table 1, since the ACM input length is set to (2N + 1)·nK, we adjust the values of N and nK to make (2N + 1)·nK locate in the optimal range. The ACM output should propagate the memory information to R-ANN, so an optimal output length also needs to search for the fiber-MMW communication system. As M × 1 one-hot vectors are encoded into nK × 1 data sequences in the T-ANN, M and nK determine the oversampling rate and spectrum efficiency of the transmitted signal in our AE network. We choose n1 = 13, and M = 32 to achieve the highest data transmission for the single-user E2E communication under the 7% HD-FEC threshold. The data rate of the single-user E2E framework can be calculated as 120/13·log2(32) = 46.2 Gbit/s. The output length of ACM is also chosen in the optimal range to provide accurate channel memory information for R-ANN. In summary, we choose N = 15 and l = 52 for the single-user E2E framework to construct the ACM input and output layer respectively with 403 and 52 nodes. As for the three-user case, we choose n3 = 39, M = 32, N = 5, and l = 52 to ensure the three-user E2E framework achieves the same data rate as the single-user case.
Figure 8(a)(c) shows the predicted waveform of the ACM constructed with the optimized parameters and based on the received data with and without ILPF. The ILPF reduces the high-frequency noise and improves the learning accuracy of the ACM. Figure 8(b)(d) shows the frequency domain predicted results of the ACM. The mismatch error between each predicted spectrum and the received spectrum is calculated as
where $\tilde{Y}$ denotes the spectrum of the ACM predicted result, and Y denotes the spectrum of the real received signal. Due to the severe frequency leakage at 29.6 GHz and other high-frequency noise, applying the received signal with full spectrum as the label of the ACM directly will increase the prediction mismatch error. The mean mismatch error of ACM trained without ILPF is 88% higher than that with ILPF and the maximum mismatch error is at 29.6 GHz. ILPF keeps the learning process of ACM within the signal bandwidth, therefore, significantly reducing the prediction mismatch error and improving the accuracy of ACM.Fig. 8. Predicted waveform of the ACM trained with the received data (a) with ILPF and (c) without ILPF; predicted frequency response of the ACM trained with the received data (b) with ILPF and (d) without ILPF.
4.3 Performance of the E2E autoencoder framework for single-user
In this section, we study the performance of the E2E Autoencoder framework for the signal-user case. Figure 9(a) shows the spectrum of the encoded signal after parallel to serial conversion, after HMNF, and after HMNF & ILPF in Fig. 6(a). Owing to the block-based concatenation of adjacent encoded sequences, the encoded signal after parallel to serial conversion has strong harmonics at frequencies that are multiples of the symbol rate. These harmonics introduce extremely high power at specific frequencies and cause large errors in the training process of the ACM as shown in Fig. 9(b). Furthermore, we also show the MSE reduction by using TSRT. Together with the application of HMNF & ILPF, the prediction errors on the received encoded data are feedback to the initial ACM for retraining in the TSRT process. The retraining helps ACM update its weights to fit the new distribution of the Tx data, improving the prediction accuracy of the channel effects on the T-ANN encoded signal. Figure 9(c) gives the validation MSE of ACM trained with HMNF when Vpp increases from 75 mV to 500 mV. The ACM operates well at the high SNR linear region as Vpp increase from 75 mV to 225 mV. However, the nonlinear effects of the amplifiers cause the prediction error of the ACM to increase when Vpp grows higher than 225 mV. The trend of this curve suggests that the ACM is appropriate for operating at the near-linear region.
Fig. 9. (a) Spectrum of the encoded signal after parallel to serial transformation, after NF, and after NF & ILPF; (b) validation losses of the ACM initially trained with and without HMNF, retrained with and without HMNF; (c) validation loss of the ACM initially trained with HMNF under different Vpp.
The 32 encoded data sequences before and after transmission are shown in Fig. 10. Each encoded sequence has a specific pattern, which consists of thirteen pulses with time-dependent amplitude variations. Figure 11(a) shows the BER performance of the E2E framework versus the peak-to-peak voltage (Vpp) under different training strategies, and here we set the received optical power (ROP) to 0 dBm in the BtB case with wireless delivery. The BER decreases as the signal Vpp increases until an optimal value is reached. This is because when the power of the driving signal is too high, EA saturation will introduce nonlinearity. As the harmonics reduce the accuracy of the ACM, the performances of the E2E system trained with the harmonics are even worse than the SC-QAM scheme. The performance of the E2E autoencoder framework is improved by applying the HMNF and the TSRT strategy. With a more accurate ACM, the E2E autoencoder framework shows better results compared with SC-QAM. Therefore, in the rest of this work, HMNF and TSRT are applied for the E2E autoencoder framework for performance study.
Fig. 10. The encoded sequence from the T-ANN (Tx symbol) and the encoded sequence after transmission (Rx symbol).
Figure 11(b) shows the BER performances of SC-QAM and E2E autoencoder frameworks versus the received optical power. To study the generalization of the proposed training strategy, we test the BER performances of the E2E autoencoder framework under three different channel configurations, including the BtB case with wireless delivery, 10-km fiber transmission without wireless delivery, and 10-km fiber with wireless delivery together. The SC-QAM scheme is evaluated in the BtB case with wireless delivery. We only train the E2E framework under the 10-km fiber-wireless transmission case and test it under the three channel configurations. The performances of the single-user E2E framework with the three configurations are summarized in Fig. 11(b). The E2E framework in the three cases achieves similar BER performances that are better than the SC-QAM scheme, which suggests the E2E framework is robust to the channel condition change. Due to the fiber dispersion, the E2E framework in the 10-km fiber-wireless case and 10-km fiber case suffers a slight performance degeneration compared to the BtB case. Since the E2E framework is trained under the 10-km fiber-wireless transmission case, the ACM embedded in the E2E framework mismatches with the channel in the 10-km Fiber case. Therefore, the E2E framework tested in the 10-km fiber shows worse performance than in the 10-km fiber-wireless case. Compared to the SC-QAM scheme, the single-user E2E framework in the 10-km E2E case achieves over 3.5 dB sensitivity gain in the receiver.
4.4 Performance of the E2E autoencoder framework for multi-user
In this section, we study the experimental performance of the E2E autoencoder framework for the three-user case. Figure 12 shows the in-band spectrum of the auto-encoded signal for each user. The spectra of the three users have different power distributions in frequency domain. The T-ANN encodes the information of three users into three orthogonal bases so that the corresponding R-ANN can extract the information from the combined multi-user signals. Figure 13(a) shows a portion of the encoded signal for each user and the received waveforms containing the information of three users. Figure 13(b) shows the 32 encoded outputs from the T-ANN for each user (U1, U2, U3). It shows that the T-ANNs encode the information of the three users on the pulse amplitudes and positions.
Fig. 13. (a) The detail of the encoded signal for each user and the received signal that contains the information of three users. (b) All 32 possible encoded data sequences from the T-ANN (the Tx symbol).
Figure 14(a) shows the relationship between the BER of the multi-user E2E framework and the signal Vpp when the ROP is 0 dBm. Here we tested the BER of each user and the average BER of the three users, and compared it with the SC-QAM signal under different driving voltages. The optimal driving Vpp is found at 175mV with the best BER performance for the three-user E2E autoencoder framework. As the Vpp increase, both the SC-QAM scheme and the E2E framework suffer nonlinear impairments, while the E2E autoencoder framework shows better performances. Then we study the BER performance of the E2E autoencoder framework for three-user as a function of ROP under three channel configurations. In Fig. 14(b), the multi-user E2E framework in the 10 km E2E case achieves very similar BER performance to the 10 km Fiber case, while their performances are both worse than the BtB E2E case. To support multi-users, a 3x times longer symbol period is applied to each encoding sequence. Therefore, more errors occur in one encoding sequence after fiber transmission due to chromatic dispersion. As the same R-ANN structure with the same hidden layers is used compared to that of the single-user framework, it reduces the training accuracy and causes a sensitivity penalty. The E2E framework in all three cases achieves better BER performances than the SC-QAM scheme when the ROP is larger than -4 dBm. In low ROP conditions, the deep-learning-based E2E framework is sensitive to the low SNR data and thus suffers significant performance penalties. As the ROP increase, the three-user E2E framework achieves a 1.5 dB sensitivity gain over the SC-QAM scheme.
4.5 Further analysis
We compare the performance of the E2E framework according to signal Vpp in Fig. 11(a) and Fig. 14(a), the BER of the three-user framework is lower than that of the single-user E2E framework. Figure 15(a) shows the peak-to-average power ratio (PAPR) of the encoded waveform when the E2E framework is trained under the Vpp of 195 mV. The PAPR of the encoded waveform from the multi-user framework is smaller than that of the single-user framework, which is also reflected by Fig. 15(b)(c). However, the PAPR reduction becomes negligible when the number of users increases to more than three. Continuing to increase the user number will significantly expand the scale of the E2E network but brings limited PAPR reduction as shown in Fig. 15(a). Additionally, as analyzed in Section 3.2, ACM accuracy is another factor that needs to consider when increasing the network scale. Therefore, the performance of the multi-user system depends on the signal PAPR, network scale, and ACM accuracy.
Fig. 15. (a) PAPR comparison of the encoded waveform in different user cases; value distribution of the encoded waveform in (c) single-user and (d) three-user E2E framework.
It should be noticed that the ACM needs to frequently retrain to maintain the prediction accuracy under dynamic wireless channels. We have utilized a similar two-step fine-tuning technique [17] to train the ACM. The retraining process increases computational complexity. Therefore, the proposed framework in the current study faces challenges in more dynamic channels. More effective learning techniques that reduces the complexity based on smaller samples, for example, the meta-learning-aided online training in [28] for MIMO-OFDM system and in [29] for E2E communication system, are worth further study for ACM retraining under different channel conditions in future work. Though the E2E framework achieves promising performance in the experiments, training the E2E framework is still complex work. To be clear, Table 2 lists the detailed computational cost of the E2E framework per symbol in one epoch. With the specific value in our experiment, the computational cost of the E2E Framework for the single-user needs 1.06 × 1012 multiplications and 1.07 × 1012 additions in the training phase, 1.17 × 1010 multiplications and 1.16 × 1010 additions in the deployment phase. The three-user E2E Framework needs 1.29 × 1012 multiplications and 1.25 × 1012 additions in the training phase, 1.51 × 1010 multiplications and 1.43 × 1010 additions in the deployment phase. As RAN is short of computing resources, it is necessary to consider the additional computing complexity brought to the system in practical applications. Network pruning and transfer learning have been reported to be effective in reducing the computation complexity in the E2E framework [30,31], which will be studied in our future work.
Table 2. The complexity analysis of the E2E framework
5. Conclusion
In this study, we evaluated a deep-learning-based E2E framework for the fiber-MMW integrated communication system. By flexibly adjusting the number of T-ANN and R-ANN pairs when training in the AE network, the framework supported single- and multi-user E2E communication in the fiber-MMW integrated platform. We used multiple training techniques to improve the prediction accuracy of the ACM, including the ILPF to filter the noise in the received data, by using NF to mitigate the influence of HM and applying a two-step RT strategy. The improved ACM provided a gradient BP path between the T-ANN and R-ANN when training the E2E framework. An experimental 46.2 Gbit/s 10-km fiber-MMW hybrid transmission was demonstrated to evaluate the enhanced performance of the proposed E2E framework. Compared with the SC-QAM scheme, the E2E framework achieved over 3.5 dB receiver sensitivity gain in the single-user case and 1.5 dB sensitivity gain in the multi-user case under the 7% HD-FEC threshold. Since the ACM has difficulty accurately predicting long received sequences, we only demonstrated the three-user E2E communication as proof of concept to validate the feasibility of the learning-based multi-user E2E framework for the fiber-MMW integrated system. In future work, the proposed E2E framework can be trained to support more users after the development of an advanced differential channel model to allow long sequence prediction.
Funding
National Natural Science Foundation of China (62171137, 62235005, 61925104); Natural Science Foundation of Shanghai (21ZR1408700); Major Key Project PCL.
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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