Machine Learning-Based Digital Pre-Distortion Scheme for RoF Systems and Experimental 5G mm-waves Fiber-Wireless Implementation

Abstract The advent of the 5th generation of mobile networks brought a large number of new use case and applications to be supported by the physical layer (PHY), which must be more flexible than all previous radio access networks (RAN). The concept of the centralized RAN (C-RAN) allows all the baseband processing to be performed in the central office, simplifying the network deployment and also allowing the operators to dynamically control the PHY according with the applications requirements. The radio-frequency (RF) signal generated by the C-RAN can be transported to the remote radio unit (RRU) by using a radio over fiber (RoF) system. In this paper, we propose two RoF approaches for composing the transport and access networks of the next-generation systems. The first investigation relies on the implementation of a machine learning-based digital pre-distortion (DPD), designed for RoF systems. In the second approach, we implement an RoF system and characterize the optical and electrical power levels aiming to reduce the RoF non-linear distortions. The overall link performance is evaluated by measuring the error vector magnitude (EVMRMS) and 590 Mbit/s is achieved with EVMRMS as low as 4.4% in a 10 m reach cell.


I. INTRODUCTION
Mobile communication systems have been continuously evolving to support new communications features and enhance user experience.The introduction of the fifth-generation of mobile network (5G) has been remodeling the way that society uses telecommunication systems.The previous mobile networks, especially the third and fourth generations (3G and 4G) were mainly focused on redesigning the radio access network (RAN) in order to increase the system throughput.On the other hand, the 5G networks aim to bring innovative services and applications, favoring new vertical services, such as security improvement, agribusiness, vehicular communications, logistics, education, and health.These new applications and services impose contrasting and conflicting requirements to the physical layer (PHY), which must be flexible to be dynamically adapted for each scenario [1]- [4].
The optical/wireless convergence brings remarkable advantages, in particular, radio over fiber (RoF) technology is a key solution for transporting high-speed communications signals.The aforementioned RoF system can reduce the deployment and operational costs of mobile networks in remote areas.However, it is necessary to assure that the signals' characteristics at the RoF output, such as root mean square error vector magnitude (EVM RMS ) and out-of-band emission (OOBE), must be preserved.This means that the non-linearities introduced by the MZM must be compensated and the DPD is an efficient approach to achieve this goal.Conventional DPD schemes are very complex [15] and might require re-calibration over time.Therefore, we are proposing an ML linearization solution that is based on a linear regression technique.The employed artificial neural network (ANN) is composed of at least one input layer, one hidden layer, and one output layer, with non-linear activation functions.
The first architecture investigated in this paper is a multi-layer perceptron (MLP) ANN, which is the simplest ANN presented in the literature.In the MLP architecture, the neurons are densely connected.Each connection has its adjustable weights and bias.During the ANN training, the weights and bias parameters are adjusted accordingly to the backpropagation algorithm.In summary, the backpropagation training method uses a loss function to estimate the discrepancy between the ANN desirable training label and the ANN estimated output.During the training, the goal is to reduce the aforementioned discrepancy by updating the weights and bias set of parameters.The details of the architecture used to build the ML-based linearization scheme are presented below.

B. Artificial Neural Network Training
Fig. 1 illustrates the ANN training process.The desirable training labels consist of samples from a baseband orthogonal frequency division multiplexing (OFDM) signal (x n ), which are given by where d m represents the quadrature amplitude modulation (QAM) symbols that are mapped into M orthogonal subcarriers and n ∈ {0, 1, . . ., N − 1} is the time index.Next, the OFDM signal is applied to the RoF TX block, which is composed by a laser diode (LD) and an MZM.The MZM has a non-linear power response, which can be represented by the base-band memoryless polynomial model, defined as [17] y where h k is the kth model coefficient, with k = 0, 1, . . ., K − 1, in which K is the model nonlinearity order.In this paper, we have used K = 5 to represent the MZM non-linearities.Since we are only interested in the MZM non-linearities, we have assumed that the single-mode fiber (SMF) and photodetector (PD) combined impulse response is g n = δ n , leading to The PD output, z n , is applied to train the ANN, whereas the training labels are the non-distorted OFDM signal, x n .During the training, the ANN learns a function that approximates the RoF TX block post-inversion response, that will be used to pre-distort the OFDM signal.
The proposed ANN is composed of one input layer, two hidden layers, and one output layer.The number of neurons used in the ℓth hidden layer, with ℓ ∈ {1, 2, . . ., L}, is denoted by O ℓ , with O 1 = 64 and O 2 = 32.The input and output layers have two neurons, i.e.O 0 = O L+1 = 2, being one for the real part and the other for the imaginary part of the OFDM signal.Table I summarizes the ANN hyperparameters that were tuned for optimizing the training process.The adaptive momentum (Adam) optimization algorithm was employed for training the ANN.It is well known that an ANN with a single hidden layer is capable of approximating any continuous function if enough data to train the ANN is provided.Considering the non-linear behavior of MZM, an elementary ANN employing non-linear activation functions can represent its non-linearities.Nevertheless, increasing the number of hidden layers also increases the non-linearities representation capability.Therefore, according to our empirical investigation and observations, a MLP ANN with two hidden layers and rectified linear unit (ReLU) activation function were enough to represent the non-linearities imposed by MZM.Furthermore, we have used a data set containing 20480 samples, which was split into a N TR = 14336 training samples and N VAL = 6144 validating samples.An early stop technique was employed to prevent overfitting in the ANN.We have set the patience hyperparameter to 100 and the training is concluded when the a mean-squared error (MSE) variation higher than 10 −9 (∆ min = 10 −9 ) is not observed during 100 epochs.

C. Performance Analysis
After training the ANN, the obtained RoF TX block post-inversion estimation response are used to pre-distort the OFDM signal.Fig. 2 depicts the block diagram of the RoF system, in which the ML-based DPD block are placed between the RF transceiver and the RoF TX block.In this diagram, x n , generated by (1), are applied to the ML-based DPD block, which has its output given by where W is a matrix of weights, x is the input vector, b is the biases vector and ϕ(.) is the nonlinear activation function.It is important to highlight that in the first layer, x is a vector produced by ( 1) containing all N samples and, in the sequential layers, x is the output of the previous layer, since the layers are fully connected in the MLP architecture.The pre-distorted signal, v n , is applied to the RoF TX block, which outputs y n by applying (2) with v n as input.Finally, the linearized version of the OFDM signal is given by (3).At the base station the linearized signal must be upconverted and amplified for the wireless transmission.Fig. 3 presents the magnitude of the RF signal in the discrete time domain, which allows us verify the influence of the DPD scheme in the waveform.The DPD block applies the RoF TX block postinversion response for pre-distorting the OFDM signal.As a result, the cascade response of the DPD block and the RoF TX block produces a linear response.Figs 3 (a) and (b) demonstrate that in the regions in which the non-linear RoF TX block response compress the signal, the DPD expands and vice versa.In other words, in the time-domain, the cascade response of the DPD block and the RoF TX block produces a signal as close as possible to x n .It is well known that OFDM waveform presents a high peak-to-average power ratio (PAPR), which further aggravates the non-linear signal degradation.Once the linearization process produces a signal as close as possible to the original OFDM signal, the The PAPR of the linearized signal will similar to the original signal's PAPR.We have also investigated the DPD effect on the OFDM signal in the frequency domain.Fig 4 (a) illustrates the normalized power spectrum density of the OFDM signal.We can note that our proposed ML-based DPD technique considerably reduces the OOBE, resulting in an adjacent channel leakage ratio (ACLR) 10.5 dB bellow than the non-linearized signal.It is important to highlight that the DPD also reduces the in-band distortions resulting in the desired linear response.The DPD effect can also be seen in the signal constellation.At the optical receiver, a variable optical attenuator (VOA) and an optical power monitor (OPM) ensured 2-dBm optical power at the PD input.The photodetector performed the optical-to-electrical conversion and launched the RF signals to a 24-dB gain broadband electrical amplification stage (EA 1 ).An electrical spectrum analyzer (ESA) has been used to measure the resultant electrical spectrum for both signals, which are presented in the insets (ii) and (iii).Afterward, a diplexer has separated the 5G-NR signals, which were individually transmitted employing proper antennas based on the frequency range.
The signal at 26 GHz has been amplified using (E 3 ) with 35-dB gain before feeding a 25-dBi gain horn antenna.On the other hand, a 20-dB gain amplifier (EA 2 ) has amplified the 3.5 GHz signal, which is subsequently transmitted by a 5-dBi gain log-periodic antenna, giving rise to 10-m wireless access implemented as a proof-of-concept.At the reception side, identical antennas have been used for receiving the 5G-NR signals.Sequentially, the received signals at 3.5 and 26 GHz have been individually amplified by (EA 4 ) and (EA 5 ) with 20-dB gain and 35-dB gain, respectively.Finally, a vector signal analyzer (VSA) has been used for evaluating the FiWi system performance based on EVM RMS .Fig. 6 shows experimental setup photographs, including the transmitter and receiver sides.

IV. EXPERIMENTAL RESULTS
This section presents an experimental investigation regarding the 5G-NR signals transport and transmission using our proposed FiWi System.Firstly, we have evaluated the transport RoF system performance, in terms of EVM RMS , at two distinct setup stages, the photodetector input and the EA 1 output.Sequentially, we have investigated the wireless transmission system by transmitting the 3.5 and 26-GHz signals over a 10-m cell reach as a proof of concept.Fig. 7 shows the EVM RMS measurements as a function of the optical power at the photodetector input for the 3.5 and 26 GHz frequencies.In this analysis, we have used two modulation orders to investigate two distinct standardized 5G-NR bandwidths.Fig. 7 (a) shows the EVM RMS performance for the 3.5-GHz 5G-NR signal modulated using 64/256-QAM and operating with 20 and 50-MHz bandwidths.One can note the EVM RMS has kept below the 3GPP requirements from -16 to 2 dBm optical power for the 64-QAM, whereas for the 256-QAM, the feasible EVM RMS has varied from -12 to 2 dBm.It is worth mentioning the photodetector maximum optical input power has established the superior limiting power (2 dBm).Fig 7 (b) shows the EVM RMS performance for the 26-GHz 5G-NR signal modulated with 16 and 64-QAM and operating with 50 and 100-MHz bandwidths.One can observe the higher operating frequency and bandwidths, in comparison to the 3.5GHz analysis, have required more optical power for achieving the 3GPP requirements, as expected.Finally, we can conclude the best RoF received optical power was about 0 dBm, considering both operating frequencies analyses.Our later analysis has consisted of varying the RF Mach-Zehnder modulator input power and measure the EVM RMS at the EA 1 output, in order to obtain the best RF transmission power.Similarly to the optical power analysis, we have used the same modulation orders and bandwidths for this evaluation.Fig. 8 (a) and (b) report the EVM RMS measure as a function of DD-MZM RF input power for the 3.5 and 26-GHz signals, respectively.The RF input power was varied from -26 to 6 dBm for the 3.5 GHz, whereas for the 26 GHz, the signal input powers varied from -8 to 6 dBm.One can note the EVM RMS has increased for RF power above 1 dBm, decreasing the signal quality for both operating frequencies.This signal degradation occurs due to the DD-MZM non-linear response, which generates significant harmonics and inter-modulation products for powers higher than 1 dBm.One more time, the analyzed signals presented the same modulation orders and bandwidths from the previous results.We have implemented a 10-m reach FiWi system with 0 dBm received optical power at PD input and 0 dBm input RF power, which were the best configuration from our previous RoF performance evaluation.Fig. 9 shows the EVM RMS measurements at the RX side for the 3.5 GHz and 26 GHz.The results show the received signals EVM RMS measurements in the FR1 and FR2 bands, which has achieved EVM RMS as low as 2.2 and 2.7% and 4.2 and 4.4%, respectively.For both operating frequencies, the FiWi system has been capable of recovering the signals with margins.These margins might be used to extend the link reach or to transmit signals with higher bandwidths.The joint transmission of signal with 50 MHz and 100 MHz bandwidths, has enabled attaining 590 Mbit/s throughput.Finally, our setup might be efficiently applied for composing the fronthaul and access networks for future communication systems.The assigned modulation order depends on the user distance from the base stations (BS), i.e., the user located at BS proximity receives the signal with higher modulation order than that one at the cell border.V. CONCLUSIONS This work reported a DPD technique based on a ML algorithm and the implementation of a multiband FiWi system for the next-generation wireless networks.The proposed technique was applied to an OFDM signal and its performance was investigated in terms of EVM RMS and ACLR.The proposed DPD scheme 10.5 dB on the signal ACLR, while improving the EVM RMS from 6.35 to 0.92%.This analysis demonstrated that ML algorithms can have a distinguish role in RoF systems employed in future FiWi communication.
We have also implemented an experimental multi-band FiWi system.In this second analysis, we were specially interested in the experimental validation of an C-RAN-based architecture for future FiWi systems.The results demonstrated our FiWi system as a potential solution for composing the transport and access network of the future communication systems.We reported an optical and electrical power characterization for the RoF transport network.Additionally, it was implemented a 10-m reach cell attaining 590 Mbit/s as a proof of concept.Futures works regard to join our two investigations, which means experimentally implement our proposed ML-based linearization technique in a multi-band 5G FiWi system.

Fig. 9 .
Fig. 9. 5G NR FiWi system EVMRMS measurement as a function of bandwidth in the FR1 and FR2 bands.

Fig 10
Fig 10 illustrates the spectrum and constellation of the received 3.5 and 26 GHz signals after 10 m reach wireless transmission.In both frequency ranges, we have allocated half of the OFDM subcarriers for one user and the other half for a second user, following the orthogonal frequency division multiple access (OFDMA) operating principle.Fig.10 (a) illustrates the 50 MHz bandwidth received signal at 3.5 GHz, whereas Fig.10 (b) exhibit the 100 MHz bandwidth signal at 26 GHz.The assigned modulation orders were 64-and 256-QAM for the signal at 3.5 GHz, and 16-and 64-QAM for the signal at 26 GHz.The assigned modulation order depends on the user distance from the base stations (BS), i.e., the user located at BS proximity receives the signal with higher modulation order than that one at the cell border.

Fig. 10 .
Fig. 10.Spectrum and constellation of the received signal after the wireless transmission: (a) 50-MHz bandwidth signal at 3.5 GHz; (b) 100-MHz bandwidth signal at 26 GHz.

TABLE I .
MULTI-LAYER PERCEPTRON ANN HYPERPARAMETERS.