Neural Network-Based Fading Channel Prediction: A Comprehensive Overview <s> A. PERFORMANCE <s> Multiple-input multiple-output (MIMO) communication may provide high spectral efficiency through the deployment of a very large number of antenna elements at the base stations. The gains from massive MIMO communication come from the use of multiuser MIMO on the uplink and downlink, but with a large excess of antennas at the base station compared to the number of served users. Initial work on massive MIMO did not fully address several practical issues associated with its deployment. This paper considers the impact of channel aging on the performance of massive MIMO systems. The effects of channel variation are characterized as a function of different system parameters assuming a simple model for the channel time variations at the transmitter. Channel prediction is proposed to overcome channel aging effects. The analytical results on aging show how capacity is lost due to time variation in the channel. Numerical results in a multiceli network show that massive MIMO works even with some channel variation and that channel prediction could partially overcome channel aging effects. <s> BIB001 </s> Neural Network-Based Fading Channel Prediction: A Comprehensive Overview <s> A. PERFORMANCE <s> Prior research has shown that delayed channel state information (CSI) severely degrades the throughput performance of multi-user (MU) multiple-input multiple-output (MIMO) transmission, resulting in a preference for single-user (SU) transmission. This paper investigates how the relative performance of MU-MIMO and SU-MIMO is affected by 1) different Doppler spectra, and 2) high-order prediction methods for channel estimation. Simulation results reveal that the often-used Jakes-Clarke spectrum is the worst case for MU performance. By evaluating the impact of other Doppler spectra and high-order channel prediction on MU-MIMO performance, we demonstrate that MU can tolerate larger CSI delays and retain its theoretical advantage over SU in practice. <s> BIB002 </s> Neural Network-Based Fading Channel Prediction: A Comprehensive Overview <s> A. PERFORMANCE <s> This paper investigates how to train a recurrent neural network (RNN) using the Levenberg–Marquardt (LM) algorithm as well as how to implement optimal control of a grid-connected converter (GCC) using an RNN. To successfully and efficiently train an RNN using the LM algorithm, a new forward accumulation through time (FATT) algorithm is proposed to calculate the Jacobian matrix required by the LM algorithm. This paper explores how to incorporate FATT into the LM algorithm. The results show that the combination of the LM and FATT algorithms trains RNNs better than the conventional backpropagation through time algorithm. This paper presents an analytical study on the optimal control of GCCs, including theoretically ideal optimal and suboptimal controllers. To overcome the inapplicability of the optimal GCC controller under practical conditions, a new RNN controller with an improved input structure is proposed to approximate the ideal optimal controller. The performance of an ideal optimal controller and a well-trained RNN controller was compared in close to real-life power converter switching environments, demonstrating that the proposed RNN controller can achieve close to ideal optimal control performance even under low sampling rate conditions. The excellent performance of the proposed RNN controller under challenging and distorted system conditions further indicates the feasibility of using an RNN to approximate optimal control in practical applications. <s> BIB003 </s> Neural Network-Based Fading Channel Prediction: A Comprehensive Overview <s> A. PERFORMANCE <s> Accurate channel state information (CSI) is a prerequisite to reap the benefits of fading-adaptive wireless communications. In practice, however, the available CSI is generally outdated due to processing and feedback delays, which deteriorate system's performance severely. Channel prediction that is able to forecast future CSI provides a promising solution. In addition to statistical methods, namely modelling a time-varying channel as an autoregressive process and using a Kalman filter to predict, artificial intelligence techniques with the capability of time-series prediction are also being discussed recently. This paper compares performance and complexity of these two kinds of predictors. The numerical results on prediction accuracy measured by mean squared error in both noiseless and noisy Rayleigh fading channels, together with their achieved performance in a transmit antenna selection system, are comparatively illustrated. <s> BIB004
In a 4×1 ULA system, 3GPP Extended Pedestrian A (EVA) and Extended Typical Urban (ETU) models with maximal Doppler shifts of f d =70Hz and 300Hz, respectively, also notated as EVA70 and ETU300, are applied to generate channel samples. Using a signal bandwidth (or sampling rate) of 1MHz, a frequency-selective channel is converted into N =64 sub-carriers via the OFDM modulation, resulting in a sub-carrier spacing around f =15KHz that is compliant with 3GPP LTE standard. From the observations in simulations, a 3-layer RNN with N H =10 hidden neurons and d=3 tapped delay is adopted. To train this network, a data set consisting of a series of channel samples during a length equivalent to 10 channel's coherence time is extracted. Starting from an initial state with random values, the weights and biases are iteratively updated by Levenberg-Marquardt BIB003 algorithm. The train can be conducted in an off-line manner or rely on other computation-intensive nodes, such as mobile edge computing platform, and then the trained RNN is deployed online for predicting instantaneous channels. In contrast, the AR model does not need a training process. Given the value of f d , the filter coefficients in BIB004 can be figured out. The simulation parameters are summerized in Table 1 . The outage probability defined as where Pr is the notation of mathematical probability and R means a target end-to-end data rate that is set to 1bps/Hz as usual, is employed to measure the performance of the prediction-aided MIMO-OFDM system. The following four different TAS strategies are compared: • The perfect mode where the best antenna for sub-carrier n at time t+D is chosen according to the perfect CSĨ H n [t+D], despite it never exists in practice owing to delay and noise. • The outdated mode in a traditional TAS system, making a selection decision based on the outdated CSIH n [t]. • The prediction mode takes advantage of the predicted CSIĤ n [t+D] that may closely approximateH n [t+D]. • The random mode that randomly selects an antenna without any consideration of CSI. The assessment is first carried out in independent and identically distributed (i.i.d.) noiseless EVA70 channels, where channel samples used to train the predictors are obtained without the impose of additive noise. The predictors are set to a multi-step mode of D=16, corresponding to a prediction length of around 1ms. Fig. 4a compares outage probabilities for the various selection strategies in the MIMO-OFDM system. The outdated CSI substantially degrades the system performance, with a relative SNR loss of around 5.5dB at P(R)=10 −3 with respect to the perfect mode. The AR model with p=1 denoted by AR(1) achieves the optimal performance as same as that of the perfect mode, followed by the RNN that have a prediction gain of over 3dB compared with the outdated mode. Although AR(1) outperforms the RNN, the performance of other AR predictors are quite differentiated. AR BIB002 and AR(3) have identical performance that is comparable to that of the outdated mode, while the AR(4) got a very worse result, with an SNR loss on the order of 10dB. To check the effect of channel correlation, we apply the matrix (see Table 1 ) recommended in 3GPP LTE standard [49] to generate correlated channel samples. Under the medium correlation indicated by α=0.3, the curves of outage probabilities for various selection strategies are comparatively drawn in Fig. 4b . In contrast to the results in i.i.d. channels illustrated in Fig. 4a , the system performance degrades collectively. That is because the available spatial diversity gain vanishes gradually with the increase of channel correlation, independently of the application of predictors. Actually, the correlation has no impact on the relativity of superiority and inferiority among the predictors. In practice, the obtained CSI is impaired by estimation errors because additive noise cannot be avoided. Under the working assumption that the signal-to-noise ratio (SNR) on pilot symbols is 20dB, the simulations in noisy ETU300 channels are also conducted. To adapt to faster channel fluctuation, the number of prediction steps is reduced to D=4, corresponding to a prediction length of 0.25ms. The results reveal that noise has a notable impact on the system performance, especially when the predictor is based on a high order AR model. As shown in Fig. 5a , the curve of AR (4) is overlapped with that of the random mode, while AR(3) also approximates them. That is to say, the AR model suffers severely from the problem of error propagation. In contrast, the RNN performs in a more stable manner and is more robust against noise compared to AR BIB002 and AR BIB001 , in comparison with their behaviours in noiseless channels in Fig. 4a . It still VOLUME 7, 2019 receives a prediction gain of over 2dB at outage probabilities on the order of 10 −3 compared with the outdated mode. In addition to estimation error due to additive noise, the interpolation error that is defined as the difference between the perfect CSI and the interpolated CSI should be taken into account. Without loss of generality, the performance results for the MIMO-OFDM system having a pilot insertion interval of N P =4 are illustrated in Fig. 5b . The interpolation has a negligible impact on the performance of the RNN predictor, while the AR predictors are substantially affected. The RNN remarkably outperforms the AR predictors with an SNR gain of at least 5dB at P(R)=10 −3 and has a loss of nearly 2dB compared with the perfect mode. In addition to outage probability, the prediction accuracy is also compared in terms of MSE, which is defined as where N is the total number of data samples used for evaluation,Ĥ[n] denotes the predicted channel matrix at time step n, and H[n] stands for its actual value. The MSE results of the RNN and the AR models with a filter length of p = 1, 2, 3, and 4 in EVA70 channels are obtained, as listed in Table 2 . The RNN has the best accuracy in noiseless and interpolated cases, while also achieving sub-optimal accuracy that very approaches the best values in noisy and correlated cases. In a nutshell, it can be concluded that the RNN predictor is effective to combat the outdated CSI in both independent and correlated channels, and shows strong robustness against additive noise and interpolation errors.