Neural Network-Based Fading Channel Prediction: A Comprehensive Overview <s> C. AUTOREGRESSIVE MODEL <s> In wireless communication systems, the direct signal and the reflected signals form an interference pattern resulting in a received signal given by the sum of these components. They are distinguished by their Doppler shifts at the mobile. Since the parameters associated with these components are slowly varying, the fading coefficients can be accurately predicted far ahead. This novel approach to fading channel prediction is combined with transmitter signal optimization to mitigate the effects of "deep fades", which severely limit the performance of mobile radio systems. This capability will potentially help to reduce power requirements for wireless channels and improve the system performance. <s> BIB001 </s> Neural Network-Based Fading Channel Prediction: A Comprehensive Overview <s> C. AUTOREGRESSIVE MODEL <s> Autoregressive stochastic models for the computer simulation of correlated Rayleigh fading processes are investigated. The unavoidable numerical difficulties inherent in this method are elucidated and a simple heuristic approach is adopted to enable the synthesis of accurately correlated, bandlimited Rayleigh variates. Startup procedures are presented, which allow autoregressive simulators to produce stationary channel gain samples from the first output sample. Performance comparisons are then made with popular fading generation techniques to demonstrate the merits of the approach. The general applicability of the method is demonstrated by examples involving the accurate synthesis of nonisotropic fading channel models. <s> BIB002 </s> Neural Network-Based Fading Channel Prediction: A Comprehensive Overview <s> C. AUTOREGRESSIVE MODEL <s> Knowledge of future channel conditions can increase the performance of many types of wireless systems. This is especially true for radio channels with multiple transmit and receive antennas, i.e., multiple-input multiple-output (MIMO) systems. This paper derives a performance bound for MIMO channel prediction. It is assumed that prediction is based upon estimating a model for the channel and then extrapolating that model to predict future values of the channel. A vector formulation of the Crame/spl acute/r-Rao bound for functions of parameters is used to find a lower bound on the prediction error. Numerical evaluation of this bound shows that substantially longer prediction lengths are possible for MIMO channels than for single antenna channels. An intuitive interpretation of this result is that more of the channel structure is revealed when using multiple antennas at both ends. Finally, the longer prediction lengths for MIMO channels are confirmed by numerical results obtained by implementing a MIMO extension of a single-antenna prediction scheme. <s> BIB003 </s> Neural Network-Based Fading Channel Prediction: A Comprehensive Overview <s> C. AUTOREGRESSIVE MODEL <s> In this paper, we analyze the outage probability and diversity order of opportunistic relay selection in a scenario based on decode and forward and where the available channel state information (CSI) is outdated. The study is conducted analytically by obtaining a closed-form expression for the outage probability, which is defined as the probability that the instantaneous capacity is below a target value. We derive high-SNR approximations for the outage probability. By doing so, we demonstrate that the diversity order of the system is reduced to 1 when CSI is outdated, being this behavior independent of the level of CSI accuracy. A physical explanation for this extreme loss of diversity is provided along with numerical results to support the analytical study. <s> BIB004 </s> Neural Network-Based Fading Channel Prediction: A Comprehensive Overview <s> C. AUTOREGRESSIVE MODEL <s> The concept of physical layer security builds on the pivotal idea of turning the channel’s imperfections, such as noise and fading, into a source of security. This is established through appropriately designed coding techniques and signal processing strategies. In this vein, it has been shown that fading channels can enhance the transmission of confidential information and that a secure communication can be achieved even when the channel to the eavesdropper is better than the main channel. However, to fully benefit from what fading has to offer, the knowledge of the channel state information at the transmitter (CSIT) is of primordial importance. In practical wireless communication systems, CSIT is usually obtained, prior to data transmission, through CSI feedback sent by the receivers. The channel links over which this feedback information is sent can be either noisy, rate-limited, or delayed, leading to CSIT uncertainty. In this paper, we present a comprehensive review of recent and ongoing research works on physical layer security with CSIT uncertainty. We focus on both information theoretic and signal processing approaches to the topic when the uncertainty concerns the channel to the wiretapper or the channel to the legitimate receiver. Moreover, we present a classification of the research works based on the considered channel uncertainty. Mainly, we distinguish between the cases when the uncertainty comes from an estimation error of the CSIT, from a CSI feedback link with limited capacity, or from an outdated CSI. <s> BIB005 </s> Neural Network-Based Fading Channel Prediction: A Comprehensive Overview <s> C. AUTOREGRESSIVE MODEL <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> BIB006
Alternatively, the discrete-time impulse response of a time-varying channel can be modelled as an autoregressive process and a Kalman filter (KF) is utilized to estimate AR coefficients so as to build a linear predictor, which extrapolates future CSI by combining weighted current and a series of past CSI BIB001 -  . According to BIB002 , a complex AR process of order p denoted by AR(p) can be generated via a time-domain recursion where w[n] denotes zero mean complex Gaussian noise with the variance of σ 2 p , and {a 1 , a 2 , . . . , a p } are AR coefficients. The corresponding power spectral density (PSD) of the AR(p) process is For Rayleigh multi-path channels, the theoretical PSD associated with either in-phase or quadrature part of a fading signal has an U-shaped band-limited form where f d is the maximum Doppler shift in Hertz. For the purpose of digital processing, the discrete-time autocorrelation function is provided by  where and Substituting the value of f m into (12)  where one-step ahead prediction can be obtained, in comparison with the continuous-time prediction provided by BIB004 . By processing a MIMO channel as a set of parallel SISO channels, ignoring the spatial dimension of arrays, (18) is able to extend to MIMO channels: where denotes the Hadamard product that is the element-wise multiplication of two matrices with same dimension, and the coefficient matrix A k is defined as and the entry a k n r n t represents the k th coefficient of the AR filter for the subchannel between transmit antenna n t and receive antenna n r . In comparison with the parametric model, the number of parameters required to estimate in the AR model is substantially reduced to only one, i.e., f d . The estimation process from BIB005 to (16) is notably simpler than that of the parametric model. Despite its simplicity, the AR model has some limitations: 1) It can only deal with the temporal correlation of a single-antenna channel, whereas the spatial dimension of antenna array is not able to exploit. 2) The predictor in BIB002 and BIB006 only enable one-step predictionĤ[t+1] rather than multi-stepĤ [t+D] . Although long-range prediction can be realized by recursively reusing predicted values at previous time instants, the problem of error propagation is raised. 3) Until now, reliable and accurate estimation for f d is still difficult from the practical perspective. The authors of BIB003 provided a performance bound for prediction of MIMO channels and revealed that the AR model is still significantly far away from that bound, indicating that other more efficient prediction schemes probably exist and a further exploration is of theoretical and practical interest, which will be the aim of RNN-based prediction introduced in the next section.