Neural Network-Based Fading Channel Prediction: A Comprehensive Overview <s> B. PARAMETRIC MODEL <s> 1. Introduction 2. The wireless channel 3. Point-to-point communication: detection, diversity and channel uncertainty 4. Cellular systems: multiple access and interference management 5. Capacity of wireless channels 6. Multiuser capacity and opportunistic communication 7. MIMO I: spatial multiplexing and channel modeling 8. MIMO II: capacity and multiplexing architectures 9. MIMO III: diversity-multiplexing tradeoff and universal space-time codes 10. MIMO IV: multiuser communication A. Detection and estimation in additive Gaussian noise B. Information theory background. <s> BIB001 </s> Neural Network-Based Fading Channel Prediction: A Comprehensive Overview <s> B. PARAMETRIC MODEL <s> In civilian communication systems, the signature sequence of the desired signal in training phase is known to the receiver. In this letter, using the mutual information, we bridge the probability density function and minimum mean-square error (MMSE) between the observed data and training sequence of the desired signal, and then employ the MMSE to construct a minimum description length (MDL) criterion for accurate source enumeration. Numerical results demonstrate that the proposed method is superior to existing MDL methods in terms of detection performance particularly for small number of snapshots and/or source angular separation. <s> BIB002 </s> Neural Network-Based Fading Channel Prediction: A Comprehensive Overview <s> B. PARAMETRIC MODEL <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> BIB003 </s> Neural Network-Based Fading Channel Prediction: A Comprehensive Overview <s> B. PARAMETRIC MODEL <s> A novel prediction scheme for polarized narrowband MIMO channels is proposed in this paper. The prediction scheme is based on estimation of the parameters of a double directional polarized propagation model. The proposed algorithm transforms the channel impulse response matrix in such a manner that a multidimensional extension of the ESPRIT algorithm can be utilized to jointly estimate the angles of arrival, angles of departure, Doppler shifts and complex polarimetric weights of the dominant multipath components. Simulation results show that the proposed algorithm outperforms repeated application of one dimensional ESPRIT based approach with similar computational complexity. <s> BIB004 </s> Neural Network-Based Fading Channel Prediction: A Comprehensive Overview <s> B. PARAMETRIC MODEL <s> This paper investigates the prediction of multiple-input–multiple-output (MIMO) narrow-band multipath fading channels for mobile-to-mobile (M-to-M) wireless communication systems. Using a statistical model for M-to-M communication in urban and suburban environments, we derive a parameterized double directional model and utilize a multidimensional extension of the ESPRIT algorithm to jointly estimate the angles of departure (AoD), angles of arrival (AoA), and effective Doppler frequencies. A simple method is also proposed for mobile velocity estimation. The parameter estimates are then used to forecast the M-to-M channel. The bound on the prediction error is derived using a vector formulation of the Cramer–Rao lower bound (CRLB). Simulations are used to evaluate the performance of the prediction scheme and to compare it to the derived error bound. <s> BIB005
The commonly used multi-path fading model BIB001 is to represent a single-antenna channel as the superposition of a finite number of complex sinusoids: where α p , φ p , and ω p denote the complex amplitude, phase, and radian Doppler frequency shift of the p th scattering source, respectively, j 2 =−1 stands for the imaginary unit, and P is the total number of scatters. Introducing the parameters of spatial dimension BIB005 , the single-antenna model in BIB003 can be extended to model a MIMO propagation channel, i.e., where θ p stands for the angle of arrival (AOA), ψ p the angle of departure (AOD), a r represents the response vector of the receive antenna array, while a t for the transmit antenna array. Using a uniform linear array (ULA) with M equally spaced elements as an example, its steering vector is defined as where x can be replaced with the angle of arrival or departure, d is the inter-antenna spacing, and λ denotes the wavelength of carrier frequency. Based on an observation that the multi-path parameters change slowly in comparison with the fading rate of channels, the future CSI within a certain range can be extrapolated if these parameters are known. Hence, predicting a MIMO channel in terms of (3)  where Q is the size of Hankel matrix and S=K −Q+1. Using (5), a spatio-temporal covariance matrix containing the temporal and spatial correlation can be calculated asĈ where (·) H denotes the Hermitian conjugate transpose. 2) Then, the number of dominant scattering sources can be estimated using the minimum description length (MDL) criterion (see BIB002 ), which is written aŝ where λ z is the z th eigenvalue ofĈ. 3) Making use of classical algorithms, such as MUltiple SIgnal Classification (MUSIC) and Estimation of Signal Parameters by Rotational Invariance Techniques (ESPRIT), {θ p ,ψ p ,ω p }P p=1 can be jointly estimated by further exploiting the invariance structure inĈ. For simplicity, the details of the calculation process are omitted but can refer to BIB005 . Substituting all estimates into (3), a parametric channel predictor is obtained where τ denotes a time range for which the CSI is to be predicted. From the estimation procedure, it is concluded that the generality and applicability of this method is highly constrained. For instance, if a different array is applied, (3) or (4) should be modified accordingly, such as BIB004 , where a set of polarization parameters is additionally employed for modelling a polarized array. The propagation models or steering vectors for some irregular arrays are probably intractable, which limits the applicability of this method. Moreover, the estimation process is tedious and the computational complexity is high due to the manipulation of high-dimensional matrices, as analyzed in BIB004 . Last but not the least, the obtained estimates expire quickly with the change of mobile propagation environments, especially in high mobility. According to  , the region of mobile movements where the propagation parameters are assumed constant is up to 50 wavelengths. It implies that the estimation process needs to be periodically and frequently conducted, resulting in extreme high complexity, which is unattractive from the viewpoint of practical implementation.