Neural Network-Based Fading Channel Prediction: A Comprehensive Overview <s> V. PREDICTION-AIDED MIMO-OFDM <s> This paper employs a high resolution quantization framework to study the effects of finite-rate feedback of the channel state information (CSI) on the performance of multiple-input-multiple-output (MIMO) systems over independently and identically distributed (i.i.d.) Rayleigh flat fading channels. The contributions of this paper are twofold. First, we extend the general distortion analysis of vector quantizers to deal with complex source variables. Necessary and sufficient conditions that guarantee a concise high-resolution distortion analysis in the complex domain is presented. Second, as an application of the proposed complex distortion analysis, tight lower bounds on the capacity loss due to the finite-rate channel quantization are provided for MIMO systems employing a fixed number of equal power spatial beams. Based on the obtained closed-form analytical results, it is shown that the system capacity loss decreases exponentially as the ratio of the quantization rate to the total degrees of freedom of the channel state information to be quantized. Moreover, MIMO CSI-quantizers using mismatched codebooks that are only optimized for high-signal-to-noise ratio (SNR) and low-SNR regimes are also investigated to quantify the penalties incurred by the use of mismatched codebooks. In addition, the analysis is extended to deal with MIMO systems using multi-mode spatial multiplexing transmission schemes with finite-rate CSI feedback. Finally, numerical and simulation results are presented which confirm the tightness of the derived theoretical distortion bounds. <s> BIB001 </s> Neural Network-Based Fading Channel Prediction: A Comprehensive Overview <s> V. PREDICTION-AIDED MIMO-OFDM <s> This paper provides an exact diversity gain analysis for transmit antenna selection in MIMO-OFDM systems with linear receivers, a topic scarcely addressed in prior literature. In a frequency-selective fading (as opposed to a frequency-flat fading) channel one of either two methods of antenna selection may be applied. We name these methods bulk selection and per-tone selection. From an implementation perspective each method presents a different complexity-performance tradeoff. Through rigorous mathematical derivation, we demonstrate that both methods realize the same diversity order. Moreover, the coding gain realized by the two selection methods is also analyzed and compared through simulation. Overall, this paper confirms the advantage of antenna selection technology in MIMO-OFDM systems, and provides comprehensive guidelines for antenna selection strategies in realistic scenarios, from both the performance and complexity perspectives. <s> BIB002 </s> Neural Network-Based Fading Channel Prediction: A Comprehensive Overview <s> V. PREDICTION-AIDED MIMO-OFDM <s> As of today, orthogonal frequency-division multiplexing (OFDM) has been the dominant technique in broadband transmission systems. However, for the application in cognitive radios, the sidelobes of rectangularly pulsed OFDM signals must be well suppressed to satisfy the rigorous spectral masks. In this context, filter-bank based multi-carrier (FBMC) transmission, which allows designing prototype filters for signal pulse shaping, is considered to be more effective. In this article, different sidelobe suppression schemes for OFDM and pulse-shaped FBMC are comparatively investigated with respect to their out-of-band power radiation and their demand in computational complexity. Our results reveal that FBMC, thanks to the excellent time-frequency localization of the pulse shape, allows for a superior isolation of the transmit signal in frequency, enabling to achieve the minimal out-of-band power leakage for the operation in both contiguous and non-contiguous spectrum. Moreover, the additional complexity required for FBMC compared to the other schemes is very moderate. <s> BIB003 </s> Neural Network-Based Fading Channel Prediction: A Comprehensive Overview <s> V. PREDICTION-AIDED MIMO-OFDM <s> A unified error analysis of multi-antenna systems with orthogonal space-time block coding (OSTBC) using transmit antenna selection (TAS) over Nakagami- $m$ channels in the presence of feedback delay and channel estimation error is presented, where the number of transmit antennas is arbitrarily selected. For imperfect channel state information (CSI), the Nakagami- $m$ channel is modeled as the sum of Nakagami- $\hat{m}$ channel and independent Gaussian channel error. By this model, accurate and closed-form approximate bit error rate (BER) expressions of TAS-OSTBC for M-ary quadrature amplitude modulation and M-ary phase-shift keying are derived by using the moment generating function of received SNR. With the approximate BER formula, the number of antennas to be selected for transmission can be adapted by minimizing the BER of the system with imperfect CSI. The diversity and coding gains of TAS-OSTBC with $K$ receive antennas and $M$ antennas selected from $N$ transmit antennas for transmission are analyzed at high SNR. For noninteger $mK$ , the upper and lower bounds of the diversity gain for different CSI and estimation error scenarios are derived. But for integer $mK$ , the results indicate that the upper and lower bounds are equal achieving the full diversity order of $mKN$ for perfect CSI, zero diversity order and partial diversity order of $mMK$ for estimation error variance being fixed and being a decreasing function of average SNR, respectively. The coding gain is affected by $M$ , $N$ , $K$ , Nakagami parameter $m$ , code rate, modulation, and channel correlation coefficients. Simulation results verify the validity of the theoretical analysis and effectiveness of the adaptive antenna selection scheme. <s> BIB004
Transmit antenna selection in a multi-antenna system has been widely recognized as a cost-effective approach due to the reduction of required number of high-power amplifiers in radio frequency chains. To select out appropriate antennas, instantaneous CSI at the transmitter is mandatory, where channel prediction can play an important role. In order to further shed light on the RNN predictor, prediction-aided TAS in a MIMO-OFDM system with N t transmit and N r receive antennas is presented as an application example. As illustrated in Fig. 3 , the fast Fourier transform (FFT) demodulator and inverse FFT (IFFT) modulator, with the aid of cyclic prefix (CP), convert a frequency-selective channel into N sub-carriers, where a payload of M data symbols denoted by d=[d BIB001  Without the consideration of null sub-carriers reserved for out-of-band radiation suppression BIB003 and direct current, we can assume that the remaining P=N −M sub-carriers are used for comb-type pilot symbols p=[p 1 , p 2 , . . . , p P ] T , inserting uniformly every N P sub-carriers. At time t, d (t) and p (t) are multiplexed and transmitted in one OFDM symbol. The receiver obtainsH p [t] through estimating p (t) . Taking advantage of frequency correlation, an interpolator can recover channel responses across the whole bandwidth including all data and pilot sub-carriers, i.e.,H n [t], n=0, 1, . . . , N −1. The traditional TAS system directly usesH n [t] to make decisions, as marked by the line with a cross originated from the channel estimator in the figure. There are two kinds of selection strategies, i.e., bulk or per-tone, as analyzed in BIB002 . Without loss of generality, we adopt the latter in this article for simplicity, i.e., each sub-carrier chooses the best antenna individually instead of the same selection for all sub-carriers. Mathematically, the traditional TAS system follows where η n [t] stands for the index of the selected antenna at time t upon sub-carrier n,h n t n [t] is the n th t column vector ofH n [t], and · denotes the Euclidean norm of a vector. The receiver feeds a set of selected antenna indices for all data sub-carriers η t = {η n [t] | 0 n N −1, n =p} back to the transmitter through a feedback channel. Assuming that the processing and feedback delays can be absorbed by the time gap of D OFDM symbols, the transmit antennas selected in terms of η t are applied for transmitting signals at time t+D. Due to the channel fading,H n [t] is outdated and may differ substantially from the actual CSIH n [t+D] at the instant of signal transmission, leading to notable performance degradation BIB004 . Due mainly to additive noise and delay, H n [t+D] is impossible to obtain in practical systems. But if a selection decision can be made according to predicted CSÎ H n [t+D] that approximates toH n [t+D], the performance can be improved. At time t, as depicted in Fig. 3,H p [t] is fed into the predictor to getĤ p [t+D] . A frequency-domain channel interpolator is applied to recover the CSI across all sub-carriersĤ n [t+D] so as to replace the outdated CSIH n [t] in the traditional TAS system. Then, the best antenna for time t+D upon sub-carrier n is selected in advance aŝ 