It has been shown recently that coding for the Gaussian Wiretap Channel can be done with nested lattices. A fine lattice intended to the legitimate user must be designed as a usual lattice code for the Gaussian Channel, while a coarse lattice is added to introduce confusion at the eavesdropper, whose theta series must be minimized. We present a design criterion for both the fine and coarse lattice to obtain wiretap lattice codes for the Rayleigh fading Wiretap Channel.
Secret sharing over the fast-fading MIMO wiretap channel is considered. A source and a destination try to share secret information over a fast-fading MIMO channel in the presence of a wiretapper who also makes channel observations that are different from but correlated to those made by the destination. An interactive authenticated unrestricted public channel is also available for use by the source and destination in the secret sharing process. This falls under the "channel-type model with wiretapper" considered by Ahlswede and Csiszar. A minor extension of their result (to continuous channel a…
In this paper, we propose a polar coding scheme for secure communication over the multiple-input, single-output, single-antenna eavesdropper (MISOSE) fading channel. We consider the case of block fading channels with known eavesdropper channel state information (CSI) and the case of fading channels with known eavesdropper channel distribution information (CDI). We use the artificial noise assisted secure precoding method to maximize the secrecy capacity in the first case, and to overcome the unawareness of the eavesdropper CSI in the second case. We show that our proposed scheme can provide bo…
In this paper, we consider the transmitter optimization problem in slow fading multiple-input-single-output (MISO) wiretap channel. The source transmits a secret message intended for $K$ users in the presence of $J$ non-colluding eavesdroppers, and operates under a total power constraint. The channels between the source and all users and eavesdroppers are assumed to be slow fading, and only statistical channel state information (CSI) is known at the source. For a given code rate and secrecy rate pair of the wiretap code, denoted by $(R_{D}, R_{s})$, we define the non-outage event as the joint …
This paper presents a polar coding scheme to achieve secrecy in block fading binary symmetric wiretap channels without the knowledge of instantaneous channel state information (CSI) at the transmitter. For this model, a coding scheme that hierarchically utilizes polar codes is presented. In particular, on polarization of different binary symmetric channels over different fading blocks, each channel use is modeled as an appropriate binary erasure channel over fading blocks. Polar codes are constructed for both coding over channel uses for each fading block and coding over fading blocks for cert…
We consider a fading wiretap channel model where the transmitter has only statistical channel state information, and the legitimate receiver and eavesdropper have perfect channel state information. We propose a sequence of non-random lattice codes which achieve strong secrecy and semantic security over ergodic fading channels. The construction is almost universal in the sense that it achieves the same constant gap to secrecy capacity over Gaussian and ergodic fading models.
We consider the multi-antenna wiretap channel in which the transmitter wishes to send a confidential message to its receiver while keeping it secret to the eavesdropper. It has been known that the secrecy capacity of such a channel does not increase with signal-to-noise ratio when the transmitter has no channel state information (CSI) under mild conditions. Motivated by Jafar's robust interference alignment technique, we study the so-called staggered multi-antenna block-fading wiretap channel where the legitimate receiver and the eavesdropper have different temporal correlation structures. Ass…
An alternative or supplementary approach named as physical layer security has been proposed to afford an extra security layer on top of the conventional cryptography technique. In this paper, an overview of secrecy performance investigations over the classic Alice-Bob-Eve wiretap fading channels is conducted. On the basis of the classic wiretap channel model, we have comprehensively listed and thereafter compared the existing works on physical layer secrecy analysis considering the small-scale, large-scale, composite, and cascaded fading channel models. Exact secrecy metrics expressions, inclu…
We furnish a procedure based on universal hash families (UHFs) that can convert an error correcting coding scheme (ECC) of rate $R$ into a semantically secure wiretap coding scheme of rate $R - ξ$ where $ξ$ is a parameter derived from the eavesdropper's point-to-point channel. This conversion is shown to be polynomial time efficient with block length and is applicable to any channel. When an ECC is chosen, our procedure induces a wiretap coding scheme that is concrete and efficient as long as the ECC is also such. To prove this induced wiretap coding scheme is semantically secure, we have cons…
Most of the well-known fading distributions, if not all of them, could be encompassed by Fox's $H$-function fading. Consequently, we investigate the exact and asymptotic behavior of physical layer security (PLS) over Fox's $H$-function fading wiretap channels. In particular, closed-form expressions are derived for secrecy outage probability (SOP), probability of non-zero secrecy capacity (PNZ), and average secrecy capacity (ASC). These expressions are given in terms of either univariate or bivariate Fox's $H$-function. In order to show the comprehensive effectiveness of our derivations, three …
In this article, the design of secure lattice coset codes for general wireless channels with fading and Gaussian noise is studied. Recalling the eavesdropper's probability and information bounds, a variant of the latter is given from which it is explicitly seen that both quantities are upper bounded by (increasing functions of) the expected flatness factor of the faded lattice related to the eavesdropper. By making use of a recently developed approximation of the theta series of a lattice, it is further shown how the average flatness factor can be approximated numerically. In particular, based…
The design of lattice coset codes for wiretap channels is considered. Bounds on the eavesdropper's correct decoding probability and information leakage are first revisited. From these bounds, it is explicit that both the information leakage and error probability are controlled by the average flatness factor of the eavesdropper's lattice, which we further interpret geometrically. It is concluded that the minimization of the (average) flatness factor of the eavesdropper's lattice leads to the study of well-rounded lattices, which are shown to be among the optimal in order to achieve these minima…
This paper presents a detailed secrecy outage performance analysis of correlated multi-antenna wiretap channels with three popular diversity combining schemes, namely maximal ratio combining, selection combining, and equal gain combining at the legitimate receiver. For single input multiple output wiretap channels, both exact and asymptotic expressions are derived for the secrecy outage probability (SOP) of these systems. The findings suggest that, compared with the scenario where all the channels are independent, correlation of the main channels alone increases the SOP by a factor of 1/ det(U…
The concept of well-rounded lattices has recently found important applications in the setting of a fading single-input single-output (SISO) wiretap channel. It has been shown that, under this setup, the property of being well-rounded is critical for minimizing the eavesdropper's probability of correct decoding in lower SNR regimes. The superior performance of coset codes constructed from well-rounded lattices has been illustrated in several simulations. In the present article, this work is extended to fading multiple-input multiple-output (MIMO) wiretap channels, and similar design criteria as…
We propose a lattice construction from totally real and CM fields, which naturally generalizes the Construction A of lattices from $p$-ary codes obtained from the cyclotomic field $\mathbb{Q}(ζ_p)$, $p$ a prime, which in turn contains the so-called Construction A of lattices from binary codes as a particular case. We focus on the maximal totally real subfield $\mathbb{Q}(ζ_{p^r}+ζ_{p}^{-r})$ of the cyclotomic field $\mathbb{Q}(ζ_{p^r})$, $r\geq 1$. Our construction has applications to coset encoding of algebraic lattice codes, and we detail the case of coset encoding of block fading wiretap co…
We consider MIMO (Multiple Input Multiple Output) wiretap channels, where a legitimate transmitter Alice is communicating with a legitimate receiver Bob in the presence of an eavesdropper Eve, and communication is done via MIMO channels. We suppose that Alice's strategy is to use a codebook which has a lattice structure, which then allows her to perform coset encoding. We analyze Eve's probability of correctly decoding the message Alice meant to Bob, and from minimizing this probability, we derive a code design criterion for MIMO lattice wiretap codes. The case of block fading channels is trea…
Despite several works on secrecy coding for fading and MIMO wiretap channels from an error probability perspective, the construction of information-theoretically secure codes over such channels remains an open problem. In this paper, we consider a fading wiretap channel model where the transmitter has only partial statistical channel state information. Our channel model includes static channels, i.i.d. block fading channels, and ergodic stationary fading with fast decay of large deviations for the eavesdropper's channel. We extend the flatness factor criterion from the Gaussian wiretap channel…
In this paper, new probability estimates are derived for ideal lattice codes from totally real number fields using ideal class Dedekind zeta functions. In contrast to previous work on the subject, it is not assumed that the ideal in question is principal. In particular, it is shown that the corresponding inverse norm sum depends not only on the regulator and discriminant of the number field, but also on the values of the ideal class Dedekind zeta functions. Along the way, we derive an estimate of the number of elements in a given ideal with a certain algebraic norm within a finite hypercube. W…
Simultaneous wireless information and power transfer (SWIPT) has recently drawn significant interests for its dual use of radio signals to provide wireless data and energy access at the same time. However, a challenging secrecy communication issue arises as the messages sent to the information receivers (IRs) may be eavesdropped by the energy receivers (ERs), which are presumed to harvest energy only from the received signals. To tackle this problem, we propose in this paper an artificial noise (AN) aided transmission scheme to facilitate the secrecy information transmission to IRs and yet mee…
The mutual information of a discrete time memoryless Rayleigh fading channel is considered, where neither the transmitter nor the receiver has the knowledge of the channel state information except the fading statistics. We present the mutual information of this channel in closed form when the input distribution is complex Gaussian, and derive a lower bound in terms of the capacity of the corresponding non fading channel and the capacity when the perfect channel state information is known at the receiver.
In this paper, we consider secure transmissions in ergodic Rayleigh fast-faded multiple-input multiple-output multiple-antenna-eavesdropper (MIMOME) wiretap channels with only statistical channel state information at the transmitter (CSIT). When the legitimate receiver has more (or equal) antennas than the eavesdropper, we prove the first MIMOME secrecy capacity with partial CSIT by establishing a new secrecy capacity upper-bound. The key step is to form an MIMOME degraded channel by dividing the legitimate receiver's channel matrix into two submatrices, and setting one of the submatrices to b…
In this paper, the secrecy analysis of physical layer when both the main and wiretap channels undergo $κ-μ$ shadowed fading channel is investigated. In particular, the average secrecy capacity (ASC), secure outage probability (SOP), the lower bound of SOP (SOP$^L$), and the probability of strictly positive secrecy capacity (SPSC) are derived by using the classic Wyner's wiretap model. Two different scenarios for the fading parameters, i.e., $μ$ and $m$ which represents the shadowing impact have been studied. These parameters are chosen first as arbitrary numbers, thus the performance metrics a…
We investigate channel equalization for Rayleigh fading channels under bounded channel uncertainties. We analyze three robust methods to estimate an unknown signal transmitted through a Rayleigh fading channel, where we avoid directly tuning the equalizer parameters to the available inaccurate channel information. These methods are based on minimizing certain mean-square error criteria that incorporate the channel uncertainties into the problem formulations. We present closed-form solutions to the channel equalization problems for each method and for both zero mean and nonzero mean signals. We…
This paper investigates the achievable information rate of phase-shift keying (PSK) over frequency non-selective Rayleigh fading channels without channel state information (CSI). The fading process exhibits general temporal correlation characterized by its spectral density function. We consider both discrete-time and continuous-time channels, and find their asymptotics at low signal-to-noise ratio (SNR). Compared to known capacity upper bounds under peak constraints, these asymptotics usually lead to negligible rate loss in the low-SNR regime for slowly time-varying fading channels. We further…
We investigate the secrecy capacity of an ergodic fading wiretap channel in which the main channel is correlated with the eavesdropper channel. In this study, the full Channel State Information (CSI) is assumed, and thus the transmitter knows the channel gains of the legitimate receiver and the eavesdropper. By analyzing the resulting secrecy capacity we quantify the loss of the secrecy capacity due to the correlation. In addition, we study the asymptotic behavior of the secrecy capacity as Signal-to-Noise Ratio (SNR) tends to infinity. The capacity of an ordinary fading channel logarithmicall…
In this paper, we study the performance of non-fading and Rayleigh fading ad hoc networks. We first characterize the distribution of the signal-to-interference-plus-noise ratio (SINR) through the Laplace transform of the inverted SINR for non-fading channels. Since most communication systems are interference-limited, we also consider the case of negligible noise power, and derive the upper and lower bounds for the signal-to-interference ratio (SIR) distribution under both non-fading and fading cases. These bounds are of closed forms and thus more convenient for theoretical analysis. Based on t…
For many wiretap channel models asymptotically optimal coding schemes are known, but less effort has been put into actual realizations of wiretap codes for practical parameters. Bounds on the mutual information and error probability when using coset coding on a Rayleigh fading channel were recently established by Oggier and Belfiore, and the results in this paper build on their work. However, instead of using their ultimate inverse norm sum approximation, a more precise expression for the eavesdropper's probability of correct decision is used in order to determine a general class of good coset…
Security constraint results in \textit{rate-loss} in wiretap channels. In this paper we propose a coding scheme for two user Multiple Access Channel with Wiretap (MAC-WT), where previous messages are used as a key to enhance the secrecy rates of both the users until we achieve the usual capacity region of a Multiple Access Channel (MAC) without the wiretapper (Shannon capacity region). With this scheme all the messages transmitted in the recent past are secure with respect to all the information of the eavesdropper till now. To achieve this goal we introduce secret key buffers at both the user…
Wireless fading channels suffer from both channel fadings and Additive White Gaussian Noise (AWGN). As a result, it is impossible for fading channels to support a constant rate data stream without using buffers. In this paper, we consider information transmission over an infinite-buffer-aided block Rayleigh fading channel in the low signal-to-noise ratio (SNR) regime. We characterize the transmission capability of the channel in terms of stationary queue length distribution, packet delay, as well as data rate. Based on the memoryless property of the service provided by the channel in each bloc…
The covert capacity is characterized for a non-coherent fast Rayleigh-fading wireless channel, in which a legitimate user wishes to communicate reliably with a legitimate receiver while escaping detection from a warden. It is shown that the covert capacity is achieved with an amplitude-constrained input distribution that consists of a finite number of mass points including one at zero and numerically tractable bounds are provided. It is also conjectured that distributions with two mass points in fixed locations are optimal.
In this letter, we consider the problem of energy detection of unknown signals in an intervehicular communication (IVC) system over n*Rayleigh fading channels (also known as cascaded Rayleigh). Novel tight approximations for the probability of detection are derived for the no-diversity and the maximum ratio combining (MRC)) diversity schemes. Moreover, we investigate the system performance when cooperative spectrum sensing (CSS) is considered with and without imperfect reporting channels. The analytical results show that the detection reliability is decreased as the fading severity parameter n…
We investigate the problem of message transmission over time-varying single-user multiple-input multiple-output (MIMO) Rayleigh fading channels with average power constraint and with complete channel state information available at the receiver side (CSIR). To describe the channel variations over the time, we consider a first-order Gauss-Markov model. We completely solve the problem by giving a single-letter characterization of the channel capacity in closed form and by providing a rigorous proof of it.
This paper investigates the limits of information transfer over a fast Rayleigh fading MIMO channel, where neither the transmitter nor the receiver has the knowledge of the channel state information (CSI) except the fading statistics. We develop a scalar channel model due to absence of the phase information in non-coherent Rayleigh fading and derive a capacity supremum with the number of receive antennas at any signal to noise ratio (SNR) using Lagrange optimisation. Also, we conceptualise the discrete nature of the optimal input distribution by posing the optimisation on the channel mutual in…
We study a hierarchical heterogeneous Rayleigh fading wireless sensor network (WSN) in which sensor nodes surveil a region of interest (RoI) and use access points (APs) as relays to transmit their sensed information to base stations (BSs). By considering both large-scale path-loss signal attenuation and small-scale signal variation due to Rayleigh fading, we formulate the node deployment problem as an optimization problem intended to minimize the network's wireless communication power consumption. Given ergodic capacity constraints on all wireless links, we study the necessary conditions for a…
We present a novel analytical framework for the evaluation of important second order statistical parameters, as the level crossing rate (LCR) and the average fade duration (AFD) of the amplify-and-forward multihop Rayleigh fading channel. More specifically, motivated by the fact that this channel is a cascaded one, which can be modelled as the product of N fading amplitudes, we derive novel analytical expressions for the average LCR and AFD of the product of N Rayleigh fading envelopes, or of the recently so-called N*Rayleigh channel. Furthermore, we derive simple and efficient closed-form app…
Except for a few simple digital modulation techniques, derivation of average bit error probability over fading channels is difficult and is an involved process. In this letter, curve fitting technique has been employed to express bit error probability over AWGN of any digital modulation scheme in terms of a simple Gaussian function. Using this Gaussian function, a generalized closed form expression for computing average probability of bit error over Rayleigh fading channels has been derived. Excellent agreement has been found between error probabilities computed with our method and the rigorou…
We consider transmission over a wireless multiple antenna communication system operating in a Rayleigh flat fading environment with no channel state information at the receiver and the transmitter with coherence time T=1. We show that, subject to the average power constraint, the support of the capacity achieving input distribution is bounded. Moreover, we show by a simple example concerning the identity theorem (or uniqueness theorem) from the complex analysis in several variables that some of the existing results in the field are not rigorous.
This paper studies dual-hop amplify-and-forward relaying over time-varying Rayleigh fading channels with differential M-PSK modulation and non-coherent detection. For the case of "two-symbol" detection, a first order time-series model is utilized to characterize the time-varying nature of the cascaded channel. Based on this model, an exact bit error rate (BER) expression is derived and confirmed with simulation results. The obtained expression shows that the BER is related to the auto-correlation of the cascaded channel and an irreducible error floor exists at high transmit power. To overcome …
Second order statistics provides a dynamic representation of a fading channel and plays an important role in the evaluation and design of the wireless communication systems. In this paper, we present a novel analytical framework for the evaluation of important second order statistical parameters, as the level crossing rate (LCR) and the average fade duration (AFD) of the amplify-and-forward multihop Rayleigh fading channel. More specifically, motivated by the fact that this channel is a cascaded one and can be modeled as the product of N fading amplitudes, we derive novel analytical expression…
In this paper, we propose novel low-complexity adaptive channel estimation techniques for mob ile wireless chan- n els in presence of Rayleigh fading, carrier frequency offsets (CFO) and random channel variations. We show that the selective p artial update of the estimated channel tap-weight vector offers a better trade-off between the performance and computational complexity, compared to the full update of the estimated channel tap-weight vector. We evaluate the mean-square weight error of th e proposed methods and demonstrate the usefulness of its via simulation studies.
Instead of against eavesdropping, this letter proposes a new paradigm in wireless security by studying how a legitimate monitor (e.g., government agencies) efficiently eavesdrops a suspicious wireless communication link. The suspicious transmitter controls its communication rate over Rayleigh fading channels to maintain a target outage probability at the receiver, and the legitimate monitor can successfully eavesdrop only when its achievable rate is no smaller than the suspicious communication rate. We propose a proactive eavesdropping via jamming approach to maximize the average eavesdropping…
We investigate the performance of multihop-intervehicular communication systems with regenerative and nonregenerative relaying. We consider the so-called "n*Rayleigh distribution" as an adequate multipath fading channel model for vehicle-to-vehicle communication scenarios. We derive a novel approximation for the outage probability of maximum ratio combining (MRC) diversity reception. In addition, we analyze the amount of fading and optimize the power allocation for the investigated scenario. Numerical results show that regenerative systems are more efficient than nonregenerative systems when t…
This paper proposes and analyses selection combining (SC) at the destination for differential amplify-andforward (D-AF) relaying over slow Rayleigh-fading channels. The selection combiner chooses the link with the maximum magnitude of the decision variable to be used for non-coherent detection of the transmitted symbols. Therefore, in contrast to the maximum ratio combining (MRC), no channel information is needed at the destination. The exact average bit-error-rate (BER) of the proposed SC is derived and verified with simulation results. It is also shown that the performance of the SC method i…
Time-varying fast fading channels present a major challenge in the design of wireless communication systems. Pilot Symbol Assisted Modulation (PSAM) has been introduced to mitigate the effects of fading and allow coherent demodulation. Our work studies the performance of \emph{non-feedback} adaptive PSAM scheme over time-varying Rayleigh fading channels. A modular method is introduced for computing the rates in an efficient manner. Moreover, four transmission policies are analyzed and we show how optimal training in terms of duration and power allocation varies with the channel conditions and …
This paper studies the performance of antenna array processing in distributed multiple access networks without power control. The interference is represented as a Poisson point process. Desired and interfering signals are subject to both path-loss fading (with an exponent greater than 2) and to independent Rayleigh fading. Using these assumptions, we derive the exact closed form expression for the cumulative distribution function of the output signal-to-interference-plus-noise ratio when optimum combining is applied. This results in a pertinent measure of the network performance in terms of th…
The second-order coding rate of the multiple-input multiple-output (MIMO) quasi-static Rayleigh fading channel is studied. We tackle this problem via an information-spectrum approach and statistical bounds based on recent random matrix theory techniques. We derive a central limit theorem (CLT) to analyze the information density in the regime where the block-length n and the number of transmit and receive antennas K and N, respectively, grow simultaneously large. This result leads to the characterization of closed-form upper and lower bounds on the optimal average error probability when the cod…
We investigate the secure communications over correlated wiretap Rayleigh fading channels assuming the full channel state information (CSI) available. Based on the information theoretic formulation, we derive closed-form expressions for the average secrecy capacity and the outage probability. Simulation results confirm our analytical expressions.
The existing investigations on artificial noise (AN) security systems assumed that only null spaces is used to send AN signals, and all eigen-subchannels should be used to transmit messages. Our previous work proposed an AN scheme that allocates some of eigen-subchannels to transmit AN signals for improving secrecy rates. Nevertheless, our previous work considered only uncorrelated MIMO Rayleigh fading channels. In fact, the correlations among antennas exist in realistic scattering channel environments. In this paper, we extend our previous AN scheme to spatially correlated Rayleigh fading cha…
In this paper, the second-order statistics of the instantaneous mutual information are studied, in time-varying Rayleigh fading channels, assuming general non-isotropic scattering environments. Specifically, first the autocorrelation function, correlation coefficient, level crossing rate, and the average outage duration of the instantaneous mutual information are investigated in single-input single-output (SISO) systems. Closed-form exact expressions are derived, as well as accurate approximations in low- and high-SNR regimes. Then, the results are extended to multiple-input single-output and …
Device activity detection and channel estimation for massive grant-free access under frequency-selective fading have unfortunately been an outstanding problem. This paper aims to address the challenge. Specifically, we present an orthogonal frequency division multiplexing (OFDM)-based massive grant-free access scheme for a wideband system with one M-antenna base station (BS), N single-antenna Internet of Things (IoT) devices, and P channel taps. We obtain two different but equivalent models for the received pilot signals under frequency-selective Rayleigh fading. Based on each model, we formul…
The recently proposed Fluctuating Two-Ray (FTR) model is gaining momentum as a reference fading model in scenarios where two dominant specular waves are present. Despite the numerous research works devoted to the performance analysis under FTR fading, little attention has been paid to effectively understanding the interplay between the fading model parameters and the fading severity. According to a new scale defined in this work, which measures the hyper-Rayleigh character of a fading channel in terms of the Amount of Fading, the outage probability and the average capacity, we see that the FTR…
In this paper, pilot-assisted transmission over Gauss-Markov Rayleigh fading channels is considered. A simple scenario, where a single pilot signal is transmitted every T symbols and T-1 data symbols are transmitted in between the pilots, is studied. First, it is assumed that binary phase-shift keying (BPSK) modulation is employed at the transmitter. With this assumption, the training period, and data and training power allocation are jointly optimized by maximizing an achievable rate expression. Achievable rates and energy-per-bit requirements are computed using the optimal training parameter…
We study the ergodic capacity of a frequency-selective Rayleigh fading channel with correlated scattering, which finds application in the area of UWB. Under an average power constraint, we consider a single-user, single-antenna transmission. Coherent reception is assumed with full CSI at the receiver and no CSI at the transmitter. We distinguish between a continuous- and a discrete-time channel, modeled either as random process or random vector with generic covariance. As a practically relevant example, we examine an exponentially attenuated Ornstein-Uhlenbeck process in detail. Finally, we gi…
We consider the problem of adaptive modulation for wideband DS-CDMA Rayleigh fading channels with imperfect channel state information (CSI). We assume a multidimensional signal subspace spanned by a collection of random spreading codes (multicoding) and study the effects of both the subspace dimension and the probability distribution of the transmitted symbols on the mutual information between the channel input and output in the presence of uncertainty regarding the true state of the channel. We develop approximations for the mutual information as well as both upper and lower bounds on the mut…
In this paper, we consider a general multiple input multiple output (MIMO) system with channel state information (CSI) feedback over time-correlated Rayleigh block-fading channels. Specifically, we first derive the closed-form expression of the minimum differential feedback rate to achieve the maximum erdodic capacity in the presence of channel estimation errors and quantization distortion at the receiver. With the feedback-channel transmission rate constraint, in the periodic feedback system, we further investigate the relationship of the ergodic capacity and the differential feedback interva…
Guessing Random Additive Noise Decoding (GRAND) is a code-agnostic decoding technique for short-length and high-rate channel codes. GRAND tries to guess the channel noise by generating test error patterns (TEPs), and the sequence of the TEPs is the main difference between different GRAND variants. In this work, we extend the application of GRAND to multipath frequency non-selective Rayleigh fading communication channels, and we refer to this GRAND variant as Fading-GRAND. The proposed Fading-GRAND adapts its TEP generation to the fading conditions of the underlying communication channel, outpe…
