Block Rayleigh Fading Channels Research Articles

Multi-Level Design for Multiple-Symbol Non-Coherent Unitary Constellations for Massive SIMO Systems

This paper investigates non-coherent detection of single-input multiple-output (SIMO) systems over block Rayleigh fading channels. Using the Kullback-Leibler divergence as the design criterion, we formulate a multiple-symbol constellation optimization problem, which turns out to have high computational complexity to construct and detect. We exploit the structure of the formulated problem and decouple it into a unitary constellation design and a multi-level design. The proposed multi-level design has low complexity in both construction and detection. Simulation results show that our multi-level design has better performance than traditional pilot-based schemes and other existing low-complexity multi-level designs.

Constrained Riemannian Noncoherent Constellations for the MIMO Multiple Access Channel

We consider the design of multiuser constellations for a multiple access channel (MAC) with <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">K</i> users, with <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">M</i> antennas each, that transmit simultaneously to a receiver equipped with <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">N</i> antennas through a Rayleigh block-fading channel when no channel state information (CSI) is available to either the transmitter or the receiver. In full-diversity scenarios where the coherence time is at least <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">T</i> ≥ ( <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">K</i> + 1) <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">M</i> , the proposed constellation design criterion is based on the asymptotic expression of the multiuser pairwise error probability (PEP) derived by Brehler and Varanasi (2001). In non-full diversity scenarios, for which the previous PEP expression is no longer valid, the proposed design criteria are based on proxies of the PEP recently proposed by Ngo and Yang (2021). Although both the PEP expression and its bounds or proxies were previously considered intractable for optimization, in this work we derive their respective unconstrained gradients. These gradients are in turn used in the optimization of the proposed cost functions in different Riemannian manifolds representing different power constraints. In particular, in addition to the standard unitary space-time modulation (USTM) leading to optimization on the Grassmann manifold, we consider a more relaxed percodeword power constraint leading to optimization on the so-called <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">oblique manifold</i> , and an average power constraint leading to optimization on the so-called <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">trace manifold</i> . Equipped with these theoretical tools, we design multiuser constellations for the MIMO MAC in full-diversity and non-full-diversity scenarios with state-of-the-art performance in terms of symbol error rate (SER).

End-to-End Deep Learning for Multipair Two-Way Massive MIMO with PA Impairments

Multipair (MP) massive multiple-input–multiple-output (MIMO) two-way relaying system is a promising solution that is able to provide excellent spectral efficiency performance. It consists in multiple pairs ( <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"><tex-math notation="LaTeX">$2K$</tex-math></inline-formula> ) of single-antenna user terminals that exchange information through of a relay using a large number of antennas <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"><tex-math notation="LaTeX">$M_{t}\gg 2K$</tex-math></inline-formula> . The relay is equipped with a large number of energy-efficient power amplifiers (PAs) and ensure the multipair two-way forwarding. In this article, we first present an analytical study focused on the effects of PAs on the considered system over block fading Rayleigh channel. We derive closed-form expressions for the symbol error rate. Then, we develop a new efficient distributed learning approach for MP two-way massive MIMO. Specifically, we design the MP two-way massive MIMO system by leveraging the concept of the autoencoder, whereas the end-to-end communication system is designed using one deep neural network (NN). Interestingly, the proposed scheme, referred to as AE-MP-mMIMO, is suited for varying block fading Rayleigh channel scenarios. Indeed, we propose to adopt one stage precoder/decoder for each UE and two-stage precoding scheme for the relay: 1) an NN-Tx is used to address the PA nonlinearity and 2) a linear zero-forcing precoder is adopted to remove the multiuser interference. The NN-Tx and the UE's precoder/decoder are trained off-line and when the channel varies, only the zero-forcing precoder changes on-line. Numerical simulations show the capability of the proposed approach to achieve competitive performance with a significantly lower complexity compared to existing literature.

Union Bound Minimization Approach for Designing Grassmannian Constellations

In this paper, we propose an algorithm for designing unstructured Grassmannian constellations for noncoherent multiple-input multiple-output (MIMO) communications over Rayleigh block-fading channels. Unlike the majority of existing unitary space-time or Grassmannian constellations, which are typically designed to maximize the minimum distance between codewords, in this work we employ the asymptotic pairwise error probability (PEP) union bound (UB) of the constellation as the design criterion. In addition, the proposed criterion allows the design of MIMO Grassmannian constellations specifically optimized for a given number of receiving antennas. A rigorous derivation of the gradient of the asymptotic UB on a Cartesian product of Grassmann manifolds, is the main technical ingredient of the proposed gradient descent algorithm. A simple modification of the proposed cost function, which weighs each pairwise error term in the UB according to the Hamming distance between the binary labels assigned to the respective codewords, allows us to jointly solve the constellation design and the bit labeling problem. Our simulation results show that the constellations designed with the proposed method outperform other structured and unstructured Grassmannian designs in terms of symbol error rate (SER) and bit error rate (BER), for a wide range of scenarios.

Irregular Repetition Slotted ALOHA Over Rayleigh Block Fading Channels: Bounds and Threshold Saturation via Spatial Coupling

Irregular Repetition Slotted ALOHA Over Rayleigh Block Fading Channels: Bounds and Threshold Saturation via Spatial Coupling

Outage Performance of Interference Cancellation-Aided Two-Way Relaying Cognitive Network with Primary TAS/SC Communication and Secondary Partial Relay Selection

In this paper, we propose a two-way relaying scheme using digital network coding in an underlay cognitive radio network. In the proposed scheme, the transmit antenna selection and selection techniques are combined using a primary transmitter and a primary receiver, respectively. In the secondary network, two source nodes that cannot directly communicate attempt to exchange their data with each other. As a result, the relaying technique using partial relay selection is applied to assist the data exchange. Particularly, at the first time slot, the selected secondary relay applies an interference cancellation technique to decode the data received from the secondary sources. Then, the selected relay uses digital network coding to send XOR-ed data to the sources at the second time slot. We first derive the outage probability of the primary network over block the Rayleigh fading channel. Then, the transmit power of the secondary transmitters including the source and relay nodes are calculated to guarantee the quality of service of the primary network. Finally, the exact closed-form formulas of the outage probability of the secondary sources over the block Rayleigh fading channel are derived, and then verified by computer simulations using the Monte Carlo method.

Performance Analysis for Covert Communications Under Faster-Than-Nyquist Signaling

In this letter, we analyze the performance of covert communications under <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">faster-than-Nyquist</i> (FTN) signaling in the Rayleigh block fading channel. Both maximum likelihood criterion- and <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">Kullback-Leibler</i> (KL) divergence-based covertness constraints are considered. Especially, for KL divergence-based one, we prove that both the maximum transmit power and covert rate under FTN signaling are higher than those under Nyquist signaling. Numerical results coincide with our analysis and validate the advantages of FTN signaling to realize covert data transmission.

The SIMO Block Rayleigh Fading Channel Capacity Scaling With Number of Antennas, Bandwidth, and Coherence Length

This paper studies the capacity scaling of non-coherent Single-Input Multiple-Output (SIMO) independent and identically distributed (i.i.d.) Rayleigh block fading channels versus bandwidth (<inline-formula> <tex-math notation="LaTeX">$B$ </tex-math></inline-formula>), number of receive antennas (<inline-formula> <tex-math notation="LaTeX">$N$ </tex-math></inline-formula>) and coherence block length (<inline-formula> <tex-math notation="LaTeX">$L$ </tex-math></inline-formula>). In non-coherent channels (without Channel State Information&#x2013;CSI) capacity scales as <inline-formula> <tex-math notation="LaTeX">$\Theta (\min (B,\sqrt {NL},N))$ </tex-math></inline-formula>. This is achievable using Pilot-Assisted signaling. Energy Modulation signaling rate scales as <inline-formula> <tex-math notation="LaTeX">$\Theta (\min (B,\sqrt {N}))$ </tex-math></inline-formula>. If <inline-formula> <tex-math notation="LaTeX">$L$ </tex-math></inline-formula> is fixed while <inline-formula> <tex-math notation="LaTeX">$B$ </tex-math></inline-formula> and <inline-formula> <tex-math notation="LaTeX">$N$ </tex-math></inline-formula> grow, the two expressions grow equally and Energy Modulation achieves the capacity scaling. However, Energy Modulation rate does not scale as the capacity with the variable <inline-formula> <tex-math notation="LaTeX">$L$ </tex-math></inline-formula>. The coherent channel capacity with a priori CSI, in turn, scales as <inline-formula> <tex-math notation="LaTeX">$\Theta (\min (B,N))$ </tex-math></inline-formula>. The coherent channel capacity scaling can be fully achieved in non-coherent channels when <inline-formula> <tex-math notation="LaTeX">$L\geq \Theta (N)$ </tex-math></inline-formula>. In summary, the channel coherence block length plays a pivotal role in modulation selection and the capacity gap between coherent and non-coherent channels. Pilot-Assisted signaling outperforms Energy Modulation&#x2019;s rate scaling versus coherence block length. Only in high mobility scenarios where <inline-formula> <tex-math notation="LaTeX">$L$ </tex-math></inline-formula> is much smaller than the number of antennas (<inline-formula> <tex-math notation="LaTeX">$L\ll \Theta (\sqrt {N})$ </tex-math></inline-formula>), Energy Modulation is effective in non-coherent channels.

Influence of loopback interference channel in energy harvesting full-duplex relaying network over block rayleigh fading channel: performance analysis

The main idea of this paper is to investigate the system performance (SP) ofenergy harvesting FD relaying network over block rayleigh fading channelunder the influence of the loopback interference channel. In the first stage,we proposed the system modeland analyzed the energy harvesting and theinformation transmission phases. Furthermore, the mathematical form for theoutage probability (OP) is analyzed and derived in two kinds of loopbackinterference: residual self-interference is modeled as AWGN vàresidual self-interference is still a random variable. All the mathematical, analyticalexpressions are verified using the Monte Carlo simulation.

Jamming Aided Covert Communication With Multiple Receivers

We consider that a transmitter covertly communicates with multiple receivers under the help of a friendly jammer. The messages intended for different receivers are transmitted in mutually orthogonal frequency bands. An adversary observes all these frequency bands aiming at detecting whether or not communication occurs, while the friendly jammer broadcasts jamming signals to degrade the detection performance of the adversary. We consider a block Rayleigh fading channel model and evaluate the performance of covert communication in two situations: 1) the wireless channels vary slowly such that the transmission ends within one channel coherent time block, and 2) the wireless channels vary fast such that the wireless channels have changed several times before the whole transmission is finished. In the former case, subject to a covertness constraint, we maximize the sum of the effective rates by optimizing the transmit power allocation and the transmission rate for each receiver. In the latter case, we take the channel training process into consideration, and subject to a covertness constraint, we maximize the sum of the ergodic rates by optimizing the power allocation and the pilot length. Though both of the two optimization problems are non-convex, we presented methods to find their global optimal solutions. Besides, we also present methods to find sub-optimal solutions with lower computational complexities. Numerical results are presented to evaluate the performance under the two situations.

Polar-Coded Non-Coherent Communication

A polar-coded transmission (PCT) scheme with joint channel estimation and decoding is proposed for channels with unknown channel state information (CSI). The CSI is estimated via successive cancellation (SC) decoding and the constraints imposed by the frozen bits. SC list decoding with an outer code improves performance, including resolving a phase ambiguity when using quadrature phase-shift keying (QPSK) and Gray labeling. Simulations with 5G polar codes and QPSK show gains of up to 2 dB at a frame error rate (FER) of 10 <sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">-4</sup> over pilot-assisted transmission for various non-coherent models. Moreover, PCT performs within a few tenths of a dB to a coherent receiver with perfect CSI. For Rayleigh block-fading channels, PCT outperforms an FER upper bound based on random coding and operates within one dB of a lower bound.

On The Performance of MIMO AF Full-Duplex Joint Antenna and Relay Selection Network

This paper investigates a multi-input multi-output (MIMO) multi-relay amplify-and-forward (AF) full-duplex (FD) network using optimal joint relay and antenna selection over Rayleigh block fading channels. For system performance analysis, outage probability (OP) is theoretically analyzed to obtain exact and asymptotic expressions of OP where asymptotic derivations using the assumption of high signal-to-noise rate (SNR) regime. Numerical results are provided to verify the validity of the derived OP expressions by comparing with the related empirical performance. The paper shows that under different scenarios the exact OP expression values are close the related empirical ones while the approximated OP expression values approach to the empirical OP under high SNR conditions.

Down-Link NOMA With Successive Refinement for Binary Symmetric Source Transmission

This paper focuses on a lossy transmission of binary symmetric source (BSS) with down-link non-orthogonal multiple access (DL-NOMA). The transmitted binary sequences are lossy-compressed descriptions of the same BSS, which are overlapped in a specified signal format, corresponding to the receivers with pre-determined distortion requirements. Despite a higher spectrum efficiency achieved by DL-NOMA, redundancy may still remain if the overlapped descriptions are correlated. In this work, a system combining DL-NOMA and successive refinement, referred to as DN-SR, is proposed. Specifically, instead of re-constructing the source by a single description, the receiver can achieve a low distortion by first recovering the basic description, and then refining it with the help of another refinement description. If the two descriptions are made independent, transmission efficiency of the conventional DL-NOMA can be further improved. As the main contribution, this paper derives the outage probability of DN-SR in closed-form, assuming block Rayleigh fading channels. The advantage of DN-SR is numerically studied in terms of the system outage probability, compared to both the conventional DL-NOMA, and a modified DL-NOMA which exploits the correlation between descriptions, referred to as DN-CE. Finally, the optimal power allocation to the two descriptions is investigated for DN-SR, aiming to minimize the system outage probability.

Outage Probability of One-Source-With-One- Helper Sensor Systems in Block Rayleigh Fading Multiple Access Channels

Two correlated sources are transmitted over a block Rayleigh fading multiple access channel (MAC), where information recovery from only one of the sources is aimed at, and the other is used as a helper which helps recover the source sequences at the destination. In this article, the successful transmission is defined as in the case the transmission rates satisfy the intersection of both the MAC region and the Slepian-Wolf (SW) region with a helper, referred to as h-SW region, even though it is a sufficient condition. Then, the outage is defined as the average probability that the two regions do not have an intersection. The explicit expressions of the outage probability of the system are derived, in the form of multiple integrals with respect to the probability density function of instantaneous signal-to-noise ratios of each link. To have an in-depth insight regarding the contributions of some special cases to the successful transmission probability, the occurrence probabilities of these cases are also evaluated. The results indicate that outage probabilities decrease as the correlation between the source and helper information increases. The impacts of geometric gains of each link and the correlation of each link's fading variation are also considered. The most significant finding of this article is that h-SW over a MAC improves the throughput efficiency compared to the orthogonal transmission both in independent and correlated block Rayleigh fading channels without sacrificing the outage probability.

Saddlepoint Approximations for Short-Packet Wireless Communications

In recent years, the derivation of nonasymptotic converse and achievability bounds on the maximum coding rate as a function of the error probability and blocklength has gained attention in the information theory literature. While these bounds are accurate for many scenarios of interest, they need to be evaluated numerically for most wireless channels of practical interest, and their evaluation is computationally demanding. This paper presents saddlepoint approximations of state-of-the-art converse and achievability bounds for noncoherent, single-antenna, Rayleigh block-fading channels. These approximations can be calculated efficiently and are shown to be accurate for SNR values as small as 0 dB and blocklengths of 168 channel uses or more.

Generalized Code Index Modulation and Spatial Modulation for High Rate and Energy-Efficient MIMO Systems on Rayleigh Block-Fading Channel

In this article, a high data rate and energy-efficient multiple-input multiple-output transmission scheme is considered by combining two popular and rational modulation techniques: spatial modulation (SM) and code index modulation-spread spectrum (CIM-SS). Since in the considered system, called generalized CIM-SM (GCIM-SM), incoming information bits determine modulated symbols, activated transmit antenna indices as well as their corresponding spreading code indices, data bits are conveyed not only by modulated symbols but also by the indices of the active antenna and spreading codes. Hence, a GCIM-SM scheme accommodates faster data rates while spending less transmission power and possessing better error performance compared to the conventional direct sequence spread spectrum (DS-SS), SM, quadrature SM (QSM), and CIM-SS systems. The mathematical expressions of the GCIM-SM system for bit error rate, throughput, energy efficiency, and the system complexity are derived to analyze the overall system performance. Besides, it has been shown via computer simulations that the GCIM-SM system has lower transmission energy, faster data transmission rate, and better error performance than DS-SS, SM, QSM, and CIM-SS systems. Performance analysis of the considered system was performed on Rayleigh block-fading channels for quadrature amplitude modulation technique.

Wireless energy harvesting meets receiver diversity: A successful approach for two-way half-duplex relay networks over block Rayleigh fading channel

Recently, energy harvesting (EH) via radio-frequency (RF) signals in wireless relay networks has been attracting a lot of interest, especially for supplying the energy to relay nodes in IoT systems so that they can help exchange the information between source nodes. In this paper, we thoroughly analyze the performance of a novel EH scheme for a two-way half-duplex relay network with two source nodes exchanging the information with the help of a single relay. The relay node harvests the energy from both sources by power splitting EH protocol before using that energy to forward the information from each source to the other. By using the selection combining (SC) at the destinations, we can exploit the direct channel between two source nodes to enhance the overall performance. Three relay strategies are considered in our analysis, namely, amplify-and-forward (AF), decode-and-forward (DF), and hybrid-decode-and-forward (HDAF) strategies. For performance evaluation, we derive the exact expressions of the system outage probability (SOP) over block Rayleigh fading channels. Finally, Monte Carlo simulations are presented to verify the theoretical derivations as well as to compare the performance of various configurations of the proposed scheme.

Exploiting Direct Link in Two-Way Half-Duplex Sensor Network over Block Rayleigh Fading Channel: Upper Bound Ergodic Capacity and Exact SER Analysis

Relay communication, in which the relay forwards the signal received by a source to a destination, has a massive consideration in research, due to its ability to expand the coverage, increase the capacity, and reduce the power consumption. In this paper, we proposed and investigated energy harvesting (EH) based two-way half-duplex (TWHD) relaying sensors network using selection combining (SC) over block Rayleigh fading channel. In this model, we proposed the direct link between two sources for improving the system performance. For the system performance analysis, we investigated and derived the closed-form of the exact and upper bound Ergodic capacity (EC) and the exact form of the symbol error ratio (SER). By using the Monte Carlo simulation, the correctness of the research results is verified in the influence of the main system parameters. From the discussions, we can see that the analytical and simulation agree well with each other.

Energy Efficiency Versus Reliability Tradeoff Improvement in Low-Power Wireless Communications

Energy efficiency (EE) and reliability are two important but conflicting objectives in low-power, short-range wireless communications, usually treated as the single objective problems under constraints. Unlike others, we treat the objectives simultaneously as a multiobjective problem without preferences and analyze the opportunity of feasible tradeoff improvement in an objective space for communication over block-fading Rayleigh channel. We consider the improvement relative to the referent case that includes the current practice, where decision space consists of packet length, the maximal number of allowed transmission attempts (MNATA), and transmission power. Our hypothesis is that we can improve the tradeoff by modifying decision space and mapping functions from decision to objective space. We consider three modification techniques applied singly and jointly: Introduction of the expected MNATA as a real variable; Pareto optimal control of transmission power and transmitter power consumption; and introduction of the new decision variable—transmission rate. We show by mathematical modeling and numerical evaluation based on SI4455 transceiver that Pareto fronts (PF) attained by the application of techniques at least weakly dominate the referent PF; PF set cardinality can even be doubled; the joint application of techniques improves EE, reliability objectives, averaged over the entire PF, by approximately 49% and 74%, respectively.

Rate Selection for Wireless Random Access Networks Over Block Fading Channels

We study uncoordinated random access over fading channels where each user independently decides whether to send a packet or not to a common receiver at any given time slot. Specifically, we develop an information theoretic formulation to characterize the overall system throughput. We consider two scenarios: classical slotted ALOHA, where no multiuser detection (MUD) capability is available and slotted ALOHA with MUD. In each case, in order to maximize the system throughput, we provide methods to obtain the optimal rates and channel activity probabilities using the user distances to the receiver (or, equivalently, their average signal to noise ratios) assuming a Rayleigh block fading channel. The results demonstrate that the newly proposed optimal rate selection solutions offer significant increase in the expected system throughputs compared to the “same rate to all users” approach commonly used in the literature. In addition to the overall throughput optimization, we also address the issue of fairness among users and propose approaches guaranteeing a minimum amount of individual throughput to each user, and design systems with limited individual outage probabilities for increased energy efficiency and reduced delay.