Majority voting is a simple mathematical function that returns the most frequently occurring value within a given set. As a popular decision fusion technique (DFT), the majority voting function (MVF) finds applications in resolving conflicts, where several independent voters report their opinions on a classification problem. Despite its importance and its various applications in ensemble learning, data crowdsourcing, remote sensing, and data oracles for blockchains, the accuracy of the MVF for the general multiclass classification problem has remained unknown. In this article, we derive a new upper bound on the accuracy of the MVF for the multiclass classification problem. More specifically, we show that under certain conditions, the error rate of the MVF exponentially decays toward 0 as the number of independent voters increases. Conversely, the error rate of the MVF exponentially grows with the number of voters if these conditions are not met. We first explore the problem for voters with independent and identically distributed (i.i.d.) outputs, where we assume that, given the true classification of the data point, every voter follows the same conditional probability distribution of voting for different classes. Next, we extend our results to encompass independent but nonidentically distributed votes. Using the derived results, we then provide a discussion on the accuracy of the truth discovery algorithms. We show that in the best-case scenarios, truth discovery algorithms operate as an amplified MVF and thereby achieve a small error rate only when the MVF achieves a small error rate too, and vice versa, achieve a large error rate when the MVF also achieves a large error rate. However, in the worst case scenario, the truth discovery algorithms may exhibit a significantly higher error rate than the MVF. Finally, we confirm our theoretical results using numerical simulations.

Holographic Metasurface Transceivers (HMTs) are emerging as cost-effective substitutes to large antenna arrays for beamforming in Millimeter and TeraHertz wave communication. However, to achieve desired channel gains through beamforming in HMT, phase-shifts of a large number of elements need to be appropriately set, which is challenging. Also, these optimal phase-shifts depend on the location of the receivers, which could be unknown. In this work, we develop a learning algorithm using a fixed-budget multi-armed bandit framework to beamform and maximize received signal strength at the receiver for far-field regions. Our algorithm, named Holographic Beam (HoloBeam) exploits the parametric form of channel gains of the beams, which can be expressed in terms of two phase-shifting parameters. Even after parameterization, the problem is still challenging as phase-shifting parameters take continuous values. To overcome this, HoloBeam works with the discrete values of phase-shifting parameters and exploits their unimodal relations with channel gains to learn the optimal values faster. We upper bound the probability of HoloBeam incorrectly identifying the (discrete) optimal phase-shift parameters in terms of the number of pilots used in learning. We show that this probability decays exponentially with the number of pilot signals. We demonstrate that HoloBeam outperforms state-of-the-art algorithms through extensive simulations.

In this work, we study the performance of an unmanned aerial vehicle (UAV)-aided mixed radio frequency (RF)/underwater acoustic communication (MRFUAC) transmission system, where the UAV transmits signals to an underwater node through the amplify-and-forward (AF) relay, such as a buoy located on the sea surface. In particular, the UAV-relay RF channel follows a Rician distribution, while κ-μ shadowed fading distribution is applied to model the UAC link. For this considered system with the fixed-gain AF relay, we obtain the statistical distributions of the end-to-end signal-to-noise ratio. To demonstrate the performance of the MRFUAC system, formulae for the outage probability and average bit-error rate are further obtained in closed form. Moreover, to obtain some interesting insights, we present the asymptotic analyses of these performance metrics. To show the validity of our analysis, the truncation error analysis is also provided and the results show that our proposed method has a smaller error than that in the previous literature. In addition, we present the analysis of the optimal height of the UAV at different horizontal distances. In addition to the fixed-gain analysis, we also provide few results for the variable-gain AF relaying MRFUAC system. Finally, the validity of the theoretical analysis is confirmed by Monte Carlo simulations.

Holographic metasurface transceivers (HMT) are an emerging technology for enhancing the coverage and rate of wireless communication systems. However, acquiring accurate channel state information in HMT-assisted wireless communication systems is critical for achieving these goals. In this paper, we propose an algorithm for learning the optimal phase-shifts at an HMT for the far-field channel model. Our proposed algorithm exploits the structure of the channel gains in the far-field regions and learns the optimal phase-shifts in the presence of noise in the received signals. We prove that the probability that the optimal phase-shifts estimated by our proposed algorithm deviate from the true values decays exponentially in the number of pilot signals. Extensive numerical simulations validate the theoretical guarantees and also demonstrate significant gains as compared to the state-of-the-art policies.

One of the core problems in millimeter wave (mmWave) massive multiple-input-single-output (MISO) communication systems, which significantly affects the data rate, is the misalignment of the beam direction of the transmitter towards the receiver. In this paper, we investigate strategies that identify the best beam within a fixed duration of time. To this end, we develop an algorithm, namedUnimodal Bandit for Best Beam (UB3), that exploits the unimodal structure of the mean received signal strength as a function of the available beams and identifies the best beam within a fixed time duration using pure exploration strategies. We derive an upper bound on the probability of misidentifying the best beam, and we prove that the upper bound is of the orderO(log2Kexp {-αnA}), whereKis the number of beams,Ais a problem-dependent constant, and αnis the number of pilots used in the channel estimation phase. In contrast, when the unimodal structure is not exploited, the error probability is of orderO(log2Kexp {-αnA/(KlogK)}). Thus, by exploiting the unimodal structure, we achieve a much better error probability, which depends only logarithmically onK. We demonstrate thatUB3outperforms the state-of-the-art algorithms through extensive simulations.

In this paper, we propose to investigate a single RF chain multi-antenna full-duplex (FD) relay built with$b$-bit analog phase shifters and passive self-interference cancellation. Next, assuming only passive self-interference cancellation at the FD relay, we derive the achievable data rate of a system comprised of a source, the proposed FD relay, and a destination. We then compare the achievable data rate of the proposed FD relaying system with the achievable data rate of the same system but with the FD relay replaced by an ideal passive RIS. Our results show that the proposed relaying system with 2-bit quantized analog phase shifters significantly outperforms the RIS-assisted system. In fact, the performance gains are so large, at least for small to intermediate numbers of antenna elements, that we believe it makes this result of interest to the wireless community. The proposed FD relay can also be built with reconfigurable holographic surfaces, one surface for the transmit-side and one for the receive-side. For such a scenario, we derive the energy efficiency of the relay-assisted system and compare it with the RIS-assisted system. Our numerical results show that the energy efficiency of the relay-assisted system built with reconfigurable holographic surfaces is significantly higher than the energy efficiency of the RIS-assisted system. Intuitively, the RIS system is at a disadvantage since there the total transmit power$P_{T}$is used entirely by the source, whereas in the FD relaying system the total transmit power$P_{T}$is shared by the source and the FD relay in addition to the noise-cleansing process performed by the decode-and-forwarding at the FD relay.

In this paper, we propose a classifier for classification of data vectors with mutually independent but not identically distributed elements. For the proposed classifier, we prove that the error probability goes to zero as the length of the data vectors goes to infinity, even when there is only one training data vector per label available. Finally, we present numerical examples where we show that the performance of the proposed classifier outperforms conventional classification algorithms when the number of training data is small.

In this paper, we combine centralized dynamic-time division duplex (D-TDD) with interference alignment (IA) for a wireless network comprised of$N$full duplex nodes. We maximize the performance of the proposed centralized D-TDD scheme utilizing IA in terms of rate region by optimizing the reception, transmission, simultaneous reception and transmission, and silence at each node in each time slot in addition to the choice of whether a node should treat the interference as noise or it should use IA. The problem of the rate region maximization of the wireless network is formulated as a non-convex optimization problem, whose optimal solution is found. The simulation results demonstrate that the proposed centralized D-TDD scheme utilizing IA achieves significant gains over the existing D-TDD schemes.

The study of optimal properties of centralized dynamic-time-division-duplex (D-TDD) employed at a wireless network consisting of multiple nodes is a highly challenging and partially understood problem in the literature. In this paper, we develop an optimal centralized D-TDD scheme for a wireless network comprised of K full-duplex nodes impaired by self-interference and additive white Gaussian noise. As a special case, we also propose the optimal centralized D-TDD scheme when part or all nodes in the wireless network are half-duplex. Thereby, we derive the optimal adaptive scheduling of the reception, transmission, simultaneous reception and transmission, and silence at every node in the network in each time slot such that the rate region of the network is maximized. The performance of the optimal centralized D-TDD can serve as an upper-bound to any other TDD scheme, which is useful in qualifying the relative performance of TDD schemes. The numerical results show that the proposed centralized D-TDD scheme achieves significant rate gains over existing centralized D-TDD schemes.

In molecular communications, the direct detection of signaling molecules may be challenging due to the lack of suitable sensors and interference from co-existing substances in the environment. Motivated by examples in nature, we investigate an indirect detection mechanism using chemical reactions between the signaling molecules and a molecular probe to produce an easy-to-measure product at the receiver. The underlying reaction-diffusion equations that describe the concentrations of the reactant and product molecules in the system are non-linear and coupled, and cannot be solved in closed-form. To analyze these molecule concentrations, we develop an efficient iterative algorithm by discretizing the time variable and solving for the space variables in each time step. We also derive insightful closed-form solutions for a special case. The accuracy of the proposed algorithm is verified by particle-based simulations. Our results show that the concentration of the product molecules has a similar characteristic over time as the concentration of the signaling molecules. We analyze the bit error rate (BER) for a threshold detector and highlight that significant improvements in the BER can be achieved by carefully choosing the molecular probe and optimizing the detection threshold.

In this paper, we focus on maximization of the instantaneous sum-rate in flexible half-duplex networks, where nodes have the flexibility to choose to either transmit, receive or be silent in a given time slot. Since the corresponding optimization problem is NP-hard, we design low-cost algorithms that give sub-optimal solutions with good performance. We first consider two existing approximation techniques to simplify the sum-rate optimization problem: arithmetic-geometric means inequality and another utilising the tight lower bound approximation. We then propose a novel pattern search algorithm that performs close to exhaustive search but with significantly lower complexity. Comparing the performance of the proposed algorithm with respect to existing resource allocation techniques, we observe that our proposed algorithm provides significant sum-rate gains.

In this paper, we introduce dynamic time-frequency-division duplex (D-TFDD), which is a novel duplexing scheme that combines time-division duplex (TDD) and frequency-division duplex (FDD). In D-TFDD, a user receives from the base station (BS) on the downlink in one frequency band and transmits to the BS on the uplink in another frequency band, as in FDD. Next, the user shares its uplink transmission (downlink reception) on the corresponding frequency band with the uplink transmission or the downlink reception of another user in a D-TDD fashion. Hence, in a given frequency band, the BS communicates with user 1 (U1) and user 2 (U2) in a D-TDD fashion. The proposed D-TFDD scheme does not require inter-cell interference (ICI) knowledge and only requires channel state information (CSI) of the local BS-U1 and BS-U2 channels. Thereby, it is practical for implementation. The proposed D-TFDD scheme increases the throughput region between the BS and the two users in a given frequency band, and significantly decreases the outage probabilities on the corresponding BS-U1 and BS-U2 channels. Most importantly, the proposed D-TFDD scheme doubles the diversity gain on both the corresponding BS-U1 and the BS-U2 channels compared to the diversity gain of existing duplexing schemes, which results in very large performance gains.

In this paper, we propose optimal centralized dynamic-time-division-duplex (D-TDD) scheme for a general network comprised of K half-duplex (HD) nodes. Specifically, for this network, we propose optimal adaptive scheduling of the reception, transmission, and silence at every node in each time slot such that the average sum signal-to-interference-plus-noise-ratio (SINR) of the network is maximized. The numerical results show that the proposed optimal centralized D-TDD scheme achieves significant SINR gains over existing centralized D-TDD schemes, especially in small crowded areas. The proposed scheme can act as an upper bound to distributed D-TDD schemes, but it can also be applicable in small crowded areas where gathering of the channel gains of all links may be practical.

In this paper, we investigate the secrecy capacity of a point-to-point, full-duplex (FD) wirelesly powered communication system in the presence of a passive eavesdropper (EVE). The considered system is comprised of an energy transmitter (ET), an energy harvesting user (EHU), and a passive EVE. The ET transmits radio-frequency energy, which is used for powering the EHU as well as for generating interference at the EVE. The EHU uses the energy harvested from the ET to transmit confidential messages back to the ET. As a consequence of the FD mode of operation, both the EHU and the ET are subjected to self-interference, which has different effects at the two nodes. In particular, the self-interference impairs the decoding of the received message at the ET, whilst it serves as an additional energy source at the EHU. For this system model, we derive an upper and a lower bound on the secrecy capacity. For the lower bound, we propose a simple achievability scheme. Our numerical results show significant improvements in terms of achievable secrecy rate when the proposed communication scheme is employed against its half-duplex counterpart, even for practical self-interference values at the ET.

We consider a molecular communication system comprised of a transmitter, an absorbing receiver, and an interference source. Assuming amplitude modulation, we analyze the dependence of the bit error rate (BER) on the duration of the detection interval, which is the time within one transmission symbol interval during which the receiver is active to absorb and count molecules. We then propose algorithms to obtain the optimal detection interval that minimizes the BER of the considered molecular communication system. Simulation and numerical evaluations are provided to highlight further insights into the optimal results. For example, we demonstrate that the optimal detection interval can be very small compared to the transmission symbol interval. Moreover, our numerical results show that significant BER improvements are achieved by using the optimal detection interval.

In this paper, we investigate the capacity of a point-to-point, full-duplex (FD) wirelessly powered communication system impaired by self-interference. This system is comprised of an energy transmitter (ET) and an energy harvesting user (EHU), which operates in the FD mode. The ET transmits energy toward the EHU. The EHU harvests this energy and uses it to transmit information back to the ET. As a result of the FD mode, both nodes are affected by self-interference. The self-interference has different effects at the two nodes. In particular, the self-interference impairs the decoding of the received information signal at the ET, whereas it serves as an additional source of energy at the EHU. In this paper, we derive the capacity of the adopted system model assuming a processing cost at the EHU and an additive white Gaussian noise channel with block fading. Thereby, we show that the capacity achieving scheme is relatively simple and therefore applicable to devices with limited resources. Moreover, our numerical results show significant improvements in terms of data rate when the capacity achieving strategy is employed compared to half-duplex transmission, even for very high self-interference at the ET. Moreover, we show the positive effects of the self-interference at the EHU, as well as the crippling effect of the processing cost.

In this paper, we investigate the fading two-hop full-duplex (FD) relay channel with self-interference, which is comprised of a source, an FD relay impaired by self-interference, and a destination, where a direct source-destination link does not exist. For this channel, we propose three buffer-aided relaying schemes with adaptive reception-transmission at the FD relay for the cases when the source and the relay both perform continuous-rate transmission with adaptive-power allocation, continuous-rate transmission with fixed-power allocation, and discrete-rate transmission, respectively. The proposed buffer-aided relaying schemes enable the FD relay to adaptively select to either receive, transmit, or simultaneously receive and transmit in a given time slot based on the qualities of the receiving, transmitting, and self-interference channels, a degree-of-freedom unavailable without buffer-aided relaying. Our numerical results show that significant performance gains are achieved using the proposed buffer-aided relaying schemes compared with conventional FD relaying, where the FD relay is forced to always simultaneously receive and transmit, and to buffer-aided half-duplex relaying, where the half-duplex relay cannot simultaneously receive and transmit. The main implication of this paper is that FD relaying systems without buffer-aided relaying miss-out on significant performance gains.

In this paper, we investigate the fading two-hop full-duplex (FD) relay channel with self- interference, which is comprised of a source, an FD relay impaired by self-interference, and a destination, where a direct source-destination link does not exist. For this channel, we propose two buffer-aided relaying schemes with adaptive reception-transmission at the FD relay for the cases when the source and the relay both perform adaptive-rate and fixed-rate transmission, respectively. The proposed buffer-aided relaying schemes enable the FD relay to adaptively select to either receive, transmit, or simultaneously receive and transmit in a given time slot based on the qualities of the receiving, transmitting, and self-interference channels; a degree-of-freedom unavailable without buffer-aided relaying. Our numerical results show that significant performance gains are achieved using the proposed buffer-aided relaying schemes compared to conventional FD relaying, where the FD relay is forced to always simultaneously receive and transmit, and to buffer-aided half-duplex relaying, where the half-duplex relay cannot simultaneously receive and transmit. The main conclusion of this work is that FD relaying systems without buffer-aided relaying miss-out on significant performance gains.

In this paper, we consider a multiple-input multiple-output wireless powered communication network, where multiple users harvest energy from a dedicated power station in order to be able to transmit their information signals to an information receiving station. Employing a practical non-linear energy harvesting (EH) model, we propose a joint time allocation and power control scheme, which takes into account the uncertainty regarding the channel state information (CSI) and provides robustness against imperfect CSI knowledge. In particular, we formulate two non-convex optimization problems for different objectives, namely system sum throughput maximization and the maximization of the minimum individual throughput across all wireless powered users. To overcome the non-convexity, we apply several transformations along with a one-dimensional search to obtain an efficient resource allocation algorithm. Numerical results reveal that a significant performance gain can be achieved when the resource allocation is designed based on the adopted non-linear EH model instead of the conventional linear EH model. Besides, unlike a non-robust baseline scheme designed for perfect CSI, the proposed resource allocation schemes are shown to be robust against imperfect CSI knowledge.

In this paper, we investigate the capacity of the Gaussian two-hop full-duplex (FD) relay channel with residual self-interference. This channel is comprised of a source, an FD relay, and a destination, where a direct source-destination link does not exist and the FD relay is impaired by residual self-interference. We adopt the worst case linear self-interference model with respect to the channel capacity, and model the residual self-interference as a Gaussian random variable whose variance depends on the amplitude of the transmit symbol of the relay. For this channel, we derive the capacity and propose an explicit capacity-achieving coding scheme. Thereby, we show that the optimal input distribution at the source is Gaussian and its variance depends on the amplitude of the transmit symbol of the relay. On the other hand, the optimal input distribution at the relay is discrete or Gaussian, where the latter case occurs only when the relay-destination link is the bottleneck link. The derived capacity converges to the capacity of the two-hop ideal FD relay channel without self-interference and to the capacity of the two-hop half-duplex (HD) relay channel in the limiting cases when the residual self-interference is zero and infinite, respectively. Our numerical results show that significant performance gains are achieved with the proposed capacity-achieving coding scheme compared with the achievable rates of conventional HD relaying and/or conventional FD relaying.

In this paper, we apply the notion of opportunistic scheduling in wireless-powered communication networks (WPCNs). The considered WPCN model consists of a base station (BS) and multiple energy harvesting users (EHUs), where the BS broadcasts radio frequency energy to the EHUs over the downlink and receives information from the EHUs over the uplink. We differentiate the WPCNs based upon the battery management policy at the EHUs, i.e., whether an EHU spends the total amount of energy harvested in its battery for each IT (WPCN type 1), or spends only a part of it for the current IT and saves the other part for future ITs (WPCN type 2). We propose two opportunistic scheduling policies, referred to as the harvest-then-select and harvest-or-select protocols, employed at the WPCN type 1 and WPCN type 2, respectively. These protocols have significant practical advantages over the state-of-the-art schemes proposed for maximizing the WPCN sum-rate, because they introduce fairness in the resource utilization by the EHUs, and require much lower amount of channel state information. Both protocols achieve these benefits at the expense of a minor rate degradation relative to the rates achieved by their counterpart protocols employing multiple access, denoted as the harvest-then-transmit and harvest-or-concurrently-transmit protocols.

We consider the two-hop half-duplex (HD) relay network, where the source-to-relay and relay-to-destination links are impaired by block fading. The relay is equipped with a buffer, which enables the relay to receive or transmit in each time slot independent of previous time slots. As a practical constraint, source and relay can transmit only at rates taken from predefined and finite sets. Thereby, it is assumed that for each time slot, the instantaneous qualities of the two links are available. For this network, we derive the optimal scheduling of reception and transmission at the relay and the optimal rate selection at source and relay, such that the throughput is maximized. Since the optimal protocol introduces unbounded delay, we also propose a buffer-aided protocol, which limits the delay. For this delay-limited protocol, we study the achieved delay and throughput by modeling the queue at the buffer as a Markov chain. Our numerical results show that the throughputs achieved with the proposed buffer-aided protocols for discrete transmission rates are significantly larger than the throughputs achieved with conventional relaying protocols where the HD relay switches between reception and transmission in a strictly alternating manner.

In this paper, we investigate a communication system comprised of an energy harvesting (EH) source, which harvests radio frequency (RF) energy from an out-of-band full-duplex relay node and exploits this energy to transmit data to a destination node via the relay node. We assume two scenarios for the battery of the EH source. In the first scenario, we assume that the EH source is not equipped with a battery and thereby cannot store energy. As a result, the RF energy harvested during one symbol interval can only be used in the following symbol interval. In the second scenario, we assume that the EH source is equipped with a battery having unlimited storage capacity in which it can store the harvested RF energy. As a result, the RF energy harvested during one symbol interval can be used in any of the following symbol intervals. For both system models, we derive the channel capacity subject to an average power constraint at the relay and an additional energy transmission cost at the EH source. We compare the derived capacities to the achievable rates of several benchmark schemes. Our results show that using the optimal input distributions at both the EH source and the relay is essential for high performance. Moreover, we demonstrate that neglecting the energy transmission cost at the source can result in a severe overestimation of the achievable performance.

In this paper, we investigate the capacity of the Gaussian two-hop full-duplex (FD) relay channel with self-interference. This channel is comprised of a source, an FD relay, and a destination, where a direct source-destination link does not exist and the FD relay is impaired by self- interference. We model the self-interference as an additive Gaussian random variable whose variance is proportional to the amplitude of the transmit symbol at the relay. For this channel, we derive the capacity and propose an explicit capacity- achieving coding scheme. Thereby, we show that the optimal input distribution at the source is Gaussian and its variance depends on the amplitude of the transmit symbol at the relay. On the other hand, the optimal input distribution at the relay is discrete or Gaussian, where the latter case occurs only when the relay- destination link is the bottleneck link. The derived capacity converges to the capacity of the two-hop ideal FD relay channel without self- interference and to the capacity of the two-hop half-duplex (HD) relay channel in the limiting cases when the self-interference is zero and infinite, respectively. Our numerical results show that significant performance gains are achieved using the proposed capacity-achieving coding scheme compared to the achievable rates of conventional FD relaying and HD relaying.

In this paper, we investigate the resource allocation algorithm design for full-duplex simultaneous wireless information and power transfer (FD-SWIPT) systems. The considered system comprises a FD radio base station, multiple single-antenna half-duplex (HD) users, and multiple energy harvesters equipped with multiple antennas. We propose a multi-objective optimization framework to study the trade-off between uplink transmit power minimization, downlink transmit power minimization, and total harvested energy maximization. The considered optimization framework takes into account heterogeneous quality of service requirements for uplink and downlink communication and wireless power transfer. The non-convex multi-objective optimization problem is transformed into an equivalent rank-constrained semidefinite program (SDP) and solved optimally by SDP relaxation under certain general conditions. The solution of the proposed framework results in a set of Pareto optimal resource allocation policies. Numerical results unveil an interesting trade-off between the considered conflicting system design objectives and reveal the improved power efficiency facilitated by FD in SWIPT systems compared to traditional HD systems.

In this paper, we investigate a communication system comprised of a wireless sensor which harvests radio frequency (RF) energy from a full-duplex relay node and exploits this energy to transmit data to a destination node via the relay node. Thereby, the relay has two functions. Namely, it transfers RF energy to the sensor via wireless power transfer and relays the information received from the sensor to the destination. Moreover, we assume that the sensor is too small to be equipped with a battery. As a result, the energy of each symbol transmitted by the sensor is limited by the energy harvested during the previous symbol interval. For this system model, we derive the capacity for an average power constraint at the relay. Thereby, we show that in order to achieve the capacity, the sensor has to harvest the RF energy that reaches the sensor when the relay transmits information to the destination. As a result, the relay does not need to dedicate energy strictly for energy harvesting since the energy spent by the relay for information transfer can also be used by the sensor to harvest energy. In a numerical example, we compare the derived capacity to the rates of two benchmark schemes. Our results show that using the optimal input distributions at both the sensor and the relay is essential for high performance.

A simple diamond half-duplex relay network composed of a source, two decode-and-forward half-duplex relays, and a destination is considered, where a direct link between the source and the destination does not exist. For this network, we study the case of buffer-aided relays, where the relays are equipped with buffers. Each relay can receive data from the source, store it in the buffer, and forward it to the destination, when the channel conditions are advantageous. Thereby, buffering enables adaptive scheduling of the transmissions and receptions over time, which allows the network to exploit the diversity offered by the fading channels. For the considered half-duplex network, four transmission modes are defined based on whether the relay nodes receive or transmit. In this paper, we derive the locally optimal scheduling of the transmission modes over time and investigate the achievable average rate, when the relays are affected by inter-relay interference. Since the proposed buffer-aided transmission policies introduce unbounded delay, we provide a sub-optimal buffer-aided transmission policy with limited delay. Moreover, for inter-relay interference cancellation, we consider two coding schemes with different complexities. In the first scheme, we employ dirty paper coding, which entails a high complexity, whereas in the second scheme, we adopt a low-complexity technique based on successive interference cancellation at the receiving relay nodes and optimal power allocation at the transmitting nodes. Our numerical results show that the proposed protocols, with and without delay constraints, outperform existing protocols for the considered network from the literature.

Although extensively investigated, the capacity of the two-hop half-duplex (HD) relay channel is not fully understood. In particular, a capacity expression which can be evaluated straightforwardly is not available and an explicit coding scheme which achieves the capacity is not known either. In this paper, we derive a new expression for the capacity of the two-hop HD relay channel based on a simplified converse. Compared to previous results, this capacity expression can be easily evaluated. Moreover, we propose an explicit coding scheme which achieves the capacity. To achieve the capacity, the relay does not only send information to the destination by transmitting information-carrying symbols but also with the zero symbols resulting from the relay's silence during reception. As examples, we compute the capacities of the two-hop HD relay channel for the cases when the source-relay and relay-destination links are both binary-symmetric channels (BSCs) and additive white Gaussian noise (AWGN) channels, respectively, and numerically compare the capacities with the rates achieved by conventional relaying where the relay receives and transmits in a codeword-by-codeword fashion and switches between reception and transmission in a strictly alternating manner. Our numerical results show that the capacities of the two-hop HD relay channel for BSC and AWGN links are significantly larger than the rates achieved with conventional relaying.

A simple diamond half-duplex relay network composed of a source, two half-duplex relays, and a destination is considered, where no direct link between the source and the destination is exists. For this network, we investigate the achievable rate when the relays are equipped with buffers. Buffer-aided relays can receive data from the source, store it in their buffers, and forward it to the destination when the channel conditions are more advantageous. Thereby, buffering enables adaptive scheduling of the transmissions and receptions over time, which allows the network to better exploit the diversity offered by the fading channel. For the considered network, because of the half-duplex relays, four transmission modes are employed based on whether the relay nodes receive or transmit. Considering these four transmission modes, in this paper, we derive the optimal transmission mode selection policy such that the received data rate at the destination is maximized. Furthermore, based on numerical examples, we show that the proposed protocol outperforms the existing protocols for the considered network in the literature.

In this paper, we consider bidirectional relay networks in which two users exchange information only via a relay node, i.e., a direct link between both users is not present. We assume that channel state information at the transmitter is not available and/or only one coding and modulation scheme is used due to complexity constraints. Thus, the nodes transmit with a fixed predefined rate regardless of the channel state. In general, the nodes in the network can assume one of three possible states in each time slot, namely, the transmit, the receive, and the silent state. Most of the existing bidirectional relaying protocols assume a prefixed schedule for the sequence in which the states of the nodes are used. In this paper, we abandon the restriction of having a fixed and predefined schedule and consider the selection of the states of the nodes as a degree of freedom that can be exploited for performance optimization. To this end, the relay has to be equipped with two buffers for storage of the information received from the two users. In Part I of this paper, we propose a delay-unconstrained protocol that, based on the qualities of the involved links, selects the optimal states of the nodes in each time slot such that the sum throughput is maximized. In Part II, several delay-constrained protocols are proposed and analyzed. Numerical results show that the proposed protocols significantly outperform the existing bidirectional relaying protocols in the literature.

This is the second part of a two-part paper considering bidirectional relay networks with half-duplex nodes and block fading where the nodes transmit with a fixed transmission rate. In Part I, it was shown that a considerable gain in terms of sum throughput can be obtained by optimally selecting the transmission modes or, equivalently, the states of the nodes, i.e., the transmit, the receive, and the silent states, based on the qualities of the involved links. To enable adaptive transmission mode selection, the relay has to be equipped with two buffers for storage of the data received from the two users. The protocol proposed in Part I was delay unconstrained and provides an upper bound for the performance of practical delay-constrained protocols. In this paper, we propose two heuristic but efficient delay-constrained protocols, which can approach the performance upper bound reported in Part I, even in cases where only a small delay is permitted. The proposed protocols not only consider the instantaneous qualities of the involved links for adaptive mode selection but also take the states of the queues at the buffers into account, i.e., the number of packets in the queues. The average throughput and the average delay of the proposed delay-constrained protocols are evaluated by analyzing the Markov chain of the states of the queues. Numerical results show that the proposed protocols outperform existing bidirectional relaying protocols for delay-constrained transmission.

The half-duplex (HD) multi-hop relay channel consists of a source, multiple HD relays connected in series, and a destination where links are present only between adjacent nodes. In this paper, we focus on decode-and-forward relays and assume that the links are impaired by block fading and additive white Gaussian noise. We design a new protocol which, unlike the conventional protocols for the multi-hop relay channel, does not adhere to a fixed and predefined pattern of using the transmit, receive, and silent states of the nodes. In particular, the proposed protocol selects the optimal states of the nodes and the corresponding optimal transmission rates based on the instantaneous channel state information (CSI) of the involved links in each fading block such that the achievable average rate from source to destination is maximized. To enable adaptive scheduling of the states of the nodes, the relay nodes have to be equipped with buffers for temporary storage of the information received from the preceding node. Additionally, we discuss and address two practical challenges arising in the implementation of the optimal protocol, namely the unconstrained end-to-end delay due to data buffering at the relays and the required CSI overhead. Numerical results confirm the superiority of the proposed buffer-aided protocols compared to existing multi-hop relaying protocols.

In the half-duplex single relay selection network, comprised of a source, M half-duplex relays, and a destination, only one relay is active at any given time, i.e., only one relay receives or transmits, and the other relays are inactive, i.e., they do not receive nor transmit. The capacity of this network, when all links are affected by independent slow time-continuous fading and additive white Gaussian noise (AWGN) , is still unknown, and only achievable average rates have been reported in the literature so far. In this paper, we present new achievable average rates for this network, which are larger than the best known average rates. These new average rates are achieved with a buffer-aided relaying protocol. Since the developed buffer-aided protocol introduces unbounded delay, we also devise a buffer-aided protocol which limits the delay at the expense of a decrease in rate. Moreover, we discuss the practical implementation of the proposed buffer-aided relaying protocols and show that they do not require more resources for channel state information acquisition than the existing relay selection protocols.

In this paper, we consider a bidirectional relay network with half-duplex nodes and block fading where the nodes transmit with a fixed transmission rate. Thereby, user 1 and user 2 exchange information only via a relay node, i.e., a direct link between both users is not present. Recently in [1], it was shown that a considerable gain in terms of sum throughput can be obtained in bidirectional relaying by optimally selecting the transmission modes or, equivalently, the states of the nodes, i.e., the transmit, the receive, and the silent states, in each time slot based on the qualities of the involved links. To enable adaptive transmission mode selection, the relay has to be equipped with two buffers for storage of the data received from the two users. However, the protocol proposed in [1] was delay-unconstrained and provides an upper bound for the performance of practical delay-constrained protocols. In this paper, we propose a heuristic but efficient delay-constrained protocol which can approach the performance upper bound reported in [1]. Moreover, the average throughput and delay of the protocol are evaluated by analyzing the Markov chain of the states of the queues.

The fading three-hop half-duplex relay network consists of a source, two half-duplex relays, and a destination connected in series where links are present only between adjacent nodes. We assume that the links are impaired by time-continuous fading and additive white Gaussian noise. For this network, we design new protocols based on buffer-aided relaying and derive their achievable average rates. We first develop a buffer-aided protocol which maximizes the average rate, but, as a side effect, introduces unbounded delay. Therefore, we also design a buffer-aided protocol which constrains the average delay, but at the expense of decrease of rate. Our numerical results show that the maximum average rate achieved with the developed buffer-aided protocol is larger than that of existing protocols for the considered network. Moreover, given a sufficiently large permissible average delay, the average rate achieved with the buffer-aided protocol with a delay constraint approaches the maximum average rate achieved without a delay constraint.

In the half-duplex single relay selection network, comprised of a source, M half-duplex relays, and a destination, only one relay is active at any given time, i.e., only one relay receives or transmits, and the other relays are inactive, i.e., they do not receive or transmit. The capacity of this network, when all links are affected by independent time-continuous fading and additive white Gaussian noise (AWGN), is still unknown. Hence, only achievable average rates have been reported in the literature so far. In this paper, we present new achievable average rates for this network which are larger than the best known average rates in the literature. These average rates are achieved with a buffer-aided relaying protocol. Since the developed buffer-aided protocol which achieves these rates introduces unbounded delay, we also devise a buffer-aided protocol which limits the delay at the expense of decrease in rate. Moreover, we show that the proposed buffer-aided relaying protocols do not require more resources for channel state information acquisition than the existing relay selection protocols.

In this paper, we consider the problem of sum throughput maximization for bidirectional relay networks with block fading. Thereby, user 1 and user 2 exchange information only via a relay node, i.e., a direct link between both users is not present. We assume that channel state information at the transmitter (CSIT) is not available and/or only one coding and modulation scheme is used at the transmitters due to complexity constraints. Thus, the nodes transmit with a fixed predefined rate regardless of the channel state information (CSI). In general, the nodes in the network can assume one of three possible states in each time slot, namely the transmit, receive, and silent state. Most of the existing protocols assume a fixed schedule for the sequence of the states of the nodes. In this paper, we abandon the restriction of having a fixed and predefined schedule and propose a new protocol which, based on the CSI at the receiver (CSIR), selects the optimal states of the nodes in each time slot such that the sum throughput is maximized. To this end, the relay has to be equipped with two buffers for storage of the information received from the two users. Numerical results show that the proposed protocol significantly outperforms the existing protocols.

The bidirectional relay channel, in which two users communicate with each other through a relay node, is a simple but fundamental and practical network architecture. In this paper, we consider the block fading bidirectional relay channel with a decode-and-forward relay and propose efficient transmission strategies that exploit the block fading property of the channel. We assume that a direct link between the two users is not present and consider two transmission modes: 1) the multiple-access mode (both users transmit to the relay) and 2) the broadcast mode (the relay transmits to both users). Most existing relaying protocols assume a fixed schedule for using these transmission modes. In contrast, we abandon the restriction of having a fixed and predefined schedule and propose to optimize the selection of the transmission modes and the associated transmission rates based on the instantaneous channel state information (CSI) of the involved links. Thereby, we consider two different types of transmit power constraints: 1) a fixed transmit power for each node and 2) a per-node long-term power constraint. To enable the use of a nonpredefined schedule for transmission mode selection, the relay has to be equipped with two buffers for storage of the information received from both users. We develop new relaying protocols based on adaptive mode selection and provide the corresponding achievable long-term rate regions. In particular, based on the CSI of the involved links, the optimal transmission mode as well as the optimal transmission rates and/or the transmit powers of the nodes are chosen in each time slot to maximize the weighted sum rate of both users. By varying the weights assigned to the users, the boundary surface of the achievable long-term rate region of the proposed protocol can be obtained. In addition, we discuss and address two practical challenges for the implementation of the proposed protocols, namely, the availability of the knowledge of the channel statistics required for the implementation of the optimal protocols, and the increase of the end-to-end delay due to the data buffering. Numerical results confirm the superiority of the proposed buffer-aided protocols compared with existing bidirectional relaying protocols.

Wireless systems that carry delay-sensitive information (such as speech and/or video signals) typically transmit with fixed data rates, but may occasionally suffer from transmission outages caused by the random nature of the fading channels. If the transmitter has instantaneous channel state information (CSI) available, it can compensate for a significant portion of these outages by utilizing power allocation. In a conventional dual-hop bidirectional amplify-and-forward (AF) relaying system, the relay already has instantaneous CSI of both links available, as this is required for relay gain adjustment. We therefore develop an optimal power allocation strategy for the relay, which adjusts its instantaneous output power to the minimum level required to avoid outages, but only if the required output power is below some cutoff level; otherwise, the relay is silent in order to conserve power and prolong its lifetime. The proposed scheme is proven to minimize the system outage probability, subject to an average power constraint at the relay and fixed output powers at the end nodes.

In this paper, we consider the problem of sum rate maximization in a bidirectional relay network with fading. Hereby, user 1 and user 2 communicate with each other only through a relay, i.e., a direct link between user 1 and user 2 is not present. In this network, there exist six possible transmission modes: four point-to-point modes (user 1-to-relay, user 2-to-relay, relay-to-user 1, relay-to-user 2), a multiple access mode (both users to the relay), and a broadcast mode (the relay to both users). Most existing protocols assume a fixed schedule of using a subset of the aforementioned transmission modes, as a result, the sum rate is limited by the capacity of the weakest link associated with the relay in each time slot. Motivated by this limitation, we develop a protocol which is not restricted to adhere to a predefined schedule for using the transmission modes. Therefore, all transmission modes of the bidirectional relay network can be used adaptively based on the instantaneous channel state information (CSI) of the involved links. To this end, the relay has to be equipped with two buffers for the storage of the information received from users 1 and 2, respectively. For the considered network, given a total average power budget for all nodes, we jointly optimize the transmission mode selection and power allocation based on the instantaneous CSI in each time slot for sum rate maximization. Simulation results show that the proposed protocol outperforms existing protocols for all signal-to-noise ratios (SNRs). Specifically, we obtain a considerable gain at low SNRs due to the adaptive power allocation and at high SNRs due to the adaptive mode selection.

For a point-to-point communication system generating its power via energy harvesting (EH), we derive the asymptotically optimal power allocation which optimizes a general utility function when the number of transmitted codewords N and the battery capacity Bmaxsatisfy N → ∞ and Bmax→ ∞. The considered family of utility functions is general enough to include the most important performance measurements in communication theory such as ergodic rate, outage probability, average signal-to-noise ratio, etc. The discovered solution is very simple. Namely, the optimal power allocation for the EH system is identical to the optimal power allocation of an equivalent non-EH communication system with infinite available energy, under the constraint that both systems use identical average transmit powers. Although the proposed solution is asymptotic, it is applicable to EH systems transmitting a large but finite number of codewords and having a battery capacity much larger than the average harvested power and/or the maximum average transmit power.

In this paper, we consider a simple network consisting of a source, a half-duplex decode-and-forward relay, and a destination. We propose a new relaying protocol employing adaptive link selection, i.e., in any given time slot, based on the channel state information of the source-relay and the relay-destination link a decision is made whether the source or the relay transmits. In order to avoid data loss at the relay, adaptive link selection requires the relay to be equipped with a buffer such that data can be queued until the relay-destination link is selected for transmission. We study both delay-constrained and delay-unconstrained transmission. For the delay-unconstrained case, we characterize the optimal link selection policy, derive the corresponding throughput, and develop an optimal power allocation scheme. For the delay-constrained case, we propose to starve the buffer of the relay by choosing the decision threshold of the link selection policy smaller than the optimal one and derive a corresponding upper bound on the average delay. Furthermore, we propose a modified link selection protocol which avoids buffer overflow by limiting the queue size. Our analytical and numerical results show that buffer-aided relaying with adaptive link selection achieves significant throughput gains compared to conventional relaying protocols with and without buffers where the relay employs a fixed schedule for reception and transmission.

We consider a simple network consisting of a source, a half-duplex decode-and-forward relay with a buffer, and a destination. We assume that the direct source-destination link is not available and all links undergo fading. We propose two new buffer-aided relaying schemes with different requirements regarding the availability of channel state information at the transmitter (CSIT). In the first scheme, neither the source nor the relay has full CSIT, and consequently, both nodes are forced to transmit with fixed rates. In contrast, in the second scheme, the source does not have full CSIT and transmits with fixed rate but the relay has full CSIT and adapts its transmission rate accordingly. In the absence of delay constraints, for both fixed rate and mixed rate transmission, we derive the throughput-optimal buffer-aided relaying protocols which select either the source or the relay for transmission based on the instantaneous signal-to-noise ratios (SNRs) of the source-relay and relay-destination links. In addition, for the delay constrained case, we develop buffer-aided relaying protocols that achieve a predefined average delay. Compared to conventional relaying protocols, which select the transmitting node according to a predefined schedule independent of the instantaneous link SNRs, the proposed buffer-aided protocols with adaptive link selection achieve large performance gains. In particular, for fixed rate transmission, we show that the proposed protocol achieves a diversity gain of two as long as an average delay of more than three time slots can be afforded. Furthermore, for mixed rate transmission with an average delay ofE{T} time slots, a multiplexing gain ofr=1-1/ (2E{T}) is achieved. As a by-product of the considered link-adaptive protocols, we also develop a novel conventional relaying protocol for mixed rate transmission, which yields the same multiplexing gain as the protocol with adaptive link selection. Hence, for mixed rate transmission, for sufficiently large average delays, buffer-aided half-duplex relaying with and without adaptive link selection does not suffer from a multiplexing gain loss compared to full-duplex relaying.

We propose a buffer-aided relaying protocol for a three node relay network comprised of a source, a half-duplex relay with buffer, and a destination. We assume a direct source-destination link is available and all links undergo fading. The proposed protocol enables the half-duplex relay to choose its reception and transmission time slots adaptively and based on the quality of the involved links. We derive the achievable ergodic rate of the considered three-node network for the proposed protocol. Our results show that this achievable ergodic rate exceeds existing unachievable ergodic capacity upper bounds for the three-node half-duplex relay channel with the relay always alternating between reception and transmission in successive time slots.

We investigate a simple three-node network consisting of a source, a half-duplex decode-and-forward relay with a buffer, and a destination. We assume that a direct source-destination link is not available and all links undergo fading. We consider the case where the source has no channel state information (CSI) and thus is forced to transmit with a fixed rate. On the other hand, the relay has full CSI and thus is able to adapt its rate to the underlaying channel. We propose a buffer-aided relaying protocol which allows the relay to choose its transmission and reception time slots adaptively and based on the quality of the source-relay and relay-destination links. For this system, we derive the maximum achievable throughput and the fraction of throughput lost due to outages. Our results reveal that compared to the conventional case when the relay always alternates between reception and transmission, a throughput gain of up to 100% is possible.

In this paper, we consider a simple network consisting of a source, a half-duplex decode-and- forward relay, and a destination. In contrast to most of the existing literature, we assume that the relay is equipped with a buffer and show that this can lead to substantial performance gains. We propose a simple protocol which chooses either the source-relay or the relay-destination link for transmission depending on the instantaneous channel state information. For this simple protocol, we derive the throughput for adaptive rate transmission and the outage probability for fixed rate transmission. Our results show that, unlike conventional relaying, buffer-aided relaying yields a diversity gain of two. In addition, throughput gains of up to 100 % compared to conventional relaying are possible.

A complete evaluation of the benefits of cooperative diversity schemes should not only include the outage and error rate performance but also the second-order statistics of the achievable information-theoretic capacity. In a non-ergodic fading channel, the system is said to be in outage when the destination cannot decode the fixed-rate transmitted signal with negligible error probability. Because of the Doppler effect, which is induced by the mobility of the wireless nodes, these outage capacity events are correlated. In this paper, we derive the average outage rate (AOR) and the average outage duration (AOD) of two well-known cooperative diversity protocols, decode-and-forward relaying and selection decode-and-forward relaying, operating in slow Rayleigh fading channels. We also analyze the asymptotic behavior of these statistical parameters for high SNRs, where it is shown that the AOR exhibits a similar behavior as the outage probability.

The outage probability is an important performance measure for cooperative diversity schemes. However, in mobile environments, the outage probability does not completely describe the behavior of cooperative diversity schemes since the mobility of the involved nodes introduces variations in the channel gains. As a result, the capacity outage events are correlated in time and second-order statistical parameters of the achievable information-theoretic capacity such as the average capacity outage rate (AOR) and the average capacity outage duration (AOD) are required to obtain a more complete description of the properties of cooperative diversity protocols. In this paper, assuming slow Rayleigh fading, we derive exact expressions for the AOR and the AOD of three well-known cooperative diversity protocols: variable-gain amplify-and-forward, decode-and-forward, and selection decode-and-forward relaying. Furthermore, we develop asymptotically tight high signal-to-noise ratio (SNR) approximations, which offer important insights into the influence of various system and channel parameters on the AOR and the AOD. In particular, we show that on a double-logarithmic scale, similar to the outage probability, the AOR asymptotically decays with the SNR with a slope that depends on the diversity gain of the cooperative protocol, whereas the AOD asymptotically decays with a slope of -1/2 independent of the diversity gain.

There are several cases in wireless communications theory where the statistics of the sum of independent or correlated Nakagami-m random variables (RVs) is necessary to be known. However, a closed-form solution to the distribution of this sum does not exist when the number of constituent RVs exceeds two, even for the special case of Rayleigh fading. In this paper, we present an efficient closed-form approximation for the distribution of the sum of arbitrary correlated Nakagami-m envelopes with identical and integer fading parameters. The distribution becomes exact for maximal correlation, while the tightness of the proposed approximation is validated statistically by using the Chi-square and the Kolmogorov-Smirnov goodness-of-fit tests. As an application, the approximation is used to study the performance of equal-gain combining (EGC) systems operating over arbitrary correlated Nakagami-m fading channels, by utilizing the available analytical results for the error-rate performance of an equivalent maximal-ratio combining (MRC) system.

We present a novel and accurate approximation for the distribution of the sum of equally correlated Nakagami-m variates. Ascertaining on this result we study the performance of Equal Gain Combining (EGC) receivers, operating over equally correlating fading channels. Numerical results and simulations show the accuracy of the proposed approximation and the validity of the mathematical analysis.

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 expressions for the average LCR and the AFD of the product of N Rayleigh fading envelopes (or of the recently so-called NRayleigh channel). Furthermore, we derive simple and efficient closed-form approximations to the aforementioned parameters, using the multivariate Laplace approximation theorem. It is shown that our general results reduce to the corresponding ones of the specific dual-hop case, previously published. Numerical and computer simulation examples verify the accuracy of the presented mathematical analysis and show the tightness of the proposed approximations.

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 approximations to the aforementioned parameters, using the multivariate Laplace approximation theorem. It is shown that our general results reduce to the specific dual-hop case, previously published. Numerical and computer simulation examples verify the accuracy of the presented mathematical analysis and show the tightness of the proposed approximations.