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Two‐user multiple‐access relay channel (MARC) with side information (SI) non‐causally known at one encoder is studied, where transmitters send a common message with rate R0, and private messages with rates R1 and R2; and derive a general achievable rate region by appropriately using superposition block Markov encoding, binning scheme, Gel'fand–Pinsker (GP) coding and partial decode‐forward (PDF) strategy at the relay. Also, it is shown that this capacity inner bound can be tight for two special classes of degraded and reversely degraded multiple‐access relay channels with one informed encoder. In order for the theoretical findings to be potentially applicable in communications performance metrics evaluations, the obtained general achievable rate region, while having all of the previous works on the point to point, relay and multiple access channels with and without SI as its special cases, is extended to the corresponding Gaussian version, the dirty paper coding of which has been a challenging and widely studied problem, and the result of which includes a variety of previously studied important Gaussian results. Finally, mathematical results are evaluated numerically.

In recent years, considerable studies have been devoted to physical-layer network coding (PLNC) in a two-way relay channel (TWRC) network with the symmetric channel. However, it may not be appropriate for the asymmetric channel in which the source-to-relay channels are not equally strong and the two sources may utilise different modulation. In this study, the authors studied the heterogeneous PLNC design in the asymmetric TWRC network with high-order modulation and proposed a relay denoising mapping approach to reduce the decoding error probability. Firstly, they put forward a cluster maximisation algorithm to enlarge one cluster by sucking the neighbour points, which satisfy the exclusive law. Then, based on this algorithm, they designed the heuristic nearest-neighbour denoising mapping (HNDM) approach. The HNDM algorithm divides the nearest neighbour superimposed constellation points into the same cluster as far as possible. Points in the same cluster are coded into a new symbol by a specific mapping that achieves a many-to-one mapping. Performance results are provided in terms of symbol error rate. Under diversity channel conditions, the performances of 16-quadrature amplitude modulator (16-QAM)-8-phase-shift keying and 16-QAM-quadrature phase-shift keying are evaluated.

In this study, the authors study the interference exploitation problem in multi-input multi-output (MIMO) multi-way relay channel, which is MIMO Y channel. In this channel, multiple users complete the exchange of information among users through a common relay in the multiple access channel phase and broadcast phase. Each user sends signals to other users and receives the signals sent by other users. For a three-user transmission model, each user and relay have three antennas, respectively. To achieve better decoding performance at the relay, they design precoding vectors on the basis of traditional signal space alignment (SSA) so that the intersection subspaces hold orthogonal. Corresponding optimisation rules are proposed for zero-forcing and maximum-likelihood decoders. It is seen from the simulation results that the proposed algorithm greatly improves the decoding accuracy compared with the traditional SSA relay decoding, and reduce the computational complexity. Because of the improvement of the performance of relay decoding, the reliability of the whole transmission system will be improved.

The discrete alphabet and memoryless relay channel (RC) with side information (SI) and its extension to the continuous alphabet Gaussian version with uncorrelated noises have been studied by Zaidi et al. Zhang et al. have studied a Gaussian RC with correlated noises and uninformed relay. Aggarwal et al. have analysed a coverage region for a RC without any SI and with uncorrelated noises. In this study, the authors have investigated the impact of SI on the coverage region as an important wireless performance factor for a wireless RC, and also derived the capacity upper and lower bounds for such a channel with SI and correlated noises. The results of this research include previous studies as special cases, and that under special circumstances, noise correlation can tighten the upper bound, and furthermore, SI enlarges the coverage region as expected intuitively. Mathematical derivations and numerical results are obtained to support the claims.

The common outage performance of an amplify-and-forward two-hop two-user channel is studied in the presence of multiple independent interferers at the destination. First, the exact integral form expression of the common outage probability is derived. Then, in order to decrease the computation complexity, a closed-form approximation of the common outage probability is derived. Finally, the asymptotic analysis is performed based on the approximation expression. Numerical results demonstrate that the integral form of the common outage probability, the corresponding approximation and the asymptotic results match well with the Monte Carlo simulations.

In this paper, the authors show that using physical layer network coding (PNC) in wireless relay systems does not always increase throughput performance, and to achieve maximum throughput, PNC should be exploited intelligently regarding to the channel conditions. In this study, they propose a selective PNC (SPNC) scheme in bidirectional relay systems for binary phase shift keying. In the proposed scheme, the relay chooses either to detect network-coded data from superimposed signal by PNC scheme or single source data by a so-called single node detection (SND) scheme, based on which offers more end-to-end throughput for current channel realisation. They analytically determine the region of channel state plane in which SPNC selects SND scheme. Also, they obtain expressions for instantaneous bit error rates (BERs) of PNC and SND protocols. Moreover, they derive upper bounds in closed-form for average BERs of PNC and SND schemes during multiple access phase at the relay. Then, they investigate SPNC with high-order modulations. Simulations and analytical results confirm that SPNC achieves considerable throughput gain over PNC in Rayleigh fading channels.

A hop-by-hop relay selection (RS) strategy for multi-hop decode-and-forward cooperative relay networks referred to as Max-DS is proposed. In this method, RS in each stage is only based on the channel state information (CSI) to relays in the next stage. In each stage, relays that successfully receive and decode the message from the previous stage form the candidate set for relaying, and among them, the relay with the largest number of ‘good’ channels to the next stage is selected for retransmission. It is shown that the proposed method can be implemented in a distributed manner without the need for a central controller. The authors analyse the performance of the proposed method in terms of end-to-end outage probability in the case of imperfect CSI of which the case of perfect CSI is a special case. Numerical results are presented from analysis which closely match those obtained from simulation. The results are compared with those from several other RS strategies, and show significant improvements.

In this work, the authors investigate a multi-user multi-input multi-output (MIMO) interference relay system, where several transmitter nodes simultaneously communicate with their respective receiver nodes through half-duplex MIMO amplify and forward (AF) relay nodes. For this system configuration, they address the problem of linear transceiver–relay design to achieve max–min fairness among all the users' data streams. Assuming perfect channel state information, this problem is formulated as the maximisation of the minimum signal-to-interference-plus-noise ratio (SINR) per stream among all the users subject to transmit power constraints at the transmitter and relay nodes. Since the formulated problem of jointly optimising all the transmitters, relays and receivers is non-convex, a globally optimal solution cannot be easily obtained. Therefore, they propose a quasi-optimal iterative algorithm to jointly optimise the transmitter precoders, relay precoding matrices and receiver filters for all the users and relays such that the minimum per stream received SINR is improved at each iteration. Simulation results show that the proposed algorithm improves fairness among data-streams of all users and outperforms existing strategies in terms of minimum user rate and bit error rate.

Energy harvesting (EH) is a promising technique for cognitive relaying transmission (CRT) where secondary users (SUs) and relaying nodes do not have a constant power supply each. Unlike conventional CRT where the end-to-end data rate is usually maximised without taking into account the energy consumption at the source and relay, in this study, the energy consumption is characterised by means of energy efficiency, defined as the achievable data rate per Joule. In particular, the energy states at each node (either at a SU or a relay) is modelled as a finite-state Markov chain and the transmit power at a node is optimally allocated by jointly accounting for the interference threshold prescribed by primary users (PUs), the maximum allowable transmit power and the harvested energy at the node. To maximise the energy efficiency, a best relay selection criterion is proposed and the subsequent optimal transmit power allocation is initially formulated as a non-linear fractional programming problem and, then, equivalently transformed into a parametric programming problem and, finally, solved analytically by using the classic Karush–Kuhn–Tucker conditions. With extensive Monte-Carlo simulation results, the effectiveness of the proposed relay selection algorithm and corresponding optimal power allocation strategy are corroborated.

Recently, it is shown that the channel polarisation phenomenon of Arikan's polar codes with their original multilevel construction happens in several levels with perfect, partially perfect and useless bit channels. On the basis of this construction, this study aims to illustrate design principles and decoding steps of cooperative decode-and-forward polar coding schemes for half-duplex relay channel. In these schemes, the authors consider the use of relay retransmission of partially perfect bit channels in time-division process. The source node transmits its polar-coded information to both the relay and the destination nodes during the first time slot. For the second transmission period, the relay first decodes the source signal then after reconstruction of the polarisation matrix, the extracted partially perfect bit channels are recoded using another polar code and finally transmitted to the destination node. At destination, the signals received from both source and relay nodes are processed by using multi-stage successive cancellation decoding for retrieving the original information bits. They demonstrate via numerical results that by carefully constructed polarisation matrix at relay node, their cooperative polar coding schemes can achieve better performances than other previous schemes.

For relay terminals in wireless communication systems, the difference of the power consumed for relaying signals means unfairness, which may reduce the network lifetime when the system is energy-constrained. Classic opportunistic relay selections always cause unequal power consumption among all relays. In this study, the authors propose a novel distributed relay selection strategy, named the fair opportunistic relay selection (FORS) strategy, for amplify-and-forward (AF) opportunistic cooperative systems. The FORS strategy is designed based on physical-layer fairness that means all available relays cumulatively consume equal power. They use a set of weight coefficients to adjust the channel fading coefficients effectively and then change the selection probabilities for all relays on the basis of proportional fair scheduling. Considering that the ‘optimal’ relay can be selected proactively in quasi-static Rayleigh fading channels based on local channel state information, the overhead of the proposed scheme is small. Then, they analyse the performance of the FORS strategy and provide an exact analytical expression for the outage probability (P out) and the average symbol error probability. Numerical simulation results validate their analysis. The results show that the FORS strategy approximately achieves the upper bound of physical-layer fairness in the AF relaying system.

A relay channel, with orthogonal components, is considered in the case that the spectrum is shared by another user. Upper bounds on the achievable capacity is obtained when noisy observations of the interference signal is non-causally available at the three nodes forming the relay channel. Then, a causal encoding technique is proposed such that the source and the relay can at first estimate the interference signal and then start transmission to the destination. In addition, rigorous numerical examples are studied to illustrate the benefit of having noisy observations of the interference signal at the three nodes forming the relay channel.

For relay-assisted system, better relay channel and instable direct transmission (DT) channel exist. The recent coding schemes always focus on how to improve the system performance when channels are in medium signal-to-noise ratios. For the instability of DT channel, a novel coding scheme with multi-dimensional constellations at relay is proposed, which make use of the robust relay channel. The design rule based on best approximate performance is given in the form of an optimisation problem, and its general solution is also shown. In addition, the optimal relay-coding matrix design for 8PSK and 16QAM has been discussed in detail. Simulation results show that the authors’ proposed coding scheme outperforms the conventional scheme with repetition and is more robust than other well designed schemes in confronting the instability of DT channel.

In this study, the authors investigate the energy-efficient (EE) relay selection (RS) and power allocation (PA) in a cooperative secured system. Their scenario includes a multiple-antenna source, a multiple-antenna destination and multiple amplify-and-forward untrusted relay nodes, where the relay nodes only have the channel-amplitude information. To prevent the untrusted relays from intercepting the source message and to achieve positive secrecy rate, the destination-based cooperative jamming technique is used. By maintaining a minimum required secrecy rate, three optimal joint RS and power minimisation schemes are studied. The first objective is minimising the total transmit power consumption, and therefore obtaining the corresponding EE-RS and PA schemes. Second, they focus on relay power minimisation, and third sum power minimisation of the relay and one mobile node by considering a weighted factor are investigated. Closed-form solutions are presented for three practical optimised networks. Finally, some numerical results are provided to show the merits of the proposed scheme. They also give some insights to system design.

In this study, the authors investigate the physical-layer security in a cognitive amplify-and-forward relay network consisting of a secondary transmitter (ST) and a secondary destination (SD) with the aid of multiple secondary relays (SRs) in the face of multiple eavesdroppers. In cognitive radio networks, increasing transmit power may not always be beneficial in terms of improving the channel capacity of cognitive transmissions, which would not only cause an extra interference to primary user, but also enhance the possibility of successfully intercepting the cognitive transmissions at an eavesdropper because an improved signal strength is received in this case. The authors propose two relay selection schemes to improve the physical-layer security of cognitive transmissions against eavesdropping attacks, which are referred to as the global and partial channel state information based relay selection, denoted by GCSIbRS and PCSIbRS, respectively. The authors analyse the intercept probability of the proposed GCSIbRS and PCSIbRS, as well as the traditional round-robin and all-relay transmission schemes. It is shown that the proposed GCSIbRS and PCSIbRS schemes both outperform the conventional round-robin and all-relay schemes in terms of their intercept probability performance.

This study proposes rate-estimation-based relay selection scheme (RERSS) for large-scale wireless networks (LSWNs) that effectively distributes traffic of packets from a source to a sink. In an LSWN, direct data transmission from a source and a sink has been becoming a challenge. This is because of longer communication distance and more interference caused by more adjacent nodes. Hence, in order to transmit data packets to the sink, the source exploits neighbour nodes as relay nodes around it to forward packets through single-hop or multi-hop until reaching the sink. Different from the conventional cooperative relaying scheme, RERSS introduces a rate-estimation parameter A to select the forwarder for relaying messages. After determining A value of each neighbour relay node using a link rate stored in the advertising packet, the relay node whose A value meets the requirement of RERSS can be qualified as a forwarder of the source or the other relay node. Simulation results indicate the potential to not only increase throughput but also decrease energy consumption and end-to-end delay.

The outage probabilities (OPs) of cognitive amplify-and-forward systems with the conventional and the switching-based partial relay selection (PRS) schemes over independent but not identically distributed Rayleigh fading channels are evaluated. The conventional PRS scheme always depends on the instantaneous channel quality of the first hop, while the switching-based PRS scheme is based on the estimated average channel state information (CSI) of the first and second hops. For the switching-based PRS scheme, the instantaneous CSI for links with the smaller average channel power in the first and the second hops for each end-to-end path is used for relay selection. Thus, the switching-based PRS scheme counts on the instantaneous CSI of either the first or second hop. The tight lower bounds and asymptotic expressions of the OP are derived. The feedback overheads of both schemes are discussed. Simulation results substantiate the theoretical analysis and also reveal that the switching-based PRS outperforms the conventional one over the cognitive relay networks in terms of OP.

Multiuser cooperative communications represent a research area of great interest constituting a key technology for future wireless networks. In this study, the authors consider a scenario of multi-user, single-relay network, where each user employs a part of the relay's transmission power taking into account the constraint of the total transmission power of the relay. The problem of relay power allocation to individual users with a view to optimising the long-term network performance is investigated. An adequate utility function is defined, in terms of outage probability, evaluating the cooperative network's performance due to the relay's cooperation. Taking into consideration the distributed nature of cooperative networks along with the coupled constraint of relay's total transmission power, the specific problem is transformed from a network-level to a user-level optimisation problem using a modern game-theoretic tool. More specifically, the initial power allocation problem is formulated as a state-based potential game for which the corresponding Nash equilibrium exists. Finally, a gradient learning mechanism is proposed to achieve the stationary state Nash equilibrium of the game that constitutes also the global optimal solution of the initial problem. The performance of the new proposed scheme is investigated through numerical simulations for various network parameters.

In this study, the authors present a novel channel estimation algorithm for three-hop multi-input multi-output (MIMO) relay systems using the PARATUCK2 tensor model. At the destination, the proposed algorithm exploits a unified formulation of the received signal as a PARATUCK2 model, and jointly estimates all of the channel matrices involved in the communication. Compared with existing algorithms, the proposed algorithm only requires the source to transmit the channel training sequences, does not need relays to perform any task of channel estimation, and yields smaller estimation error. Moreover, the proposed algorithm can be extended to multi-hop MIMO relay systems with any number of hops. Numerical examples are shown to demonstrate the effectiveness of the PARATUCK2-based channel estimation algorithm.

Cooperative communication significantly improves the performance of wireless systems. Transmission of signal in such a system can be accomplished by the help of intermediate relay nodes. However, due to the selfish nature of network nodes, an incentive mechanism is required to stimulate relay nodes to cooperate. On the other hand, the authors assume that the source nodes are ill-informed about channel conditions of the relay nodes, which may result in asymmetry of information. In this study, the authors propose a distributed power allocation and price assignment algorithm over cooperative wireless networks. The proposed solution aims to achieve optimum power allocation to the source nodes and best price of power at the relay nodes, in the presence of asymmetric channel state information. To this end, the authors combine contract theory and auction mechanism in order to provide the highest possible utility for both the source and the relay nodes. The proposed distributed approach benefits the source nodes by preventing the relay nodes from cheating behaviour. Additionally, it favours the relay nodes by letting them assign the final price of power. Finally, the authors present simulation results in order to demonstrate efficiency of the proposed distributed multi-user algorithm.

In this study, for a network-coded two-way relay channel (TWRC), the authors propose three different relaying schemes that satisfy certain quality of service requirements at both transceivers. In these schemes, the relay decides independently whether to help each transceiver or not based on the instantaneous signal-to-noise ratios received from the transceivers. Under the assumption of error propagation, they analyse the performance of the system in terms of the end-to-end bit error rate (BER), the outage probability , the average spectral efficiency (ASE) and the diversity order. All of these performance measures depend on two thresholds employed by the relay node. By optimising these thresholds under three different criteria, they achieve three different relaying schemes: (i) the BER­ optimal scheme that minimises the end-to-end BER; (ii) the outage-constrained scheme that minimises the end-to­ end BER under an outage probability constraint; and (iii) the BER-constrained scheme that maximises the ASE under an end-to-end BER constraint. The analysis of the system shows that the BER-optimal scheme guarantees the full diversity gain at both transceivers; the outage-constrained scheme results in a bidirectional relaying scheme with a constant outage probability; and the BER-constrained scheme makes use of spectrum as efficiently as possible while maintaining the target BER.

In this study, a problem of efficient spectrum sensing and power allocation is studied. A network of cognitive radio adopting the technique of two-way relay is considered. A relay node, sitting between two secondary users, carries out spectrum sensing and helps the two secondary users to realise bidirectional relay communications. For such a system, an optimisation problem which targets at maximising the average rate between the two secondary users while guaranteeing the detection probability above a predefined threshold, is formulated. Although the problem is shown to be non-convex which means the global optimal solution is hard to be obtained, the authors solve the formulated problem global optimally by using a combination of bilevel optimisation and monotonic programming. Numerical results are provided to present the effectiveness of the authors' proposed algorithm.

From practical and theoretical viewpoints, performance analysis of communication systems by using information-theoretic results is important. In this study, first, the authors obtain a general achievable rate region for three-user discrete memoryless multiple-access relay channel (MARC) via partial decode and forward strategy and regular block Markov encoding/backward decoding. Also by extending the discrete alphabet results to the continuous alphabet channel, an inner bound for three-user Gaussian MARC (GMARC) is achieved. Next, based on the inner bound of three-user GMARC, they analyse the impact of a relay on the coverage region of MARC, as a basic model for uplink communications between a base station and users with the help of a relay. This analysis includes the coverage region for the multiple-access channel and two-user GMARC as special cases. Considering rate regions for the GMARC and fading GMARC, it is proved that in a fixed transmission rate, the relay extends coverage region of the MARC. Numerical illustrations confirm their theoretical results.

With the wide-spread wireless applications and services, the spectrum scarcity has become a challenging problem. Thus, it is necessary to find a solution to have more spectrum bands. One from these solutions is the cognitive relay network, where we can increase the spectrum utilization by combining the cognitive radio (CR) with cooperative spectrum sharing systems. In this paper, the performance of cognitive relay networks under interference power constraints from the primary user (PU) is studied. Here, the system models are studied by utilizing different scenarios. The first scenario is by using a single amplify-and-forward (AF) relay, and the second one is by using a single AF relay with selection diversity. Tabulated expressions for the outage probability (OP) are derived over independent and non-identically distributed Nakagami-m fading channels. Numerical results show that the cooperative spectrum sharing transmission with a single AF relay and selection diversity outperforms both the direct transmission and the transmission using a single AF relay for the underlay cognitive relay networks. Furthermore, the results show that the outage performance depends on the minimum fading severity parameters of the two hops of the secondary user (SU) and the OP decreases as the PU moves away from the SU network.

In cognitive radio networks, primary users can share some licensed spectrums with secondary users in exchange for cooperation. In this study, an overlay scenario is investigated where a secondary node provides two-way relaying service to a pair of primary users and thus is allowed to transmit its own messages by using some licensed spectrums. Orthogonal channelisation is assumed for the two-way relay channel to form a number of parallel subchannels. Hence, the licensed spectrums can be partitioned between primary and secondary signals transmitted by the relay in the broadcast phase. Moreover, subchannels in the two phases of two-way relaying can be permutated to further improve performance. The authors seek to maximise achievable data rate of secondary transmission subject to data rate requirements of the two primary users under individual power constraints. The joint spectrum partition, subchannel permutation, and power allocation problem is formulated into a mixed combinatorial programming problem, which is then transformed into a solvable form and finally yield an asymptotically optimal solution through dual decomposition method. They further prove that the solution to the relaxed problem is exactly the same as that to the original problem. Numerical results demonstrate performance gain of the proposed algorithm.

In this study, the authors consider two multiple-antenna transceivers exchanging information through a relay-assisted network using a single-carrier communication scheme. The authors assume that the propagation delay in different relaying path is negligible and the relay nodes are synchronous. As a result, the end-to-end multipath channel is not frequency-selective (time-dispersive) and hence, the successive arriving signals at the transceivers do not interfere with each other. Otherwise, inter-symbol-interference (ISI) will be inevitable and cyclic insertion and removal matrices will be required to combat ISI. In such a two-way network, the relay nodes harvest energy from the surrounding environment and utilise this energy to forward their received messages using a harvest-then-forward protocol. For different receiver diversity combining techniques, the authors design an optimal relay beamforming to maximise the quality of the received signals at the transceivers subject to the energy casualty constraint at the relay nodes (the energy consumed for transmission of each block cannot exceed the accumulative harvested energy). For each diversity combining technique, a closed-form solution is obtained for the optimal signal-to-noise ratio (SNR) that shows how adjusting the data transmission rate of the transceivers and the amount of energy harvested at the relays affects the received SNR.

Recently researches show that significant energy saving can be achieved by introducing mobile relays into wireless sensor networks. However, due to the extra transceiver circuit energy and the mobility energy consumed by the mobile relay, it is not always better to pass data through the relay rather than to send it from source to destination directly. In this study, the authors study a novel link selection problem in a two-hop relay scenario where the relay has the ability to move. In this scenario, data from source can be passed through three kinds of links: the direct link, the initial relay link and the adjusted relay link. From the energy-saving perspective, the optimal moving direction, the position adjustment criterion and the optimal position of the mobile relay are firstly studied through mathematical analysis. Based on a comprehensive discussion of the energy performances of these three kinds of links, and energy-efficient link selection scheme is then presented. Both the amount of data to be sent and the distance between source and destination are shown to be closely related to the link selection scheme. Finally numerical simulations are carried out to verify the theoretical results.

A joint optimisation of power allocation (PA) and relay location is proposed for decode-and-forward relaying over multi-hop, independent, log-normal fading channels. Optimisation is carried out at high signal-to-noise ratio (SNR) and low SNR scenarios to minimise the outage probability with a constraint on total transmit power and end-to-end relaying distance. End-to-end average bit error rate is also minimised assuming the same constraints. Optimisation is carried out to find optimal PA (OPA) for a given relay location, optimal relay location (ORL) for a given PA and joint OPA and relay location. All the optimisation problems reformulated from the original problems are shown to be convex except relay location optimisation minimising outage probability at low SNR scenario. It is then solved using properties of concave minimisation. Optimal allocation factors do not depend on the instantaneous channel state information. It also does not depend on total available power in the system except allocation factors evaluated by optimising outage at high SNR. It is observed that OPA allocates more power to weaker links and ORL allocates less distance to weaker links. It is also observed that performance improvement increases with increase in link unbalance and distance-based allocation is most effective.

This study proposes a transmit power allocation (TPA) scheme for bi-directional relay networks with an objective of minimising the total power consumption to meet both the service quality (i.e. the outage probability) and individual power requirements. This new scheme focuses on the amplify-and-forward protocol-based multiple-access broadcast mode with asymmetric network traffics where the bi-directional relay channel (BDRC) statistics are assumed to be available at the transmitters. A two-step method is devised to solve the optimisation problem pertaining to the total power minimisation. In the proposed method, the system outage probability is first minimised subject to both the individual and total power constraints, and then the total power consumption of the network is minimised subject to the given service quality constraint based on the preliminary solutions achieved in the first step. This two-step optimisation mechanism leads to a novel TPA algorithm for the relay and two sources of the network. Simulation results are provided to validate the proposed algorithm, showing that the proposed new power allocation scheme can significantly reduce the total power consumption, especially when the BDRC or the network traffic is asymmetric.

In this study, two diversity achieving schemes in two-way relay channel (TWRC) under Nakagami-m fading are proposed. A general network of N r relays is considered where each relay is equipped with N a antennas. It is also assumed that the relays operate in decode-and-forward (DF) mode. The data transmission is divided into two phases, multiple access (MAC) phase and broadcast (BC) phase. In the MAC phase, the sources send their data to the relays simultaneously and after decoding, one relay is selected with MAX–MIN relay selection criterion and then in the BC phase retransmit the decoded symbols using the proposed transmission schemes at the selected relay. With evaluating the asymptotic behaviour of the bit error rate (BER) of the proposed schemes, it is proved that the diversity order of them is N r N a m. As a result, the proposed schemes achieve full diversity order.

Rate regions of a multi-way relay channel with direct links (MWRC-DLs), where K users exchange their messages via a relay terminal and all users can overhear each other directly, are studied in this study. Under the assumption that a restricted encoder is employed at each user, the cut-set outer bound on the capacity region is derived first. Then, achievable rate regions of the MWRC-DLs with decode-and-forward (DF) and compress-and-forward (CF) strategies are characterised. Meanwhile, the explicit expressions of the outer bound and the achievable rate regions for the Gaussian MWRC-DLs are also derived. It is shown that the rate regions of the DF and CF strategies for the two-way relay channel and the multiple-access relay channel can be obtained from those of the MWRC-DLs. To give more insights on the two strategies of the MWRC-DLs system, the common rates of a symmetric Gaussian network are analysed. It is shown that the CF strategy achieves common rates within 1/2(K − 1) bits of the capacity when the relay's power is at least (K − 1) times as large as the user power. Numerical examples are also provided to verify the theoretical analysis.

In this study, the authors consider a new space-time coding scheme for two-hop amplify-and-forward (AF) relay multiple-input multiple-output (MIMO) relay communication systems. This scheme, called multiple Khatri–Rao space-time coding, which combines symbol stream blocking, spatial precoding and time-domain spreading. The authors show that the received signals at the destination node can be formulated as two parallel factor (PARAFAC) models, and then a novel semi-blind receiver is derived using a two-stage iterative fitting algorithm for joint symbol and channel estimation. Under the assumption that channel state information (CSI) is not available neither at the relay nodes nor at the destination node, the proposed semi-blind receiver operates close to the zero forcing receiver with perfect CSI. Moreover, without any channel training sequence, the proposed semi-blind receiver provides the destination node with full knowledge of all channel matrices involved in the transmission. Simulation results illustrate the performance of the proposed semi-blind receiver in comparison with alternative approaches.

In this study, the authors consider the min–max mean squared error (MSE)-based linear transceiver–relay design for multiple-input–multiple-output (MIMO) interference relay channel, where a finite number of half-duplex MIMO amplify and forward relays assist the communication between multiple source–destination pairs. The problem is formulated as minimising the maximum MSE among all data streams of all users subject to individual transmit power constraints at each source and relay node. Since the optimisation problem is non-convex, globally optimal solution cannot be guaranteed. They propose a suboptimal solution based on alternating minimisation, where the beamforming matrices at all the source, relay and destination nodes are jointly computed in an iterative manner. Numerical simulations show that the proposed algorithm not only ensures fairness among all users’ data streams, but also achieves good sum-rate and bit error rate performance.

To exchange information between two sources in a two-way relaying network with multiple potential relays, most researches focus on two-hop relay system with single-relay-selection (SRS) scheme. Comparing with SRS scheme, the authors first design a paired-relay-selection (PRS) scheme in which a pair of ‘best’ relays broadcast network-coded information to other nodes (source or relay). They propose an optimal selection algorithm and a suboptimal algorithm that selects the pair of ‘best’ relays in the PRS scheme and they describe how the nodes exchange information in a frame consisting of four timeslots. Both the analytical and simulation results show that when the pathloss exponent is large and/or there is a sufficient number of relays to choose from, using two relay nodes can provide a lower outage compared with using only one relay node even under the same total transmit power in uniformly distributed relay networks. In addition, to reduce the overhead of the PRS scheme, they propose an iterative-PRS (I-PRS) scheme in which the paired relay is selected in an iterative and opportunistic way. Simulation results show that the I-PRS scheme has nearly the same outage performance as the PRS scheme under time-invariant channels and significantly outperforms the PRS scheme under time-varying channels.

The outage probability of two-way relaying network with orthogonal space–time block coded (STBC) transmission is analysed. Two sources equipped with different numbers of antennas send orthogonal STBC coded signals with different parameters. The channel gain between two antenna elements is assumed to be Rayleigh faded. The amplify-and-forward (AaF) relay with a single antenna repeats the received signal after power scaling. Exact expressions for the outage probabilities are provided, where the authors integrate out the outage probability over one of the three different regions on the plane defined by the inverses of channel gains. According to the orthogonal STBC code rates and the source and relay powers, one integration region is selected among the three. The closed-form expression is verified via a set of comparisons with the simulation results. The authors also show that the maximum diversity is attained when the orthogonal STBC is applied at both sides of the two-way channel.

In this paper, we consider a delay-limited hybrid automatic repeat request (HARQ) protocol that makes use of incremental redundancy over the three-node decode-and-forward (DF) relay fading channel where one source cooperates with a relay to transmit information to the desti nation. We provide an estimate of the diversity-multiplexing tradeoff (DMT) at finite signal to noise ratio (SNR) based on t ight bounds on outage probabilities for two channel models. The results for the long term quasi-static channel highlight the distributed diversity, ie. the cooperative sp ace diversity, and the HARQ coding gain, achieved by soft combining the successive transmitted punctured codewords via incremental redundancy. On the other hand, the results for the short term quasi-static channel illustrate the diversity gains obtained thanks to cooperative space diversity and time diversity, along with the HARQ coding gain. Using the DMT formulation, we show that equal power partitioning between the source and the relay nodes provides close to optimal performance. Furthermore, thanks to the extension of the finite-SNR DMT to the finite-SNR diversity-multiplexing-delay tradeoff, we show that, unl ike the asymptotic SNR analysis, the ARQ delay, defined as the number of retransmissions rounds, impacts the performance of the HARQ relay protocol for high effective multiplexing gain.

Cooperative communication can improve the performance of communication systems under multi-path fading conditions through relaying. Increasing the number of relays will also boost the performance of the system, but since relays transmit through orthogonal channels, this improvement is obtained at the cost of bandwidth or rate of the system. Best relay selection is a well-known technique to achieve full order of diversity and use bandwidth efficiently in a cooperative two-hop multi-relay network. A new beamforming at the relay is proposed that selects the best two among several relays and then the selected relays forward their detected symbols in a common channel to the destination. For achieving full diversity order at the destination, a modified maximal ratio combining detector is proposed. In the proposed beamforming scheme, the phase of the selected relays is adjusted in such a way to compensate the channel between the relays and the destination and achieve acceptable performance at the receiving end. The selected relays require two-bit quantised phase information of the channel gain between the relay and the destination, which can be sent to the relay by the destination. It is shown that the proposed method achieves full diversity order and has considerable performance gain in comparison with the best relay selection method.

In this study, two relay selection methods in the half-duplex decode-and-forward relaying for cooperative multiple-input multiple-output-orthogonal frequency division multiplexing (MIMO-OFDM) systems have been introduced. The relay selections are implemented using the symbol-based and subcarrier-based methods. By considering different number of antennas for source, each relay, and destination, the authors have derived closed-form outage expressions for these proposed methods. The MIMO channel model for each subcarrier, between source–relay and relay–destination is considered as a MIMO Rician fading channel with independent but not necessary identically distributed. Moreover, the outage expressions for MIMO independent and identically distributed Rician and Rayleigh fading channels are derived as special cases. Furthermore, the correlation among the OFDM subchannels is analysed. In addition, the implementation issues of both relay selection methods are also investigated. Monte Carlo simulations are performed to validate the outage analysis where the excellent agreement between the analytical and simulation results is observed.

In this study, the authors apply a generalised quantise-and-forward (GQF) relaying scheme for multiple access relay channel (MARC). The authors find achievable rate regions of GQF on MARC for both discrete memoryless case and additive white Gaussian channel. They assume that the relay has no access to channel state information (CSI) of the relay–destination link. Through numerical examples, they show that in the absence of CSI at the relay, the GQF scheme outperforms other relaying schemes. They also show that the outage probability of the individual users is lower than that of classic compress-and-forward scheme.

In amplify-and-forward wireless relay networks, channel state information is required at the destination for signal detection when coherent distributed space-time coding is performed at the relays. The authors consider in this study signal detection in the case of imperfect partial channel knowledge at the destination. For the case of maximum a posteriori signal detection, they propose a modified detector formulation that takes the variance of channel estimation errors into account, and reduces the impact of channel uncertainty on the receiver performance. They show that the proposed modification permits a significant performance improvement, while increasing only slightly the receiver's complexity. It is of special interest for non-constant modulus signal constellations of relatively large size, as well as for relatively low pilot powers.

A relay communication system where its nodes are equipped with multiple antennas is considered. The relay applies a transformation matrix on its received signal and forwards it to the destination. The authors show that, given a limited relay transmit power, the transformation matrix which maximises the signal-to-noise power ratio (SNR) is almost surely a rank-one matrix. Such a singular transformation matrix prevents accurate channel estimation. As a remedy, they impose a constraint on the condition number (CN) of the relay transformation matrix. They prove that the optimal relay matrix under this new constraint has up to two distinct singular values. Thus, the relay transmits some power in all directions, and this small energy allows better channel estimation. The author's simulation results show that imposing the CN constraint on the relay matrix results in some small loss in the SNR which is quantified in this study; however, the optimal relay matrix enables the receivers to track the channel state information.

In this study, a dual-hop multiple-input-multiple-output relay network with the N th-best relay selection scheme in the presence of co-channel interference is studied. Specifically, the N th-best relay is selected based on the channel state information (CSI) of the first hop. The authors first consider the CSI is perfect feedback and derive exact as well as asymptotic closed-form expressions for the outage probability. Results reveal that the diversity order of N R × min{ N S ( K-N + 1), N D } is achieved when there is no feedback delay, where N S , N R and N D represent the number of antennas at the source, the relays and the destination, respectively, K is the number of the relays and N (1 ≤ N ≤ K ) represents the rank of relay chosen. Then, they investigate the outage performance of the system with feedback delay, and exact and asymptotic outage probability expressions are also obtained. Results illustrate that outdated CSI degrades the diversity order of the system to min{ N R , N D }, which is independent of the number of antennas at the source, the number of relays and the rank of the relay chosen. The findings of the study provide valuable insights into the practical system design.

In this work, the impact of outdated channel state information because of feedback delay is evaluated for the performances of several generalised relay selection schemes. Multi-hop amplify-and-forward relaying is considered over Rayleigh fading channels. Numerical results show that different relay selection schemes suffer from different performance degradations when the hop index increases. Interestingly, for generalised relay selection, numerical results also show that selecting more relays does not necessarily lead to better power outage probability and bit error rate performances. These observations provide useful guidance on relaying system designs.

A full-duplex wireless communications system is considered where K user wants to exchange common messages and private messages via a relay with multiple antennas simultaneously. The proposed scheme combines signal space alignment with zero forcing during multiple access channel phase and broadcast channel phase to cancel self-interference. The authors can achieve high degree of freedom by using successive network coding and aligning multiple interfering signals. The result is extended to a more generalised Y channel circumstance where they can transfer each message with different interference-free streams.

This study proposes an optimal time allocation scheme for two-way relay channel (TWRC) using the physical-layer network coding (PNC). In other words, this study analytically determines the optimal transmit time durations for the first and the second time slot, which maximise the achievable sum rate under a sum time constraint for a given squared magnitude of the channel coefficients and transmit power values. Numerical results show that the achievable sum rate for the proposed optimal time allocation is greater than or equal to that for equal time allocation.

In this study, the authors investigate the diversity-multiplexing tradeoff (DMT) of a wireless system in which user equipments (UEs) are equipped with only one antenna while the destination has multiple antennas. Each UE is assisted by M half-duplex cooperative users serving as relay nodes. They combine the opportunistic relaying scheme and the cooperative spatial multiplexing (C-SM) scheme to produce an opportunistic C-SM (OC-SM) scheme. The fraction of time allocated to the source–relay link and the relay–destination link is treated as a design parameter to minimise the outage probability of the system. At high signal-to-noise ratio regime, the optimal time allocated factor is obtained in a closed-form expression through DMT analysis. Based on the DMT result of the proposed OC-SM scheme, an adaptive OC-SM (AOC-SM) approach in which the system can switch between different C-SM models adaptively based on the rate transmitted is proposed. To reduce the complexity of the relay nodes, an AOC-SM scheme with relay selection (SAOC-SM) in which a constant number of relay nodes is selected from the set of relay nodes that have successfully decoded the source message is investigated. The DMT results of the SAOC-SM scheme and the AOC-SM scheme are obtained and compared.

In this study, the authors propose a cross layer design strategy that consists of a cooperative maximum likelihood detector operating in conjunction with link selection for cooperative multiple-input multiple-output relay networks. The system considered is a two phase relaying model, with amplify-and forward relays. The model considers the effect of relay placement and of large scale shadowing. The authors develop a cooperative maximum likelihood detector for an arbitrary number of relays, and link selection schemes are devised for two scenarios relating to the available knowledge at the destination node, which considers relay combination, with complexity analysis. The authors also propose a cooperative list sphere decoder that processes soft information and implements an iterative detection and decoding scheme. The results of simulations of the systems are presented, with comparisons to system models used in previous literature, and show how the cooperative detector and the proposed link selection schemes affect the bit error rate performance at the destination node, for both the hard decision non-iterative case, and the soft information iterative processing case.

In this study, the authors present a novel channel estimation scheme for a two-hop non-regenerative multiple-input multiple-output relay system. The proposed scheme has two stages. In the first stage, the source node transmits channel training sequence to the relay node. The relay node amplifies the received signal and forwards it to the destination node. During the second stage, the relay node amplifies the pre-received signal with another amplification matrix, and forwards it to the destination node. Based on the proposed scheme, by using parallel factor (PARAFAC) analysis, they further propose a low complexity channel estimation algorithm, where full knowledge of all channel matrices involved in the communication can be estimated at the destination node. Compared with existing algorithms, the proposed algorithm yields smaller channel estimation error with lower complexity. Numerical examples are shown to demonstrate the effectiveness of the low complexity PARAFAC-based channel estimation algorithm.

Using relays to receive and forward packets between a network base station and network users is a promising solution to address the cellular coverage issue. In this study, we consider time division duplexing (TDD) networks and explore the use of network coding for implementing the relays. Several transmission scenarios are investigated, including direction transmissions, one-way relay and two-way relay. In addition, we propose an adaptive TDD network, which enables the network to adaptively configure frame structures based on channel conditions to support direct transmissions, cooperative relay and two-hop relay (one-way and two-way). An opportunistic decoding scheme and a relay operation scheme are introduced to realise the proposed adaptive TDD network in a distributed manner. Both throughput and outage probability are derived. Performance evaluations show that the proposed adaptive TDD network based on network coding achieves the maximum throughput, as compared with one-way relay (without network coding), and extends the cell coverage range (compared with direct transmissions).