Half-duplex Relay Research Articles

MIMO Gaussian Bidirectional Broadcast Channels with Common Messages

In this work, the MIMO Gaussian bidirectional broadcast channel (BBC) with common messages is studied. The problem is motivated by the concept of bidirectional relaying in a three-node network, where a half-duplex relay node establishes a bidirectional communication between two other nodes using a decode-and-forward protocol and thereby adds an own multicast message to the communication. The capacity region of the broadcast phase is derived and the corresponding transmit covariance matrix optimization problem is analyzed in detail. Thereby, it is shown that the transmit covariance optimization problem is strongly connected to the corresponding one of the MIMO Gaussian BBC without common messages. In particular, this knowledge can be exploited to transfer results such as optimal transmit strategies from one scenario to the other one.

Recovering Cooperative Multiplexing Gain in Wireless Relay Networks

We consider an uplink communication in a wireless network where each source-user is assisted by M half-duplex relays. The source users and relays are equipped with single-antenna whereas the destination has N antennas. We show that the degree of freedom (d.o.f.) of this network is limited by the links from the source to the collection of relays and destination. This phenomenon is referred to as a "d.o.f. bottleneck problem" which compromise the cooperative multiplexing gain (CMG) and the achievable rate of the system. To improve the CMG, we propose an auxiliary frequency bands (AFBs)-based approach to tackle the d.o.f. bottleneck problem. Information theoretic analysis and numerical results show that the proposed scheme can achieve a CMG of min(M+1,N) when the number of AFBs is sufficiently large. As compared with conventional cooperative communications, the improved multiplexing gain of the proposed scheme is translated into tremendously increased achievable rate at a relatively high SNR.

Spectral efficient half-duplex relaying with interference suppression

Two-hop relaying systems suffer spectral efficiency loss due to the half-duplex property of relays. This paper proposes an efficient relaying protocol which can recover the spectral efficiency loss but still work with half-duplex relays. However, there exists inter-relay interference which degrades the performance of the protocol. With this consideration, a power control policy is derived to suppress the interference using game theory, and then an algorithm is given to facilitate distributed implementation. Furthermore, impact of deploying more destination antennas on performance of the relaying protocol is investigated. Simulation results show that, with the power control policy, the proposed relaying protocol can achieve high spectral efficiency.

Convergence and Performance of Distributed Power Control Algorithms for Cooperative Relaying in Cellular Uplink Networks

We investigate an application of distributed power control (DPC) and opportunistic power control (OPC), respectively, to cooperative relaying systems that consist of multiple sources, multiple relays, and a single destination. Two types of relaying gains are considered for half-duplex amplify-and-forward (AF) relays: fixed and variable gains, respectively. Using half-duplex AF relays, remote users benefit by making the path loss smaller by two shorter paths. However, they lose bandwidth and suffer from additional interference due to amplification of the noise at the relays and the unnecessary signal from the relays, where power control plays an important role. We begin with redefining and extending the existing power control algorithms to be fit for the relaying environments and then, using standard techniques, construct the convergence, except when the number of variable-gain relays is even. With numerical investigation, we show the advantages and disadvantages of the power-controlled systems with relays in terms of the outage probability, the average transmit power consumption, and the transmission capacity. Simulation results show that DPC with relays achieves significant improvement in the outage performance and power consumption. On the other hand, in OPC, some negative effects arise by using the relays in the capacity since the relays increase the interference that severely affects the opportunistic capacity.

Optimal Duplex Mode for DF Relay in Terms of the Outage Probability

This paper deals with a full-duplex relay (FDR) system over Rayleigh fading channels. The exact outage probability of FDR is derived as a closed form to consider interferences from full duplex. Then, we obtain the conditions of the signal-to-noise ratio (SNR) and the signal to interface ratios (SIRs) for cases of FDR showing a lower outage probability than that of the half-duplex relay (HDR) system under the target outage probability. According to this condition, FDR is superior to HDR with lower SIRs in the low-SNR region rather than in the high-SNR region. In addition, the target outage probability is only satisfied when the SNR and SIRs are within the boundaries. These boundaries vary due to the target rate, the channel states of each link, and the target outage probability.

Beamforming-Based Physical Layer Network Coding for Non-Regenerative Multi-Way Relaying

We propose non-regenerative multi-way relaying where a half-duplex multi-antenna relay station (RS) assists multiple singleantenna nodes to communicate with each other. The required number of communication phases is equal to the number of the nodes, N. There are only one multiple-access phase, where the nodes transmit simultaneously to the RS, and N - 1 broadcast (BC) phases. Two transmission methods for the BC phases are proposed, namely, multiplexing transmission and analog network coded transmission. The latter is a cooperation method between the RS and the nodes to manage the interference in the network. Assuming that perfect channel state information is available, the RS performs transceive beamforming to the received signals and transmits simultaneously to all nodes in each BC phase. We address the optimum transceive beamforming maximising the sum rate of non-regenerative multi-way relaying. Due to the nonconvexity of the optimization problem, we propose suboptimum but practical signal processing schemes. For multiplexing transmission, we propose suboptimum schemes based on zero forcing, minimising the mean square error, and maximising the signal to noise ratio. For analog network coded transmission, we propose suboptimum schemes based on matched filtering and semidefinite relaxation of maximising the minimum signal to noise ratio. It is shown that analog network coded transmission outperforms multiplexing transmission.

Diversity-Multiplexing Tradeoff for the MIMO Static Half-Duplex Relay

In this paper, we investigate the diversity-multiplexing tradeoff (DMT) of the multiple-antenna (MIMO) static half-duplex relay channel. A general expression is derived for the DMT upper bound, which can be achieved by a compress-and-forward protocol at the relay, under certain assumptions. The DMT expression is given as the solution of a minimization problem in general, and an explicit expression is found when the relay channel is symmetric in terms of number of antennas, i.e., the source and the destination have n antennas each, and the relay has m antennas. It is observed that the static half-duplex DMT matches the full-duplex DMT when the relay has a single antenna, and is strictly below the full-duplex DMT when the relay has multiple antennas. Besides, the derivation of the upper bound involves a new asymptotic study of spherical integrals (that is, integrals with respect to the Haar measure on the unitary group <i xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">U</i> (n)), which is a topic of mathematical interest in itself.

Distributed power allocation in multi-user multi-channel cellular relay networks

In this paper, we consider the amplify-and-forward relaying transmission in the downlink of a multi-channel cellular network with one base station and multiple relay-destination pairs. Spatial reuse of the relaying slot by allowing simultaneous transmissions from the relays is adopted to avoid the spectral loss incurred by the half-duplex relays. The relays are modeled as rational agents engaging in a non-cooperative game. In order to maximize its individual rate, each relay node iteratively allocates its power across different subchannels based on local information, while treating the signals from the other users as additive noise. First, we propose a distributed algorithm based on best response that is applicable in any signal to interference plus noise ratio (SINR) regions. Then, by focusing on the low SINR region, we propose a modified iterative water-filling algorithm. The existence of Nash equilibrium (NE) is guaranteed and the sufficient condition to reach a NE iteratively is determined. Next, we consider medium to high SINR regions and propose a distributed algorithm based on the sub-optimal response, which can be shown to reduce to the classic Gaussian interference channel model, for which analytical sufficient conditions for the convergence to the unique NE can be readily obtained. Finally, we extend the analysis to a general network topology wherein the users having different channel conditions coexist. The results show that, in low SINR regions, the proposed modified iterative water-filling algorithm yields a higher average sum rate than two simplified algorithms, i.e., the equal power allocation scheme and the conventional time-division based protocol, while in medium to high SINR regions, the sub-optimal-response based algorithm outperforms these two simplified algorithms in terms of the average sum rate

Relay Scheduling in the Half-Duplex Gaussian Parallel Relay Channel

This study investigates the problem of communication for a network composed of two half-duplex parallel relays with additive white Gaussian noise (AWGN). There is no direct link between the source and the destination. However, the relays can communicate with each other through the channel between them. Two protocols, i.e., simultaneous and successive relaying, associated with two possible relay schedulings are proposed. The simultaneous relaying protocol is based on the Broadcast-Multiaccess with Common Message (BCM) scheme considered in . For the successive relaying protocol: (i) a non-cooperative scheme based on the Dirty Paper Coding (DPC) and (ii) a cooperative scheme based on the Block Markov Encoding (BME) are considered. The composite scheme of employing BME in at most one relay and DPC in at least another one is also proposed. It is proved that this scheme achieves at least the same rate when compared to the cooperative and non-cooperative schemes for the Gaussian case. A Simultaneous-Successive Relaying based on Dirty Paper Coding scheme (SSRD) is also proposed. The optimum scheduling of the relays, and hence the capacity of the half-duplex Gaussian parallel relay channel in the low and high signal-to-noise ratio (SNR) scenarios, is derived. In the low SNR scenario, it is revealed that under certain conditions for the channel coefficients the ratio of the achievable rate of the simultaneous relaying based on BCM to the cut-set bound tends to be 1. On the other hand, as SNR goes to infinity it is proved that successive relaying, based on the DPC, asymptotically achieves the capacity of the network.

Multi-hop MIMO relay networks: diversity-multiplexing trade-off analysis

A multi-hop relay network with multiple antenna terminals in a quasi-static slow fading environment is considered. The fundamental diversity-multiplexing gain tradeoff (DMT) is analyzed in the case of half-duplex relay terminals. While decode-and-forward (DF) relaying achieves the optimal DMT in the full-duplex relay scenario, it is shown that the dynamic decode-and-forward (DDF) protocol achieves the optimal DMT if the relay is constrained to half-duplex operation. For the latter case, static DF protocols are considered as well, and the corresponding DMT performance is shown to fall short of the optimal performance, which indicates that dynamic channel allocation is required for optimal DMT performance. The optimal DMT is expressed as the solution of a convex optimization problem and explicit DMT expressions are presented for some special cases. In the case of multiple relays, it is shown that the optimal diversity gain, which is achieved by exploiting the available "hop-diversity", is dominated by the neighboring two-hops with the minimum diversity gain.

A nearly optimal amplify-and-forward relaying scheme for two-hop MIMO multi-relay networks

This letter proposes a nearly optimal amplify-and-forward (AF) relaying scheme for two-hop and half-duplex distributed relay networks with one source, one destination, and multiple relays, each equipped with multiple antennas. The system mutual information is first analyzed under the assumption of known channel state information (CSI), revealing that it is possible to maximize the information rate by designing properly the relay precoder as a block-diagonal matrix. Then, the maximum transmission rate issue is investigated under a total relay power constraint, leading to an optimal relaying scheme for moderate to high levels of total relay power. A simulation study is undertaken to show the effectiveness of the proposed solution.

Analysis and optimization of a rateless coded joint relay system

We consider the code design for a half-duplex 4-node joint relay system with two sources, one relay, and one destination. The relay combines the information from both sources and transmits it to the destination together with both sources. We consider two coding schemes for information combining at the relay, namely, the superposition coding (SC) and the Raptor coding (RC). The Raptor codes are employed at the sources as well as the relay. The relay and the destination perform iterative a posteriori probability (APP) detection and soft Raptor decoding. For both SC and RC, the profiles for Raptor codes are optimized based on the extrinsic information transfer (EXIT) function analysis. For both the additive white Gaussian noise (AWGN) and block fading channels, the joint relay system with optimized profiles exhibits significant performance gains over that employing the code profile optimized for either the singleuser AWGN channel or the 2-user multiple-access channel.

Performance evaluation of half-duplex relay-based opportunistic cooperation diversity

Cooperative diversity is proposed as a means to improve the wireless transmission performance, which can effectively combat the wireless fading through sharing the antennas between source and relay nodes. In this paper, considering the practicability, we investigate the use of half-duplex relay, rather than full-duplex relay, for the opportunistic cooperation diversity. Two combining methods, namely selection diversity combining (SDC) and maximum ratio combining (MRC), are utilized for the implementation of the half-duplex relay-based opportunistic cooperation. Closed-form expressions of outage probability are derived for the proposed opportunistic cooperation as well as the known deterministic cooperation over Rayleigh fading channels. Numerical results show that the opportunistic cooperation is superior to the traditional deterministic cooperation in terms of outage probability and, moreover, the MRC-based case outperforms the SDC-based case no matter which duplex mode relay (i.e., half-duplex and full-duplex) is used for the opportunistic cooperation.

Sum rate analysis of multiantenna multiuser relay channel

In this study, the authors introduce two types of relay operations such as a half-duplex relay (HDR) and a full-duplex relay (FDR) and analyse the corresponding sum rate of a multiantenna multiuser relay system. Especially for FDR, a precoding scheme based on block diagonalisation (BD) is proposed to suppress the self-interference as well as to support multiple users at the same time slot. Simulation results show that the proposed FDR scheme enhances significantly the sum rate performance compared to HDR.

Spectral efficient cooperative transmission for half-duplex relay communications

A new transmission protocol using MIMO (Multiple Input Multiple Output) half-duplex relays is proposed to improve the capacity and the diversity gain of uplink relay communication systems. The proposed protocol employs two half-duplex DF (Decode-and-Forward)relays and Alamouti coded 2×2 MIMO communication for links between each relay and the destination. A low complexity receiver using maximum ratio combining and Alamouti decoding is introduced to detect the signal of the proposed protocol. Performance is evaluated by theoretical analysis and computer simulations, and the results show that the proposed protocol outperforms conventional IEEE 802.16j systems in terms of ergodic capacity and outage probability.

Multi-source multi-destination relay network: constrained optimisation for higher diversity

The authors consider a cooperative communication system where multiple sources transmit data to multiple destinations, being helped by multiple half-duplex relay nodes: relay nodes perform `amplify and forward` as their cooperative technique, with the use of complex weights for forwarding; complex forwarding weights are optimised, based on the obtained channel information, to improve data transmission performance, especially its corresponding diversity order. In particular, the authors investigate the constrained optimisation on the forwarding weights, under the two constraints of interference-free data reception at all destinations and total forwarding power at all relays, to (i) maximise the signal-to-noise ratio (SNR) of any given source`destination pair; (ii) optimise (here maximise the minimum among) the SNRs of all source`destination pairs. Performance (especially diversity order) analysis and Monte-Carlo simulations show the achieved diversity order and the consistence between analytical and numerical results.

On the optimal transmit strategy for the MIMO bidirectional broadcast channel

In this work the transmit covariance matrix optimization problem for the discrete memoryless MIMO Gaussian bidirectional broadcast channel is studied. A half-duplex relay node establishes bidirectional communication between two nodes using a decode-and-forward protocol. In the initial multiple access phase both nodes transmit their messages to the relay node. In the succeeding phase the relay broadcasts an optimal re-encoded message so that both nodes can decode the other's message using their own message as side information. The capacity region of the bidirectional broadcast channel is completely characterized by a weighted rate sum maximization problem, which can be solved by a simple iterative fixed point algorithm. If an efficient transmit covariance matrix is invariant with respect to the joint subspace spanned by the channels, then different combinations of the part transmitted on the orthogonal subspaces result in equivalent transmit strategies with different ranks. A closed-form procedure to obtain the optimal transmit covariance is derived for the case where the rank of the channels is equal to the number of antennas at the relay node and a full-rank transmission is optimal. It shows the complicated structure of the optimal eigenspace, which depends on the weights and the mean transmit power constraint. For parallel channels the optimal solution is completely characterized and discussed, which also solves the optimal power allocation problem for a single-antenna OFDM system.

Full-rate cooperative communications with spatial diversity for half-duplex uplink relay channels

This paper proposes a full-rate cooperative communication technique with spatial diversity for single-carrier transmissions. In order to achieve both the spatial diversity and the full-rate, data streams are simultaneously transmitted through all direct and relay channels with different phase rotation and cyclic delay patterns. The phase rotation and cyclic delay patterns are derived in the sense of minimizing interlayer interference and a corresponding destination structure is presented for decoupling each layer at the destination. Simulation results show that the proposed technique achieves spatial diversity without sacrificing spectral efficiency and outperforms conventional full-rate cooperative communication techniques.

On the Diversity Gain of AF and DF Relaying With Noisy CSI at the Source Transmitter

The problem of optimizing resource allocation over a half-duplex relay channel with noisy channel state information at the source transmitter (CSIT) is studied, with a focus on the asymptotically high signal-to-noise ratio (SNR) regime. A novel upper bound on the diversity-multiplexing tradeoff (DMT) is derived, taking into account the quality of the CSIT. It is shown that from a DMT perspective, the decode-and-forward (DF) protocol is strictly optimal over a certain range of the multiplexing gains. When the quality of the CSIT is sufficiently high, the DMT performance of the DF protocol with noisy CSIT equals that of the dynamic DF protocol shifted above by a constant diversity gain, which depends only on the quality of the CSIT about the source-destination link. When the quality of the CSIT reduces, DF relaying is still DMT-optimal, but only over a smaller range of the multiplexing gains. In an intermediate range of the multiplexing gains, nonorthogonal schemes provide some additional gains when the CSIT quality is sufficiently low. It is also shown that the DMT of the amplify-and-forward (AF) protocol is offset by a constant term depending on the quality of the CSIT of the source-destination link only.

On achievable rates of two-path successive relaying

This letter studies the achievable rates of the two-path relay channel (TPRC), where two half-duplex relays successively in turn forward messages from a source to a destination. It is shown that the conventional analogue and digital relaying schemes incur non-negligible throughput losses due to a socalled "inter-relay-interference (IRI)" phenomenon. This letter presents a new digital relaying scheme at the source transmitter to mitigate the IRI by applying the "dirty-paper-coding (DPC)" technique. It is shown that the proposed scheme achieves the capacity of the symmetric TPRC.