Half-duplex Relay Research Articles

Half-Duplex Relaying Over Slow Fading Channels Based on Quantize-and-Forward

The focus of this paper is to study the performance of the quantize-and-forward (QF) scheme over a half-duplex relay channel that is slowly fading, with the assumption that the channel state information (CSI) is available only at the receiver side. In order to do so, three steps are taken. The first step is to characterize the achievable rate of the QF scheme over a discrete memoryless half-duplex relay channel. Then, the achievable rate over a corresponding additive white Gaussian noise channel is obtained (the specific assumption regarding the CSI in this paper makes this step nontrivial). With the results from the first two steps, performance measures such as outage probability, expected rate, and diversity-multiplexing tradeoff (DMT) over slow fading channels are evaluated. It is shown that the QF scheme can significantly outperform the compress-and-forward scheme at finite signal-to-noise ratio (SNR) and it can achieve the optimal DMT at asymptotically high SNR. Moreover, it is shown that simple feedback from the destination node to the relay node can further improve the performance of the QF scheme.

Coding and system design for quantize-map-and-forward relaying

In this paper we develop a low-complexity coding scheme and system design framework for the half duplex relay channel based on the Quantize-Map-and-Forward (QMF) relaying scheme. The proposed framework allows linear complexity operations at all network terminals. We propose the use of binary LDPC codes for encoding at the source and LDGM codes for mapping at the relay. We express joint decoding at the destination as a belief propagation algorithm over a factor graph. This graph has the LDPC and LDGM codes as subgraphs connected via probabilistic constraints that model the QMF relay operations. We show that this coding framework extends naturally to the high SNR regime using bit interleaved coded modulation (BICM). We develop density evolution analysis tools for this factor graph and demonstrate the design of practical codes for the half-duplex relay channel that perform within 1dB of information theoretic QMF threshold.

Whether and where to code in the wireless packet erasure relay channel

The throughput benefits of random linear network codes have been studied extensively for wirelined and wireless erasure networks. It is often assumed that all nodes within a network perform coding operations. In energy-constrained systems, however, coding subgraphs should be chosen to control the number of coding nodes while maintaining throughput. In this paper, we explore the strategic use of network coding in the wireless packet erasure relay channel according to both throughput and energy metrics. In the relay channel, a single source communicates to a single sink through the aid of a halfduplex relay. The fluid flow model is used to describe the case where both the source and the relay are coding, and Markov chain models are proposed to describe packet evolution if only the source or only the relay is coding. In addition to transmission energy, we take into account coding and reception energies. We show that coding at the relay alone while operating in a rateless fashion is neither throughput nor energy efficient. Given a set of system parameters, our analysis determines the optimal amount of time the relay should participate in the transmission, and where coding should be performed.

LDPC codes for soft decode-and-forward in half-duplex relay channels

We investigate the use of rate-compatible lowdensity parity-check (RC-LDPC) codes as part of a soft decodeand- forward (SDF) protocol over the half-duplex relay channel. We propose a new methodology to design the degree distribution of the RC-LDPC codes with a lower triangular parity-check matrix, enabling the additional parity bits to be linearly and systematically encoded at the relay. Our proposed methodology introduces the concept of a K-layer doping matrix to represent the structure of a lower triangular parity-check matrix. As a result of our methodology, the asymptotic performance of RC-LDPC codes can be analyzed and predicted using the multi-edge-type density evolution. Then, we derive the soft-re-encoding of the additional parity symbols at the relay using our designed RCLDPC codes. Moreover, we propose a novel method, which we refer to as soft fading, to compute the log-likelihood ratio (LLR) of the received signal at the destination for the SDF protocol. We demonstrate that our proposed soft fading method outperforms the best known method in the literature by up to 0.7 dB in terms of BER performance. Finally, we derive a new bound for the power multiplication factor at the relay, which limits the amount of soft-errors forwarded by the relay to the destination. The BER performance of our new RC-LDPC codes improves significantly once the power multiplication factor at the relay satisfies this bound.

Bilayer LDPC Convolutional Codes for Decode-and-Forward Relaying

In this paper we present bilayer LDPC convolutional codes for half-duplex relay channels. Two types of codes, bilayer expurgated LDPC convolutional codes and bilayer lengthened LDPC convolutional codes, are proposed for decode-and-forward (DF) relaying. In the case of the binary erasure relay channel, we prove analytically that both code constructions achieve the capacities of the source-relay link and the source-destination link simultaneously, provided that the channel conditions are known when designing the codes. Meanwhile, both codes enable the highest transmission rate possible with DF relaying for a wide range of channel parameters. In addition, the regular degree distributions can easily be computed from the channel parameters, which significantly simplifies the code optimization. The code construction and performance analysis are extended to the general binary memoryless symmetric channel, where a capacity-achieving performance is conjectured. Numerical results are provided for both types of codes with finite node degrees over binary erasure channels and binary-input additive white Gaussian noise channels, which verify the aforementioned theoretical analysis.

The Diversity-Multiplexing Tradeoff of the MIMO Half-Duplex Relay Channel

The fundamental diversity-multiplexing tradeoff of the three-node, multi-input, multi-output (MIMO), quasi-static, Rayleigh faded, half-duplex relay channel is characterized for an arbitrary number of antennas at each node and in which opportunistic scheduling (or dynamic operation) of the relay is allowed, i.e., the relay can switch between receive and transmit modes at a channel dependent time. In this most general case, the diversity-multiplexing tradeoff is characterized as a solution to a simple, two-variable optimization problem. This problem is then solved in closed form for special classes of channels defined by certain restrictions on the numbers of antennas at the three nodes. The key mathematical tool developed here that enables the explicit characterization of the diversity-multiplexing tradeoff is the joint eigenvalue distribution of three mutually correlated random Wishart matrices. Besides being relevant here, this distribution result is interesting in its own right. Previously, without actually characterizing the diversity-multiplexing tradeoff, the optimality in this tradeoff metric of the dynamic compress-and-forward protocol based on the classical compress-and-forward scheme of Cover and El Gamal was shown by Yuksel and Erkip. However, this scheme requires global channel state information at the relay. In this paper, the so-called quantize-map and forward (QMF) coding scheme is adopted as the achievability scheme with the added benefit that it achieves optimal tradeoff with only the knowledge of the (channel dependent) switching time at the relay node. Moreover, in special classes of the MIMO half-duplex relay channel, the optimal tradeoff is shown to be attainable even without this knowledge. Such a result was previously known only for the half-duplex relay channel with a single antenna at each node, also via the QMF scheme. More generally, the explicit characterization of the tradeoff curve in this study enables the in-depth comparisons herein of full-duplex versus half-duplex relaying as well as static versus dynamic relaying, both as a function of the numbers of antennas at the three nodes.

Analysis of decode-and-forward, compress-and-forward and combined protocols for multiterminal half-duplex relay networks with random schedules

In this paper, protocols based on compress-and-forward, decode-and-forward and a combined approach are discussed, achievable rates are derived, and a performance analysis for a multiterminal half-duplex relay network is carried out. Half-duplex relays are subject to an orthogonality constraint, which prohibits simultaneous receiving and transmitting on a time-frequency resource. With this constraint, this paper investigates random transmission schedules, such that the sequence of transmit and receive slots serves as information bearer. This concept is applied to a network of decode-and-forward relays, which decode the full source message or parts of it. Then a compress-and-forward protocol with regular encoding is introduced. Regular encoding for compress-and-forward overcomes the limitations due to the source-channel-coding separation, which is a particular bottleneck in multiterminal networks. Based on the partial decode-and-forward and compress-and-forward protocol, a protocol with one compress-and-forward and one decode-and-forward based relay is presented. Similar to the cut-set bound, both relays operate in a mode in which only one is transmitting whereas the second one is listening to exploit additional information transmitted by the other relay.For the considered scenarios and by contrast to the full-duplex channel, protocols based on compress-and-forward outperform decode-and-forward protocols for a wide range of parameters. Furthermore, the introduced combined approach provides achievable rates close to the cut-set bound for scenarios in which both relays are well separated or very close to each other. If the inter-relay interference is too low for an efficient interference cancellation but also too strong to be ignored, compress-and-forward also outperforms the combined strategy. Copyright © 2012 John Wiley & Sons, Ltd.

Optimal Power Allocation and Outage Analysis for Cognitive Full Duplex Relay Systems

This paper investigates the use of full duplex relaying (FDR) in cognitive radio systems. Cognitive full duplex relay networks (CogFRNs) offer the advantage not only of increasing spectral efficiency by spectrum sharing but also of extending coverage through the use of relays. Concurrent transmissions at the source and relay in CogFRNs can overcome a loss of resource efficiency in a way that conventional half duplex relay (HDR) systems cannot. However, in CogFRNs, the primary user experiences interference from the secondary source and relay simultaneously due to the effects of full duplexing. Satisfying the interference constraint by simply reducing transmission power results in performance degradation for the secondary user. What is therefore needed is a way to optimize the transmission powers at the secondary source and relay. To address this need, we propose an optimal power allocation scheme based on minimizing the outage probability in CogFRNs. We then analyze the outage probability of the secondary user in the noise-limited and interference-limited environments. In addition, we also propose an outage-constrained power allocation scheme which does not require the instantaneous channel state information (CSI) for the link between the primary and secondary users. Simulation results show that the proposed schemes achieve performance improvement in terms of outage probability.

Least Square Error Detection for Noncoherent Cooperative Relay Systems

In this paper, noncoherent cooperative amplify-and-forward (AF) half-duplex relay systems are considered. For such systems, an asymptotic formula of pairwise error probability (PEP) for the least square error (LSE) detector is derived by using the perturbation theory on the eigenvalues. The result shows that the full-diversity-gain function mimics coherent cooperative AF half-duplex relay systems, whereas the coding gain function mimics noncoherent multiple-input-multiple-output (MIMO) systems. In addition, it is proved that, for any given nonzero received signal, the unique blind identification of both the equivalent channel and the transmitted signals in a noise-free case is equivalent to full diversity with the LSE detector in a Gaussian noisy environment. In particular, for the noncoherent AF half-duplex protocol with three nodes, a full-diversity unitary diagonal distributed space-time block code (STBC) is designed by utilizing the full-diversity criterion established in this paper and recently developed uniquely factorable constellation. Furthermore, the generalized likelihood ratio test receiver is derived for this specific coded protocol. Simulation results show that the code presented in this paper substantially outperforms the differential code and the optimally precoded training scheme in the current literature.

Mimicking Full-Duplex Relaying Using Half-Duplex Relays With Buffers

We propose a new relaying scheme referred to as space full-duplex max-max relay selection (SFD-MMRS), which uses relay selection and half-duplex (HD) relays with buffers to mimic full-duplex (FD) relaying. SFD-MMRS allows the selection of different relays for reception and transmission, which, in turn, enables the relays selected for reception and transmission to simultaneously receive and transmit. With SFD-MMRS, the prelog factor 1/2 is removed from the capacity expression, and better performance in terms of both throughput and outage probability is achieved. We provide a comprehensive analysis of the capacity and outage probability of the proposed scheme for a decode-and-forward (DF) protocol in Rayleigh fading. This analysis reveals that the proposed scheme provides better performance, compared with HD MMRS and HD best relay selection (BRS). Moreover, our simulation results show that the capacity of the proposed scheme with HD relays exceeds twice the capacity of BRS with HD relays for any number of relays. Furthermore, the proposed scheme provides full diversity and large signal-to-noise ratio (SNR) gains, compared with competing schemes in the literature.

Distributed Beamforming for Relay Assisted Multiuser Machine-to-Machine Networks

We consider signal transmission with the aid of multiple half-duplex single-antenna relay nodes using the amplify-and-forward (AF) strategy for a multiuser wireless machine-to-machine (M2M) communication system. In such a scenario, relay beamforming has been proved to be an effective way to improve system performance by employing spatial diversity gains. Early works have mostly focused on various centralized relay beamforming schemes based on global channel state information (CSI). Since global CSI is often unavailable due to geometric locations, power limitation, or other constraints of the relay nodes in M2M networks, our work aims to develop distributed algorithms that each relay node individually learns its own beamforming weights with local CSI. We propose two suboptimal relay beamforming schemes that only require local CSI to minimize mean square error (MSE) for all the users with nonorthogonal channels. For multiuser systems with orthogonal channels, we divide the optimization problem into multiple single user problems which then can be solved by each relay independently. Numerical simulations for the proposed algorithms are presented showing the performance of the proposed schemes is close to that of the optimal scheme with global CSI in terms of bit error rate (BER) criterion.

Compressive cooperation for gaussian half-duplex relay channel

Motivated by the compressive sensing (CS) theory and its close relationship with low-density parity-check code, we propose compressive transmission which utilizes CS as the channel code and directly transmits multi-level CS random projections through amplitude modulation. This article focuses on the compressive cooperation strategies in a relay channel. Four decode-and-forward (DF) strategies, namely receiver diversity, code diversity, successive decoding and concatenated decoding, are analyzed and their achievable rates in a three-terminal half-duplex Gaussian relay channel are quantified. The comparison among the four schemes is made through both numerical calculation and simulation experiments. In addition, we compare compressive cooperation with a separate source channel coding scheme for transmitting sparse sources. Results show that compressive cooperation has great potential in both transmission efficiency and its adaptation capability to channel variations.

A Novel Distributed Antenna Selection Scheme for Fixed-Gain Amplify-and-Forward Relaying Systems

This paper proposes a novel distributed transmit antenna selection (AS) concept for dual-hop fixed-gain amplify-and-forward (AF) relaying systems, where a multiantenna source transmits information to a single-antenna destination by using a single-antenna half-duplex relay. By invoking a local channel information exploitation/decision mechanism along with decision feedback between terminals, a distributed AS (DAS) scheme is formulated. Compared with the optimal/suboptimal AS, DAS can maintain a low and constant delay/feedback overhead, irrespective of the number of transmit antennas. Moreover, asymptotic outage analysis reveals that DAS can still achieve full diversity order. In addition, it is numerically shown that when the relay is deployed in an outage-optimal manner, DAS can attain very close outage performance to that of the optimal AS.

Outage Probability and Power Allocation of Two-Way Amplify-and-Forward Relaying with Channel Estimation Errors

We consider a two-way amplify-and-forward (AF) relaying system consisting of two source nodes and a half-duplex relay. We assume that the source nodes are equipped with the linear minimum mean squared error (LMMSE) channel estimators. We investigate the effect of uncertainty due to channel estimation error on the system outage probability, considering the imposed bandwidth and energy costs of channel estimation. For a fixed transmission block length and a total transmit power constraint, we provide a compact-form expression for the system outage probability upper bound and we explore the optimal number of training symbols, the optimal power allocation between data and training, and the optimal power allotment between the two users and the relay, such that this bound is minimized. Our numerical results show that channel estimation error does not limit the performance in high signal-to-noise ratio (SNR). Also, the optimal power allocation between data and training and between the users and the relay provides a significant SNR improvement, compared with the suboptimal schemes, including fixed power allocation. The optimization gain increases as the relay moves away from the middle point.

Privacy in Bidirectional Relay Networks

In this work, the bidirectional broadcast channel (BBC) with confidential 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 transmits additional confidential information to one of them in the broadcast phase. The corresponding confidential message is transmitted at a certain secrecy level which characterizes the amount of information that can be kept secret from the non-legitimate node. The capacity-equivocation and secrecy capacity regions of the BBC with confidential messages are established where the latter characterizes the communication scenario with perfect secrecy, which means that the confidential information is completely hidden from the non-legitimate node. Thereby, it is shown that the optimal processing exploits ideas and concepts of the BBC with common messages and of the classical broadcast channel with confidential messages.

Dynamic Resource Allocation in MIMO-OFDMA Systems with Full-Duplex and Hybrid Relaying

In this paper, we formulate a joint optimization problem for resource allocation and scheduling in full-duplex multiple-input multiple-output orthogonal frequency division multiple access (MIMO-OFDMA) relaying systems with amplify-and-forward (AF) and decode-and-forward (DF) relaying protocols. Our problem formulation takes into account heterogeneous data rate requirements for delay sensitive and non-delay sensitive users. We also consider a theoretically optimal hybrid relaying scheme as a performance benchmark, which allows a dynamic selection between AF relaying and DF relaying protocols with full-duplex and half-duplex relays. We show that under some mild conditions the optimal transmitter precoding and receiver post-processing matrices jointly diagonalize the MIMO-OFDMA relay channels for all considered relaying protocols transforming the resource allocation and scheduling problem into a scalar optimization problem. Dual decomposition is employed to solve this optimization problem and a distributed iterative resource allocation and scheduling algorithm with closed-form power and subcarrier allocation is derived. Simulation results not only illustrate that the proposed distributed algorithm converges to the optimal solution in a small number of iterations, but also demonstrate the potential performance gains achievable with full-duplex relaying protocols.

How Does Channel Estimation Error Affect Average Sum-Rate in Two-Way Amplify-and-Forward Relay Networks?

This paper studies the impact of channel estimation error on the performance of a two-way amplify-and-forward (AF) relay network and investigates the optimal transmit resource allocation that minimizes the impact. In particular, we consider a three node network, consisting of two user terminals \mathbb{T}_A and \mathbb{T}_B and a half duplex relay node \mathbb{R}, where only \mathbb{T}_A and \mathbb{T}_B are equipped with channel estimators. Assuming block flat fading channel model, we adopt two estimation theoretic performance metrics, namely the Bayesian Cramer-Rao lower bound (CRLB) and the mean-squared error (MSE) of the linear minimum mean square error (LMMSE) channel estimate, and an information theoretic performance metric, namely the average sum-rate lower bound, as our optimality criteria. For a fixed transmission block length and under the total transmit power constraint, we investigate the optimal training vector design, the optimal number of training symbols in the training vector, the optimal power allocation between training and data in a transmission block, and the optimal power allotment between three nodes, such that these performance metrics are optimized, via utilizing bi-objective optimization methods. Our simulation results demonstrate that the optimal solutions corresponding to each performance metric vary, as the relay location and the system signal-to-noise ratio (SNR) change. They also reveal interesting symmetry relationship between these optimal solutions and the relay location.

A practical scheduling and power/constellation allocation for three relay networks

Relays are being deployed in both fourth generation cellular systems and wide metropolitan area networks in order to increase coverage and spectral efficiency. In this article, we consider a network with three half-duplex relays assisting the transmission from a source towards a destination. By assuming that transmission time consists of a sequence of phases, we develop a transmission scheme in which spatial multiplexing is achieved by alternating the transmission of a single relay in odd phases and a couple of relays employing Slepian-Wolf encoding in even phases. Moreover, to simplify Slepian-Wolf decoding (consisting of a scheme with successive interference cancelation), we propose a suboptimal scheme in which cooperative relays employ quantized QAM constellations to yield at the destination the desired QAM constellation with no interference. We formalize the problem of maximizing network spectral efficiency optimizing (a) QAM size, (b) power allocation, (c) time allocation, and (d) relays transmitting and receiving at each phase. The performance of the proposed scheme is compared against existing techniques in typical wireless scenarios showing the merits of the proposed approach.

Max-Max Relay Selection for Relays with Buffers

In this paper, we propose a new relay selection scheme for half-duplex relays with buffers. The proposed scheme is referred to as max-max relay selection (MMRS) since the relays with the best source-relay and the best relay-destination channels are selected for reception and transmission, respectively, which is only possible without data loss if the relays have buffers of infinite size. To relax this idealized assumption, we propose hybrid relay selection (HRS) for relays with buffers of finite size. HRS is a combination of conventional best relay selection (BRS) and MMRS and takes into account both the channel state and the buffer state for relay selection. We provide a comprehensive analysis of the outage and symbol error probabilities of both MMRS and HRS for a decode-and-forward protocol in Rayleigh fading. This analysis reveals that BRS, HRS, and MMRS achieve the same diversity gain. However, for N relays, MMRS achieves a signal-to-noise ratio (SNR) gain of 3(1-1/N) dB compared to BRS, and HRS closely approaches the SNR gain of MMRS for moderate buffer sizes (e.g. 30 transmission intervals).

Comparison of FDR and HDR Under Adaptive Modulation With Finite-Length Queues

To identify the optimal duplex mode and maximize the offered gain in the relay system, we compare the performances of half-duplex relay (HDR) and full-duplex relay (FDR). Finite-state Markov chain (FSMC) models are presented, showing the joint effects of finite-length queues and adaptive modulation (AM) under uncorrelated Rayleigh fading channels. Transmission efficiency, packet loss rate, and delay are derived and compared based on these models. According to our results, FDR is superior to HDR in the low-signal-to-noise ratio (SNR) region but loses its advantage as the SNR increases. When the size of the queue is large enough, FDR can be superior to HDR, even in the high-SNR region.