Relay Channel Research Articles

Backscatter Relay Communications Powered by Wireless Energy Beamforming

The integration of wireless power transfer (WPT) with the low-power backscatter communications provides a promising way to sustain battery-less wireless networks. In this paper, we consider a backscatter communication network wirelessly powered by a power beacon station (PBS). Each backscatter radio uses the harvested energy to power its data transmissions, in which some other radios can help as the wireless relays with an aim to improve throughput performance by cooperative transmission. Under this setting, we formulate a throughput maximization problem to jointly optimize WPT and the relay strategy of the backscatter radios. An iterative algorithm with reduced complexity and communication overhead is proposed to decompose the original problem into two sub-problems distributed at the PBS and the backscatter receiver. Moreover, we take uncertain channel information into consideration and formulate robust counter-parts of the throughput maximization problem when either the backscatter or relay channel is subject to estimation errors. The difficulty of the robust counter-part lies in the coupling of the PBS’ power allocation and relay strategy in matrix inequalities, which is addressed by alternating optimization with guaranteed convergence. Numerical results reveal that the cooperative relay strategy of the backscatter radios significantly improves the throughput performance.

Performance Analysis and Beamforming Designs of MIMO AF Relaying With Hardware Impairments

This paper investigates outage performance analysis and beamforming designs of a dual-hop multiple-input multiple-output (MIMO) amplify-and-forward (AF) relay channel with hardware impairments. We derive analytical closed-form expressions of the exact outage probability with fixed-gain and variable-gain relaying beamforming schemes. Moreover, asymptotic outage probability expressions are analyzed at high signal-to-noise ratio (SNR), which show that how hardware impairments and the number of relay antennas affect the system performance. We find that the outage probability in both relaying beamforming schemes has lower bounds with the increase of the SNR. Especially in the fixed-gain relaying beamforming scheme, we obtain a simple floor of the outage probability that is a monotone increasing function of hardware impairments’ level. To further compensate the performance loss brought by hardware impairments, we optimize the beamforming matrix for the dual-hop MIMO AF relay network by maximizing the end-to-end signal-to-noise-and-distortion ratio with the relay's power constraint. We derive optimal beamforming designs for sum-power constraint and for per-antenna power constraints. Our results show that the performance of the variable-gain relaying is superior to the fixed-gain relaying, especially for the case with varying scaling factor of the relay beamforming matrix. It is also shown that more performance gains can be attained with the proposed optimal beamforming designs.

Gaussian degraded relay channel with lossy state reconstruction

We consider a state reconstruction problem where the additive state process to a Gaussian degraded relay channel (GRC) is to be reconstructed at the receiver subject to some distortion/fidelity constraints. The state process we consider is Gaussian, independent and identically distributed (i.i.d.) and known a priori at the encoder as well as the relay. The receiver has to perform a lossy estimation of the state process, to within some prescribed distortion tolerance under a squared error distortion criterion. The setting also involves communicating messages across to the receiver, in addition to the estimation. Naturally, there is a tension between communication rate and state reconstruction fidelity. We are interested in the optimal trade-off between the distortion incurred at the receiver versus the rate at which messages can be communicated. We provide a complete characterization of the optimal rate versus distortion performance. The main contribution of the paper is a characterization of the fundamental limits of achievable rate versus distortion pairs in the Gaussian degraded relay model under consideration.

Approximate capacity of symmetric two‐pair one‐way relay channel with overhearing links

Approximate capacity of symmetric two‐pair one‐way relay channel with overhearing links

Positioning of a Wireless Relay Node for Useful Cooperative Communication

<span>Given the exorbitant amount of data transmitted and the increasing demand for data connectivity in the 21st century, it has become imperative to search for pro-active and sustainable solutions to the effectively alleviate the overwhelming burden imposed on wireless networks. In this study a Decode and Forward cooperative relay channel is analyzed, with the employment of Maximal Ratio Combining at the destination node as the method of offering diversity combining. The system framework used is based on a three-node relay channel with a source node, relay node and a destination node. A model for the wireless communications channel is formulated in order for simulation to be carried out to investigate the impact on performance of relaying on a node placed at the edge of cell. Firstly, an AWGN channel is used before the effect of Rayleigh fading is taken into consideration. Result shows that performance of cooperative relaying performance is always superior or similar to conventional relaying. Additionally, relaying is beneficial when the relay is placed closer to the receiver. </span>

Degrees of Freedom of the Circular Multirelay MIMO Interference Channel in IoT Networks

In this paper, we study the degrees of freedom (DoF) of a new network information flow model named the circular multirelay multiple-input multiple-output interference channel (CMMI). In this model, there are two clusters and each of them contains three users. Each user equipped with $M$ antennas in one cluster intends to deliver data streams to another user in the same cluster in a circular one-way transmission via the common distributed $K~N$ -antenna relay nodes. The CMMI network model can be considered as a basic component to construct the complicated Internet of Things networks. By assuming linear processing at the users and the relays, we show that the original analysis of DoF comes down in finding solutions of some nonlinear matrix equations with rank constraints. Toward this end, by using linear precoding and post-processing techniques, we propose two different approaches to solve the nonlinear matrix equations based on different antenna configurations. We show that a DoF of $\text{max} \{ {\text{min} \{ M,({{\sqrt {6K} }}/{12}) \}{,}~\text{min} \{ {({M}/{3}),({KN}/{2})} \}} \}$ is achievable for ${\forall ({M}/{N}) \in ({0, + \infty })}$ . In addition, to assess the optimal DoF, the cut-set approach is used for deriving the DoF upper bound by innovatively separating certain users to form two-pair two-way relay channels. We show that the DoF of CMMI is upper bounded by ${\text{max} \{{\text{min} \{{M,({KN}/{3})} \}, \text{min} \{ {({2M}/{3)},({KN}/{2})} \}} \}}$ . By combining the achievable DoF and the upper bound, we finally show that the optimal DoF of CMMI can be achieved for ${({M}/{N}) {\in } [{0,({{\sqrt {6K} }}/{12})}] {\cup } [{({3K}/{2}), + \infty }),{\forall } {K \ge 1}}$ .

Physical-Layer Network Coding for Fading Bidirectional Relay Channels with <i>M</i>-CPFSK

Physical-Layer Network Coding for Fading Bidirectional Relay Channels with <i>M</i>-CPFSK

Secure transmission scheme for parallel relay channels based on polar coding

This paper considers the use of polar codes to enable secure transmission over parallel relay channels. By exploiting the properties of polar codes over parallel channels, a polar encoding algorithm is designed based on Channel State Information (CSI) between the legitimate transmitter (Alice) and the legitimate receiver (Bob). Different from existing secure transmission schemes, the proposed scheme does not require CSI between Alice and the eavesdropper (Eve). The proposed scheme is proven to be reliable and shown to be capable of transmitting information securely under Amplify-and-Forward (AF) relay protocol, thereby providing security against passive and active attackers.

Joint Wireless Information and Energy Transfer in Two-Way Relay Channels

Joint Wireless Information and Energy Transfer in Two-Way Relay Channels

Multilevel Coded Modulation for the Full-Duplex Relay Channel

We investigate coded modulation for full-duplex relay channels, proposing and analyzing a multilevel coding (MLC) framework with capacity approaching performance and practical features. Sufficient conditions are derived under which multilevel coding meets the known achievable rates for decode-and-forward relaying. The effect of a bit additive superposition and the linearity of multilevel code components on the performance of the system are studied. It is shown that linearity of the relay component codes imposes no penalty on rate, however, the linearity of the source-to-relay component codes may impose a performance penalty especially for small modulation constellations. We show that this rate loss occurs because a linearity constraint on codebooks at the source node introduces a new tension between optimality of rate allocation in multilevel coding layers and optimality of source/relay codebook correlations. Motivated by this insight, an alternative modulation labeling is proposed that minimizes the rate loss. The results are extended to multi-antenna relays. Slow fading and fast Rayleigh fading without channel state at the transmitter are also analyzed. The error exponent of the proposed scheme is studied. Finally, the frame- and bit-error rate performance of the proposed scheme is studied via simulations using point-to-point LDPC codes, showing that the proposed MLC relaying has excellent performance.

Low complexity resource allocation in the relay channels with energy harvesting transmitters

Energy Harvesting (EH) is a novel technique to prolong the lifetime of the wireless Ad-hoc and sensor networks with replenishable nodes. In this sense, it has emerged as a promising technique for Green Communications. On the other hand, cooperative communication with the help of relay nodes improves the performance of wireless communication networks. In this paper, we investigate the cooperation in EH nodes. We consider the optimal power and rate allocation in the full-duplex Gaussian relay channel in which source and relay can harvest energy from their environments. In our model, the energy arrivals at the source and the relay are general stochastic processes with known EH times and amounts before the start of transmission. This problem has a constrained min-max optimization form that is not easy to solve. We propose a method based on a mathematical theorem to decompose it into two problems: the first problem has a tractable convex optimization form and can be solved efficiently. We show that the second problem is an unconstrained discrete convex optimization problem, which has the complexity of O(K2), instead of O(2K), where K is the dimension of variables. Also, we provide some numerical examples that confirm our results.

On scalability of physical layer network coding with modulo‐sum mapping over N‐way relay channels

SummaryIn this manuscript, fundamental limits of physical layer network coding with modulo‐sum mapping (to avoid of large cardinality), in terms of the number of superimposed signals that still render an acceptable probability of error, are studied. It is expected that (1) for a given bit error rate or throughput, an upper bound on the number of superimposed signals may exist and (2) if a large network is considered as a set of small subnetworks, and the proposed network code is used in each subnetwork, a significant increase in network throughput can be achieved. Answering these questions sheds light on the scalability of multiuser physical layer network coding with bit error rate or throughput constraints. Theoretical calculations, as well as simulation results, indicate the extraction of network coded signal from more than 2 (which is special case known as 2‐way relay channel) superimposed signals can be practical and lucrative.

Achievable Rates for Discrete Memoryless Multicast Networks With and Without Feedback

Discrete memoryless multicast network (DM-MN) is considered in this paper. We analyze the lower bounds of noisy network coding (NNC) and distributed decode-forward (DDF) for DM-MN, and show that both NNC and DDF ignore the channel output observed at the transmitter. Motivated by this observation, new coding schemes are proposed to improve NNC and DDF by exploiting the transmitter’s observation and applying hybrid relaying strategies. We first study a special case when the transmitter’s observation is rate-limited feedback signals, and propose a scheme that strictly improves NNC when feedback rates are sufficiently large. For the relay channel with perfect relay-transmitter feedback, our achievable rate reduces to Gabbai and Bross’s rate, which is strictly larger than NNC, DDF, and all known lower bounds on the achievable rates proposed for the setup without feedback. In our scheme, both relays and receivers compress their received signals like NNC, and the relays decode independent “common” and “private” parts of the source message. The generated compression indices are sent to the transmitter through feedback, from which the transmitter reconstructs the receivers’ and relays’ inputs and can thus cooperate with the receivers and relays. We then extend our idea to DM-MN without feedback. For this case, although the transmitter observes channel output, both NNC and DDF simply ignore it, while our new scheme has the transmitter utilize its channel output to decode a set of relays’ and receivers’ compression indices, which achieves some cooperation levels between the transmitter and the receivers and relays. An enhanced relay channel is introduced to show that our scheme strictly outperforms NNC and DDF.

AWGN and Rayleigh Fading Behavior of the Wireless Decode-and-Forward Relay Channel with Arbitrary Time and Power Allocation

Relying has in use for decades to tackle some of the challenges of wireless communication such as extending transmitting distance, transmitting over rough terrains. Diversity achieved through relaying is also a means to combat the random behavior of fading channels. In this work, effect of time and power allocation on relay performance is studied. The channel considered is the three-node channel with half-duplex constraint on the relay. The relaying technique assumed is decode-and-forward. Mutual information is used as the criteria to measure channel performance. There is half-duplex constraint and a total transmission power constraint on the relay source node and the relay node. A model is established to analyze the mutual information as a function of time allocation and power allocation in the case of AWGN regime. The model is extended to the Rayleigh fading scenario. In both AWGN and Rayleigh fading, results showed that the importance of relaying is more apparent when more resources are allocated to the relay. It was also shown that quality of the source to destination link has direct impact on the decision to relay or not to relay. Relatively good source to destination channel makes relaying less useful. The opposite is true for the other two links, namely the source to relay channel and the relay to destination channel. When these two channels are good, relaying becomes advantageous. When applied to cellular systems, we concluded that relaying is more beneficial to battery-operated mobile nodes than to base stations.

Relay performance optimisation based on signal space reconstruction

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.

Design and Analysis of Anytime Codes for Relay Channels

Anytime codes are known to be useful for tracking and controlling unstable systems over noisy channels. Although practical anytime codes have been developed for point-to-point communication, to date no practical code constructions and tractable analysis of anytime codes are known to exist for relay networks. In this paper, we study the design and theoretical analysis of anytime codes for a three-terminal relay network. We propose bilayer codes for anytime transmission over the relay network and consider two transmission schemes for the relay-destination link. For both schemes, we analytically derive the delay-exponents and show that they closely match the corresponding numerical results obtained from density evolution. Through simulation, we also show the finite-length performance of the proposed bilayer anytime code.

Impact of relay side information on the coverage region for the wireless relay channel with correlated noises

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.

Relay Selection for Multi-Channel Cooperative Multicast: Lexicographic Max–Min Optimization

Cooperative multicast has been demonstrated to achieve significant performance gain over the classic source–destination transmission paradigm by exploiting spatial diversity through the participation of multiple relay nodes. As a major technical challenge, the selection of relays for a multicast session has significant impact on the multicast performance. The challenge is even more pronounced when the number of channels is limited as the relay selection is in this context coupled with channel allocation. The goal of this paper is to design a fair multicast relay selection scheme with limited channel resources. Specifically, we establish an analytical framework for this joint relay selection and channel allocation problem and develop a lexicographic max–min multicast relay selection scheme. Our design consists of two technical steps. First, we consider the maximization of the minimal data rate. By decoupling relay selection and channel allocation, the problem is transformed to a max–min–max problem, which is difficult to solve. To make this problem tractable, we reformulate it as a convex optimization problem via relaxation and smoothing, and prove the asymptotic equivalence from a geometrical perspective. Second, we propose an adjustment algorithm based on the initial max–min solution, and prove that the proposed scheme achieves lexicographic optimality. Finally, our proposed algorithm is evaluated by simulation to show its superiority over the conventional schemes.

Design of Channel Coded Heterogeneous Modulation Physical Layer Network Coding

In a two-way relay channel network (TWRC), the integration of channel coding into symmetric physical layer network coding (PNC) has been well studied, where both sources use exactly the same channel coding and modulation schemes and the relay decodes and reencodes the codewords obtained from the superimposed signals. How to integrate the channel coding into heterogeneous modulation PNC (HePNC), where the sources apply different modulations, is an open issue. In this paper, we propose a channel coded HePNC (CoHePNC) scheme under asymmetric TWRC. For repeat-accumulate (RA) codes applied at the sources, a full-state sum-product decoding algorithm is proposed which enables the relay to decode the superimposed signals from the sources to the raw decoding results firstly, and then re-encode and obtain the network-coded codewords by mapping the raw decoding results according to the proposed bit-level mapping functions. We further optimized the bit-level mapping functions according to the two source-relay channel conditions. Extensive simulation results demonstrated that the proposed CoHePNC outperforms the existing channel coded PNC schemes in terms of the relay decoding error rate and the end-to-end bit error rate under asymmetric TWRC scenarios.

Performance Analysis of Lossy Decode-and-Forward for Non-Orthogonal MARCs

Non-orthogonal transmission is considered to be one of the promising techniques for improving the throughput of the existing and future wireless communication networks. We concentrate on the transmission of both independent and correlated binary sources over a non-orthogonal multiple access relay channel (MARC), which consists of two sources, one relay, and one destination. The lossy decode-and-forward (DF), developed from the conventional DF, is adopted at the relay. Two time slots are required with non-orthogonal transmission over such network setup, while three time slots are required with the conventional orthogonal transmission. We analyze the outage probability of transmission of independent binary sources over the non-orthogonal MARC based on the theorem of multiple access channel (MAC) with a helper, which combines the Slepian-Wolf rate region and the MAC capacity region. For the performance verification, we implement a practical coding-decoding chain, which is applicable to the transmission of both independent and correlated binary sources. Exclusive-OR based multi-user complete decoding is introduced at the relay node, and iterative joint decoding is utilized at the destination by taking into consideration the estimated intra-link error probability and correlation information between the sources. The practical simulation results are well matched with the theoretical analyses.