Full-duplex Relay Channel Research Articles

Multiuser Full-Duplex Relaying: Enabling Dual Connectivity via Impairments-Aware Successive Interference Cancellation

In this article, we consider the downlink of a cellular communication network, where dual-connectivity at the end-users is enabled with the assistance of a full-duplex (FD) massive-multiple-input-multiple-output (mMIMO) relay. In particular, the base station transmits separate data streams through the cochannel direct link as well as the FD relay channel, utilizing the successive-interference-cancellation (SuIC) capability at the receiver. As a result, the downlink communication data can be interchangeably loaded to separate subcarriers, employing an orthogonal multicarrier strategy, or to different available links, i.e., direct or FD relay link, employing the nonorthogonal SuIC at the receiver. In order to reliably model the SuIC operation at the receiver, the collective sources of impairments, including the nonlinear transmit and receiver chain distortions as well as the channel state information inaccuracy are incorporated. An optimization problem for joint subcarrier and power allocation is then devised in order to maximize system sum-rate, which belongs to the class of smooth difference-of-convex problems. An iterative optimization solution is then proposed, utilizing successive inner approximation framework, which converges to the point that satisfies Karush–Kuhn–Tucker optimality conditions. Numerical results show performance and robustness gain of proposed SuIC scheme in terms of sum-rate compared to previously proposed single-connectivity and half-duplex relaying schemes.

Energy Efficiency of Amplify-and-Forward Full-Duplex Relay Channels

In this letter, the energy efficiency (EE) for a three-node full-duplex (FD) relay channel with the amplify-and-forward (AF) scheme is studied. In particular, both the residual self-interference (RSI) and the circuit power consumption for imperfect self-interference cancellation (SIC) are considered and modeled as linear functions over the relay transmission power. Under this setup, the EE maximization problem for the AF FD relay channel is formulated and efficiently solved. Moreover, the EE performance of the direct transmission (DT), half-duplex (HD), and FD modes are compared under different channel conditions.

Securing Untrusted Full-Duplex Relay Channels in the Presence of Multiple External Cluster-Based Eavesdroppers

We investigate the physical layer security of a wireless cooperative network where communication between Alice and Bob is assisted by a full-duplex (FD) untrusted relay, Ray, in the presence of multiple external eavesdroppers, Eves. A cluster-based colluding eavesdropping setting is considered, where illegitimate nodes with common interests are grouped in a cluster. To confuse the different eavesdropping clusters, we employ artificial-noise (AN) aided beamforming at the source node. Moreover, FD relay jamming is used to improve the system's security. To maintain secure communications against the untrusted relay node, an FD destination jamming scheme is adopted. Our proposed scheme is designed based on the channel state information of the legitimate nodes only. We optimize the transmit power allocation factors between data and AN signals, the data and AN precoders at Alice, the AN precoder at Bob, and the data and AN precoders at Ray. Numerical results show that the optimal power allocation factor between data and AN depends on the total number of antennas of the different colluding eavesdropping clusters.

On the Achievable Rates of Virtual Full-Duplex Relay Channel

We study a multihop “virtual” full-duplex relay channel as a special case of a general multiple multicast relay network. For such a channel, quantize-map-and-forward (QMF) [and its generalization of noisy network coding (NNC) and short message NNC] achieves the cut-set upper bound within a constant additive gap, where the gap grows linearly with the number of relay stages K. This gap, however, may not be acceptable for practical communication systems with multihop transmissions (e.g., a wireless backhaul operating at high frequencies). Recently, we improved the capacity scaling by using a forward sliding-window (SW) decoding and by optimizing the quantization level at each relay, obtaining the gap that grows logarithmically as log K. Furthermore, the improved scheme has lower decoding complexity and delay than the general QMF and NNC approaches. In this paper, we further improve the performance by presenting a mixed scheme in which each relay can perform either decode-and-forward (DF) or the improved QMF (with SW decoding) and can choose to perform rate-splitting to enable partial interference cancellation. In general, the optimization of the relay DF/QMF configuration is combinatorial. Nevertheless, we provide that a simple greedy algorithm finds an optimal configuration under some practically reasonable assumptions. We derive an achievable rate that is easily computable and show that the proposed mixed scheme outperforms the QMF-only schemes. We demonstrate that the performance improvement increases with K, which indicates that the mixed scheme is indeed beneficial for multihop transmission.

Near-Maximum-Likelihood Decoding for Convolutionally Coded Physical-Layer Network Coding Over the Full-Duplex Two-Way Relay Channel

The full duplex (FD) two-way relay channel (TWRC) has recently been shown to be a feasible way to improve the network throughput in practical communications. In this correspondence, we consider the convolutionally coded physical-layer network coding over the TWRC in which two sources work in the FD mode and there exists a direct link between them. Every source receives two packets, one packet from the other source and one network coded packet from the relay. A near-maximum-likelihood decoding algorithm for the sources is proposed. A salient feature of the proposed algorithm is that it exploits the code structure to mitigate the error propagation induced by the relay. Furthermore, we derive the near maximum-likelihood decoding bound on end-to-end BER for the system. Simulation results indicate that the performance of the proposed algorithm matches well the bound.

Rate-Splitting Robustness in Multi-Pair Massive MIMO Relay Systems

Relay systems improve both coverage and system capacity. Toward this direction, a full-duplex (FD) technology, being able to boost the spectral efficiency by transmitting and receiving simultaneously on the same frequency and time resources, is envisaged to play a key role in future networks. However, its benefits come at the expense of self-interference (SI) from their own transmit signal. At the same time, massive multiple-input massive multiple-output systems, bringing unconventionally many antennas, emerge as a promising technology with huge degrees-of-freedom. To this end, this paper considers a multi-pair decode-and-forward FD relay channel, where the relay station is deployed with a large number of antennas. Moreover, the rate-splitting (RS) transmission has recently been shown to provide significant performance benefits in various multi-user scenarios with imperfect channel state information at the transmitter (CSIT). Engaging the RS approach, we employ the deterministic equivalent analysis to derive the corresponding sum-rates in the presence of interferences. Initially, numerical results demonstrate the robustness of RS in half-duplex (HD) systems, since the achievable sum-rate increases without bound, i.e., it does not saturate at high signal-to-noise ratio. Next, we tackle the detrimental effect of SI in FD. In particular, and most importantly, not only FD outperforms HD, but also RS enables increasing the range of SI over which FD outperforms HD. Furthermore, increasing the number of relay station antennas, RS appears to be more efficacious due to imperfect CSIT, since SI decreases. Interestingly, increasing the number of users, the efficiency of RS worsens and its implementation becomes less favorable under these conditions. Finally, we verify that the proposed DEs, being accurate for a large number of relay station antennas, are tight approximations even for realistic system dimensions.

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.

Buffer-aided relaying for the two-hop full-duplex relay channel with self-interference

In this paper, we investigate the two-hop full-duplex (FD) relay channel with self-interference and fading, which is comprised of a source, an FD relay, and a destination, where a direct source-destination link does not exist and the FD relay is impaired by self-interference. For this channel, we propose three buffer-aided relaying schemes with adaptive reception-transmission at the FD relay for the cases when the source and the relay both perform adaptive-power allocation, fixed-power allocation, and fixed-rate transmission, respectively. The proposed buffer-aided relaying schemes significantly improve the achievable rate and the throughput of the considered relay channel by enabling the FD relay to adaptively select to either receive, transmit, or simultaneously receive and transmit in a given time slot based on the qualities of the receiving, transmitting, and self-interference channels. Our numerical results show that significant performance gains are achieved using the proposed buffer-aided relaying schemes compared to conventional FD relaying, where the FD relay is forced to always simultaneously receive and transmit, and to buffer-aided half-duplex relaying, where the half-duplex relay cannot simultaneously receive and transmit.

Spectral Efficiency and Relay Energy Efficiency of Full-Duplex Relay Channel

Full-duplex relaying has the potential to improve the spectral efficiency (SE) of cooperative communication systems. Due to residual self-interference (RSI), increase of the relay power does not always contribute to SE improvement. To fully utilize full-duplex relaying in cooperative communications, the effect of RSI on the SE achieved by different relay schemes need to be investigated. In this paper, we study bounds on the SE of full-duplex relay channel with decode-forward (DF) relaying, compress-forward (CF) relaying, and amplify-forward (AF) relaying in the presence of RSI. For respective schemes, optimal relay power and the corresponding maximal SE are derived in closed-form. Bounds on the relay energy-efficiency (REE) are presented for different schemes, which are useful for system design under per-node energy efficiency constraint. Based on the SE performance, the conditions of employing full-duplex relay, criteria for selecting relay scheme among DF, CF, and AF schemes, and the conditions of adopting hybrid full-duplex or half-duplex mode are elaborated regarding to RSI strength. In summary, this paper investigates the relationship among SE, REE, and system design by taking into account the effect of RSI for a general class of cooperation schemes.

Capacity of the Gaussian Two-Hop Full-Duplex Relay Channel With Residual Self-Interference

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

LDPC Lattice Codes for Full-Duplex Relay Channels

Low-density parity-check (LDPC) lattices were the first family of lattices to show efficient decoding in high dimensions. We consider a case of these lattices with one binary LDPC code as an underlying code. We employ encoding and decoding of the LDPC lattices in a cooperative transmission framework. We establish two efficient shaping based on hypercube and Voronoi shaping, to obtain LDPC lattice codes. Then, we propose the implementation of block Markov encoding for one-way and two-way relay networks using LDPC lattice codes. An efficient method is also required for decomposing full-rate codebook into lower rate codebooks. We apply different decomposition schemes for one-way and two-way relay channels, which are the altered versions of the decomposition methods of low density lattice code (LDLC) lattices. Due to the lower complexity of the decoding for LDPC lattices comparing with LDLCs, the complexity of our schemes is significantly lower than the ones proposed for LDLCs. The efficiency of the proposed schemes is presented using simulation results that indicate the outperforming behavior of LDLCs over LDPC lattice codes in the same dimensions. However, having lower decoding complexity enables us to increase the dimension of the lattice to compensate the existing gap between the performance of the LDPC lattice codes and the LDLCs.

Coherent Signaling for Full-Duplex Relay Channel With Self-Interference

To improve the spectral efficiency (SE), coherent signaling is investigated for full-duplex relay channel (FDRC) in the presence of residual self-interference. First, we propose a novel coherent amplify-forward scheme and derive the SE achieved by both forward decoding and backward decoding. Condition on selecting forward/backward decoding is clearly given. Then, we elaborate the signal design for coherent decode-forward scheme and derive the optimal correlation coefficient for signaling. The optimal relay power that maximizes the SE is obtained in the closed form. Representative numerical results show that coherent signaling brings significant SE gain for FDRC.

Artificial-Noise-Aided Secure MIMO Full-Duplex Relay Channels With Fixed-Power Transmissions

This letter studies the physical-layer security of a full-duplex (FD) multiple-input multiple-output relay channel. A legitimate source node (Alice) communicates with her destination node (Bob) through an FD relay node in the presence of a cooperative FD jammer and a potential eavesdropper (Eve). The cooperative jammer is assumed to be an FD node that is solely charged by the ambient radio-frequency transmissions. We investigate the self-energy recycling at the cooperative jammer and derive a sufficient condition for the cooperative jammer to operate as a node with reliable energy supply. Without knowing the eavesdropper’s channel state information at the legitimate nodes, we propose a precoded artificial-noise (AN) injection scheme to secure the legitimate transmissions. The numerical results demonstrate that our proposed AN-aided secure scheme achieves a significant average secrecy rate improvement compared with the case of no cooperative jammer.

Outage Probability of Full-Duplex AF Relaying With Processing Delay and Residual Self-Interference

This letter investigates the outage performance in a full-duplex relay (FDR) channel that adopts an amplify-and-forward (AF) protocol. We provide a new closed-form expression for the outage probability that captures the joint effect of residual self-interference (RSI) and a direct link. In addition, when the processing delay of the relay is larger than 1, which is often the case in practice, the proposed closed-form outage performance expression still applies. Finally, all the theoretical results are validated through numerical simulations. The results indicate that AF-FDR can outperform selective decode-and-forward FDR (SDF-FDR) in the low-to-intermediate-rate regions because of less processing delay.

Low-Density Lattice Codes for Full-Duplex Relay Channels

We propose a class of practical efficient lattice codes for real-valued full-duplex one- and two-way relay channels. First, we investigate the problem from a theoretical perspective, proposing lattice-coding instantiations of superposition block Markov encoding. Our encoding/decoding strategies recover the well-known decode-and-foward rates for the one-way relay channel and a previously-proven rate region for the two-way relay channel. Then, we construct practical, low-complexity implementations of these schemes using low-density lattice codes. Simulations show that our schemes achieve performance as close as 2.5 dB away from theoretical limits. Finally, we show that, due to features inherent to full-duplex relaying and practical codes, the gap to theoretical limits depends on the channel gains and transmit power of the relay relative to the source(s). We characterize this gap analytically, providing insight into the design of practical full-duplex relay systems.

Grassmannian Signalling Achieves Tight Bounds on the Ergodic High-SNR Capacity of the Noncoherent MIMO Full-Duplex Relay Channel

This paper considers the ergodic noncoherent capacity of a multiple-input multiple-output frequency-flat block Rayleigh fading full duplex relay channel at high signal-to-noise ratios (SNRs). It is shown that, for these SNRs, restricting the input distribution to be isotropic on a compact Grassmann manifold maximizes an upper bound on the cut-set bound. Furthermore, it is shown that, from a degrees of freedom point of view, no relaying is necessary and Grassmannian signalling at the source achieves the upper bound within an SNR-independent gap. When the source-relay channel is sufficiently stronger than the source-destination and relay-destination channels, it is shown that, with the number of relay transmit antennas appropriately chosen, a Grassmannian decode-and-forward scheme, which is devised herein, achieves the ergodic noncoherent capacity of the relay channel within an approximation gap that goes to zero as the SNR goes to infinity. Closed-form expressions for the optimal number of relay transmit antennas indicate that this number decreases monotonically with the source transmit power.

On the Outage Performance of Full-Duplex Selective Decode-and-Forward Relaying

We evaluate the outage performance in a three-terminal full-duplex relay channel that adopts a selective decode-and-forward protocol, taking relay self-interference into account. Previous work focused on coverage extension scenarios where direct source-destination transmissions are neglected or considered as interference. In this work, we account for the relay self-interference, and exploit the cooperative diversity offered by the independently fading source/relay message replicas that arrive at the destination. We present an approximate, yet accurate, closed-form expression for the end-to-end outage probability that captures their joint effect. With the derived expression in hand, we propose a relay transmit power optimization scheme that only requires the relay knowledge of channel statistics. Finally, we corroborate our analysis with simulations.

Design of Multi-Edge-Type Bilayer-Expurgated LDPC Codes for Decode-and-Forward in Relay Channels

We consider the design of bilayer-expurgated low density parity-check (BE-LDPC) codes as part of a decode and-forward protocol for use over the full-duplex relay channel. A new ensemble of codes, termed multi-edge-type bilayer expurgated LDPC (MET-BE-LDPC) codes, is introduced where the BE-LDPC code design problem is transformed into the problem of optimizing the multinomials of a multi-edge-type LDPC code. We propose two design strategies for optimizing MET-BE-LDPC codes; the bilayer approach is preferred when the difference in SNR between the source-to-relay and the source to-destination channels is small, while the bilayer approach with intermediate rates is preferred when this difference is large. In both proposed design strategies multi-edge-type density evolution is used for code optimization. The resulting MET-BE-LDPC codes exhibit improved threshold and bit-error-rate performance as compared to previously reported bilayer LDPC codes.

The Diversity-Multiplexing Tradeoff of the Dynamic Decode-and-Forward Protocol on a MIMO Half-Duplex Relay Channel

The diversity-multiplexing tradeoff of the dynamic decode-and-forward protocol is characterized for the half-duplex three-terminal (m, k, n)-relay channel where the source, relay and the destination terminals have m, k and n antennas, respectively. The tradeoff curve is obtained as a solution to a simple, two-variable, convex optimization problem which is explicitly solved in closed-form for certain special classes of relay channels, namely, the (1, k, 1) relay channel, the (n, 1, n) relay channel and the (2, k, 2) relay channel. Moreover, the tradeoff curves for a certain class of relay channels, such as the (m, k, n >; k) channels, are found to be identical to those for the decode-and-forward protocol for the full duplex channel while for other classes of channels they are marginally lower at high multiplexing gains. Our results also show that for some classes of relay channels and at low multiplexing gains the diversity orders of the dynamic decode-and-forward protocol are greater than those of the static compress-and-forward protocol which in turn is known to be tradeoff optimal over all static half duplex protocols. In general, the dynamic decode-and-forward protocol has a performance that is comparable to that of the static compress-and-forward protocol which, unlike the dynamic decode-and-forward protocol, requires global channel state information at the relay node. Its performance is also close to that of the decode-and-forward protocol over the full-duplex relay channel thereby indicating that the half-duplex constraint can be compensated for by the dynamic operation of the relay wherein the relay switches from the receive to the transmit mode based on the source-relay channel quality.

Lower Bounds on the Capacity of the Relay Channel with States at the Source

We consider a state-dependent three-terminal full-duplex relay channel with the channel states noncausally available at only the source, that is, neither at the relay nor at the destination. This model has application to cooperation over certain wireless channels with asymmetric cognition capabilities and cognitive interference relay channels. We establish lower bounds on the channel capacity for both discrete memoryless (DM) and Gaussian cases. For the DM case, the coding scheme for the lower bound uses techniques of rate-splitting at the source, decode-and-forward (DF) relaying, and a Gel'fand-Pinsker-like binning scheme. In this coding scheme, the relay decodes only partially the information sent by the source. Due to the rate-splitting, this lower bound is better than the one obtained by assuming that the relay decodes all the information from the source, that is, full-DF. For the Gaussian case, we consider channel models in which each of the relay node and the destination node experiences on its link an additive Gaussian outside interference. We first focus on the case in which the links to the relay and to the destination are corrupted by the same interference; and then we focus on the case of independent interferences. We also discuss a model with correlated interferences. For each of the first two models, we establish a lower bound on the channel capacity. The coding schemes for the lower bounds use techniques of dirty paper coding or carbon copying onto dirty paper, interference reduction at the source and decode-and-forward relaying. The results reveal that, by opposition to carbon copying onto dirty paper and its root Costa's initial dirty paper coding (DPC), it may be beneficial in our setup that the informed source uses a part of its power to partially cancel the effect of the interference so that the uninformed relay benefits from this cancellation, and so the source benefits in turn.