Leonardo Jiménez Rodríguez

Performance of Full-Duplex AF Relaying in the Presence of Residual Self-Interference

This paper investigates the error and diversity performances of full-duplex (FD) amplify-and-forward (AF) singlerelay systems under the effect of residual self-interference. The variance of this interference is assumed to be proportional to the λ-th power of the transmitted power (0 ≤ λ ≤ 1). The study considers the cooperative linear relaying protocol with direct source-destination link and the dual-hop scheme without direct link, both under uncoded and coded frameworks. At first, closed-form pairwise error probability expressions are derived for the uncoded systems, which are then used to obtain tight bounds to the bit error rate (BER) of the coded systems. To shed an insight on the diversity behavior, asymptotic expressions at high transmission powers are also presented. Different from previous works that treat the direct link as interference, this paper shows that FD linear relaying systems with a suitable precoder can attain the same diversity function as their half-duplex (HD) counterparts. However, further analysis shows that HD orthogonal AF using a superposition constellation is asymptotically optimal in terms of maximum coding gain. In addition, it is shown that the diversity of FD dual-hop systems is a decreasing function of λ and is equal to zero when λ = 1. Although HD relaying is asymptotically optimal under the considered protocols and interference model, illustrative results show that FD relaying is advantageous at practical BER levels when λ is sufficiently small.

Physical layer security in wireless cooperative relay networks: state of the art and beyond

Cooperative relaying is an effective method of increasing the range and reliability of wireless networks, and several relaying strategies have been adopted in major wireless standards. Recently, cooperative relaying has also been considered in the context of PHY security, which is a new security paradigm to supplement traditional cryptographic schemes that usually handle security at the upper layers. In wireless PHY security, relay nodes can be used to exploit the physical layer properties of wireless channels in order to support a secured transmission from a source to a destination in the presence of one or more eavesdroppers. While some breakthroughs have been made in this emerging research area, to date, the problem of how to effectively adopt advanced relaying protocols to enhance PHY security is still far from being fully understood. In this article, we present a comprehensive summary of current state-of-theart PHY security concepts in wireless relay networks. A case study is then provided to quantify the benefits of power allocation and relay location for enhanced security. We finally outline important future research directions in relaying topologies, full-duplex relaying, and cross-layer design that can ignite new interests and ideas on the topic.

Bandwidth-Efficient Bit-Interleaved Coded Modulation Over NAF Relay Channels: Error Performance and Precoder Design

This paper investigates the error performance and precoder design for a bandwidth-efficient bit-interleaved coded modulation (BICM) system over a nonorthogonal amplify-and-forward (NAF) half-duplex single-relay channel. A tight union bound on the asymptotic bit error probability (BEP) is first derived for an arbitrary block length of 2N, which corresponds to the case of using a 2N × 2N precoder. This bound provides a useful tool for predicting the error performance. Attention is then paid to the coded NAF system that uses a 2 × 2 precoder, where a closed-form expression of the bound is obtained. Based on this expression, an optimal class of 2 × 2 precoders with respect to the asymptotic performance is then developed. Unlike the optimal precoders that are designed for uncoded systems, the derived precoder indicates that the source only needs to send the superposition of the first symbol and the rotated version of the second symbol in the first time slot while being silent in the remaining slot to achieve the best asymptotic performance. For good convergence property, it is further shown that a rotation angle that maximizes the minimum Euclidean distance of the superposition constellation should be used. An optimal rotation angle is then analytically determined for various modulation schemes. Both analytical and simulation results show that the proposed precoders not only exploit full cooperative diversity but offer a significant coding gain over the optimal precoders for uncoded NAF systems as well.

Optimal Power Control and Error Performance for Full-Duplex Dual-Hop AF Relaying Under Residual Self-Interference

This paper investigates optimal power allocation schemes at the relay and their impact on the error performance for a full-duplex, dual-hop, amplify-and-forward system using finite constellations and under residual self-interference. The variance of the interference is assumed to be proportional to the λ-th power of the transmitted power. The worst-case pairwise error probability (PEP) is considered as the performance criterion. To find the optimal power allocation, we first derive a closed-form expression for the derivative of the PEP. A simple bisection method is then applied to obtain the optimal scheme. An asymptotically optimal allocation in closed form is also obtained assuming high power regions. From this analysis, it is shown that power allocation leads to a better diversity performance than full power transmission. In addition, the error floor behavior observed in previous works can be eliminated through power allocation. Numerical results are finally presented to illustrate the advantage of the proposed scheme over full power usage.

Achievable Rate and Power Allocation for Single-Relay AF Systems Over Rayleigh Fading Channels at High and Low SNRs

In this paper, we propose a general method to analyze the achievable rate and to characterize the optimal power-allocation (PA) scheme for a wide range of half-duplex single-relay amplify-and-forward (AF) protocols over Rayleigh fading channels in high and low signal-to-noise-ratio (SNR) regimes. These include one-way (OW) dual-hop AF (DHAF) systems, OW nonorthogonal AF (NAF) systems, and two-phase two-way AF (2P TWAF) systems using either fixed-gain (FG) or variable-gain (VG) amplification coefficients. At high-SNR regimes, our main idea is to exploit the capacity of a two-branch maximal-ratio combining (MRC) system to obtain tight yet simple approximations to the achievable rates. In low-SNR regions, we use a simple approximation to the logarithm to compute the asymptotic achievable rates. For all considered AF protocols, the closed-form approximations are tight and easy to analyze since they involve only the exponential integral. Then, using the derived approximations, we analytically quantify the asymptotic PA schemes among the nodes to achieve the maximum rate and the sum rate for OW and TW schemes, respectively. The OW and TW protocols of interest are finally compared with the direct transmission (DT) scheme. Although OW relaying is inferior in terms of capacity in high- and low-SNR regimes, the 2P TW system might become advantageous in terms of sum-rate performance at high SNRs under the right channel conditions.

Optimal Power Adaptation for Cooperative AF Relaying With Channel Side Information

In this paper, we develop optimal power adaptation schemes by means of power amplification coefficients at the relay for half-duplex single-relay amplify-and-forward (AF) cooperative systems with channel side information (CSI) available at the relay. We consider both the orthogonal AF (OAF) and the nonorthogonal AF (NAF) transmission protocols. In particular, assuming that the relay has full knowledge of the channel gains, optimal power adaptation schemes under a long-term average power constraint are established in closed form using the mutual information (MI) and pairwise error probability (PEP) criteria with Gaussian inputs at the source. The proposed solutions can be understood as multidimensional (multi-D) distributed water filling in time and space. Numerical results show that the proposed power amplification methods provide a significant improvement over conventional schemes using either channel distribution information (CDI) or channel inversion (CI). The gain is observed with regard to the MI with Gaussian inputs and the bit-error-rate (BER) performance using finite constellations for both coded and uncoded systems.

Secrecy capacity of the full-duplex AF relay wire-tap channel under residual self-interference

This paper studies a wire-tap channel in which a source node wants to communicate securely to a destination node in the presence of an eavesdropper and under the aid of an amplify-and-forward (AF) relay operating in full-duplex (FD) mode. The residual self-interference due to FD transmission is explicitly taken into account. The secrecy capacity and the respective optimal power allocation schemes for this system are examined under both individual and joint power constraints. At first, the related optimization problems are shown to be quasi-concave. As such, the globally optimal solution exists and is unique. Due to the non-linearity of the derivative, we apply a simple bisection method for root finding and obtain a simple expression for the optimal power allocation scheme. To further provide some insight on the solutions, we apply the method of dominant balance to analyze the capacity and power allocations in different high power regions. It is then demonstrated that full relay power is only needed when the power at the relay is sufficiently small compared to the power at the source. Comparisons with half-duplex (HD) relaying also revealed that FD can achieve a significantly higher secrecy capacity. Finally, numerical results are presented to confirm the optimality of the solutions.

Bandwidth-Efficient Bit-Interleaved Coded Modulation over NAF Relay Channels: Error Performance and Precoder Design

This paper investigates the error performance and precoder design for a bandwidth-efficient bit-interleaved coded modulation (BICM) system over a non-orthogonal amplify-and-forward (NAF)half-duplex single-relay channel. A tight union bound on the bit error probability (BEP) is first derived for an arbitrary block length of

Optimal power adaption for NAF relaying with channel side information

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Multiple-Frame Precoding for NAF Relaying Over Rayleigh Fading Channels

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