Multiple Amplify-and-forward Relays Research Articles

Capacity and outage performance of multiple AF relays based cooperative OFDM-QIM system

In this paper, we propose a multiple amplify-and-forward (AF) relays based cooperative orthogonal frequency division multiplexing (OFDM) with quadrature index modulation (C-OFDM-QIM) system to enhance the spectral efficiency and the transmission reliability, where two independent subcarrier subsets are activated to convey the real and imaginary symbol vectors, respectively, and the per-subcarrier relay selection (RS) scheme is adopted to select the relay with the maximum end-to-end signal-to-noise ratio (SNR) for each active subcarrier. Both fixed-gain AF and variable-gain AF protocols are investigated at the selected relays. Based on the order statistics and the max-flow min-cut theory, the closed-form average outage probability (AOP) and the average capacity are derived, respectively. Numerical results demonstrate that the theoretical AOP is correct and accurate and the proposed C-OFDM-QIM system outperforms the traditional cooperative OFDM with index modulation (C-OFDM-IM) system in the spectral efficiency, the outage performance, and the average capacity.

Analysis of SWIPT based dual-hop AF relay with SSK modulation over Nakagami-m fading channel

Space shift keying (SSK) modulation performance is analyzed with simultaneous wireless information and power transfer (SWIPT) based cooperative amplify-and-forward (AF) relaying system over the Nakagami-m fading channel. SWIPT technique can remove the need for power supply at the relays in cooperative communication. In contrast, SSK is a low complex index modulation technique that eliminates inter antenna synchronization, inter-channel interference and reduces the number of radiofrequency chains. Closed-form expression for average bit error probability (ABEP) is derived using a single AF relay with selection combining (SC) at the receiver, and an Upper bound ABEP expression is derived for multiple AF relays with the direct link (DL) from source to destination. The partial relay selection (PRS) technique has been proposed with energy harvesting (EH) to reduce the hardware complexity compared to the multiple relays. Numerical and computer simulation results are presented with the discussion. The result demonstrates that EH with SSK modulation can improve the system performance.

Secrecy Sum Rate Optimization in Nonorthogonal Multiple Access AF Relay Networks

In this paper, nonorthogonal multiple access (NOMA) technique is employed to an amplify-and-forward (AF) relay system, which consists of a source, a relay, several users, and an eavesdropper. We aim to maximize the achievable secrecy sum rate by jointly designing power allocation at the source and cooperative beamforming at the relay, under the achievable rate constraints at the weak users and the transmit power constraints at the source and the relay. The formulated optimization problem is nonconvex due to the coupled variables. We proposed to decouple the problem into two subproblems and solve power allocation and relay beamforming in an iterative manner. Simulation results demonstrate that the proposed NOMA AF network can achieve a higher achievable secrecy sum rate than the conventional orthogonal multiple access AF relay network.

Robust Transmission in Non-Orthogonal Multiple Access AF Relay Networks

As an emerging technique, non-orthogonal multiple access (NOMA), which has superior spectral efficiency, is expected to be widely used in future wireless networks. This letter is to study a robust sum rate optimization problem in a NOMA amplify-and-forward (AF) relay network, where the channel uncertainties are modeled by a worst-case model. Our goal is to maximize the worst-case sum rate by jointly designing power allocation and relay beamforming subject to the weak users’ quality of service requirements and the transmit power constraint at the relay. The proposed optimization problem is non-convex. To efficiently solve this problem, we employ the cutting-set method, which is an iterative algorithm. In each iterative step, we solve two subproblems, i.e., a joint relay beamforming and power allocation optimization problem for given channels, and a pessimization problem to determine the worst-case channel uncertainties with given relay beamforming and power allocation. Simulation results demonstrate the effectiveness of the proposed robust scheme for NOMA AF relay networks.

Joint Power Allocation and Relay Beamforming in Nonorthogonal Multiple Access Amplify-and-Forward Relay Networks

In this paper, we investigate joint power allocation and relay beamforming design problem for a nonorthogonal multiple access (NOMA) amplify-and-forward (AF) relay network, which employs successive interference cancellation to decode signals. Our objective is to maximize the achievable rate of the destination, which has the best channel condition subject to achievable rate constraints at other destinations and individual transmit power constraints. We propose an alternating optimization-based algorithm where, given power allocation, we transform the problem into a second-order cone programming and, given relay beamforming, we transform the problem into a convex linear-fractional programming. When the number of destinations is two, we propose a semidefinite programming-based one-dimensional search algorithm which achieves the globally optimal solution. Simulation results demonstrate that our proposed NOMA AF relay network outperforms the conventional orthogonal multiple access AF relay network.

Secure Multiple Amplify-and-Forward Relaying Over Correlated Fading Channels

This paper quantifies the impact of correlated fading on secure communication of multiple amplify-and-forward (AF) relaying networks. In such a network, the base station (BS) is equipped with multiple antennas and communicates with the destination through multiple AF relays, while the message from the relays can be overheard by an eavesdropper. We focus on the practical communication scenario, where the main and eavesdropper’s channels are correlated. In order to enhance the transmission security, transmit antenna selection is performed at the BS, and the best relay is chosen according to the full- or partial-relay selection criterion, which relies on the dual-hop relay channels or the second-hop relay channels, respectively. For these criteria, we study the impact of correlated fading on the network secrecy performance, by deriving an analytical approximation for the secrecy outage probability and an asymptotic expression for the high main-to-eavesdropper ratio. From these results, it is concluded that the channel correlation is always beneficial to the secrecy performance of full relay selection. However, it deteriorates the secrecy performance if partial-relay selection is used, when the number of antennas at the BS is less than the number of relays.

Space-Time Network Coding With Multiple AF Relays Over Nakagami- $m$ Fading Channels

This paper first analyzes the symbol error rate (SER) performance of the space-time network coding (STNC) over independent but not necessarily identically distributed (i.n.i.d) Nakagami- $m$ fading channels, where multiple sources transmit information symbols to a destination through multiple helping amplify-and-forward (AF) relays. The exact expressions of the overall end-to-end received signal-to-noise ratio (SNR) via multiple STNC-AF relays and its moment generating function (MGF) are derived. Based on these results, the closed-form expression of STNC-AF for the SER with $M$ -ary phase-shift keying and $M$ -ary quadrature-amplitude modulation (QAM) modulations are then presented by adopting the unified MGF method. Furthermore, an approximate SER expression with low computational complexity is also given. In order to observe the performance limit, the diversity order and the nonorthogonality of STNC codes are discussed. Simulation results demonstrate our analytical results and it is illustrated that the diversity order of the STNC with multiple AF relay nodes is a sum function of the fading index of the direct link and the minimal fading indices of the multiple two-hop links.

Physical Layer Authentication Enhancement Using Maximum SNR Ratio Based Cooperative AF Relaying

Physical layer authentication techniques developed in conventional macrocell wireless networks face challenges when applied in the future fifth-generation (5G) wireless communications, due to the deployment of dense small cells in a hierarchical network architecture. In this paper, we propose a novel physical layer authentication scheme by exploiting the advantages of amplify-and-forward (AF) cooperative relaying, which can increase the coverage and convergence of the heterogeneous networks. The essence of the proposed scheme is to select the best relay among multiple AF relays for cooperation between legitimate transmitter and intended receiver in the presence of a spoofer. To achieve this goal, two best relay selection schemes are developed by maximizing the signal-to-noise ratio (SNR) of the legitimate link to the spoofing link at the destination and relays, respectively. In the sequel, we derive closed-form expressions for the outage probabilities of the effective SNR ratios at the destination. With the help of the best relay, a new test statistic is developed for making an authentication decision, based on normalized channel difference between adjacent end-to-end channel estimates at the destination. The performance of the proposed authentication scheme is compared with that in a direct transmission in terms of outage and spoofing detection.

Adaptive modulation and coding for two‐way relaying with amplify‐and‐forward protocols

In this study, the authors introduce adaptive modulation and coding in a two-way amplify-and-forward (AF) relay network to improve the system performance. They consider a cooperative system where two user nodes exchange information with the assistance of multiple two-way AF relays. In the proposed scheme, the user nodes adaptively choose the appropriate modulation and coding scheme to ensure that the frame error rate (FER) satisfies the system requirement; all relays are utilised to forward the received signals to the user terminals. Furthermore, they provide a better approximation of the cumulative distribution function of the destination signal-to-noise ratio; and thus, derive more accurate expressions including average spectral efficiency and average FER in closed-form, over Rayleigh fading channels. The theoretical analysis is verified by numerical results.

Relay Selection Schemes and Performance Analysis Approximations for Two-Way Networks

This paper studies relay selection schemes for two-way amplify-and-forward (AF) relay networks. For a network with two users that exchange information via multiple AF relays, we first consider a single-relay selection (SRS) scheme based on the maximization of the worse signal-to-noise ratio (SNR) of the two end users. The cumulative distribution function (CDF) of the worse SNR of the two users and its approximations are obtained, based on which the block error rate (BLER), the diversity order, the outage probability, and the sum-rate of the two-way network are derived. Then, with the help of a relay ordering, a multiple-relay selection (MRS) scheme is developed. The training overhead and feedback requirement for the implementation of the relay selection schemes are discussed. Numerical and simulation results are provided to corroborate the analytical results.

On the SEP of Cooperative Diversity with Opportunistic Relaying

We analyze the exact symbol error probability (SEP) of cooperative diversity with opportunistic amplify-and-forward (AF) relaying. The benefit of this opportunism to the SEP is assessed by comparing with maximal ratio combining of orthogonal multiple AF relay transmissions.

A Low-Complexity LMMSE Channel Estimation Method for OFDM-Based Cooperative Diversity Systems with Multiple Amplify-and-Forward Relays

Orthogonal frequency division multiplexing- (OFDM-) based amplify-and-forward (AF) cooperative communication is an effective way for single-antenna systems to exploit the spatial diversity gains in frequency-selective fading channels, but the receiver usually requires the knowledge of the channel state information to recover the transmitted signals. In this paper, a training-sequences-aided linear minimum mean square error (LMMSE) channel estimation method is proposed for OFDM-based cooperative diversity systems with multiple AF relays over frequency-selective fading channels. The mean square error (MSE) bound on the proposed method is derived and the optimal training scheme with respect to this bound is also given. By exploiting the optimal training scheme, an optimal low-rank LMMSE channel estimator is introduced to reduce the computational complexity of the proposed method via singular value decomposition. Furthermore, the Chu sequence is employed as the training sequence to implement the optimal training scheme with easy realization at the source terminal and reduced computational complexity at the relay terminals. The performance of the proposed low-complexity channel estimation method and the superiority of the derived optimal training scheme are verified through simulation results.

Duality and Rate Optimization for Multiple Access and Broadcast Channels With Amplify-and-Forward Relays

In this paper, we consider multihop multiple access (MAC) and broadcast channels (BC) where communication takes place with the assistance of relays that amplify and forward (AF) their received signals. For a two-hop parallel AF relay MAC, assuming a sum power constraint across all relays we characterize optimal relay amplification factors and the resulting optimal rate regions. We find the maximum sum rate and the maximum rate for each user in closed form and express the optimal rate pair (R <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">1</sub> , R <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">2</sub> ) that maximizes mu <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">1</sub> R <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">1</sub> +mu <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">2</sub> R <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">2</sub> as the solution of a pair of simultaneous equations. We find that the parallel AF relay MAC with total transmit power of the two users P <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">1</sub> +P <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">2</sub> =P and total relay power P <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">R</sub> is the dual of the parallel AF relay BC where the MAC source nodes become the BC destination nodes, the MAC destination node becomes the BC source node, the dual BC source transmit power is P <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">R</sub> and the total transmit power of the AF relays is P. The duality means that the rate region of the AF relay MAC with a sum power constraint P on the transmitters is the same as that of the dual BC. The duality relationship is found to be useful in characterizing the rate region of the AF relay BC as the union of MAC rate regions. The duality is established for distributed multiple antenna AF relay nodes and multiple (more than 2) hops as well.