Amplify-and-forward Relay Networks Research Articles

End-to-End Learning-Based Framework for Amplify-and-Forward Relay Networks

We study end-to-end learning-based frameworks for amplify-and-forward (AF) relay networks, with and without the channel state information (CSI) knowledge. The designed framework resembles an autoencoder (AE) where all the components of the neural network (NN)-based source and destination nodes are optimized together in an end-to-end manner, and the signal transmission takes place with an AF relay node. Unlike the literature that employs an NN-based relay node with full CSI knowledge, we consider a conventional relay node that only amplifies the received signal using CSI gains. Without the CSI knowledge, we employ power normalization-based amplification that normalizes the transmission power of each block of symbols. We propose and compare symbol-wise and bit-wise AE frameworks by minimizing categorical and binary cross-entropy loss that maximizes the symbol-wise and bit-wise mutual information (MI), respectively. We determine the estimated MI and examine the convergence of both AE frameworks with signal-to-noise ratio (SNR). For both these AE frameworks, we design coded modulation and differential coded modulation, depending upon the availability of CSI at the destination node, that obtains symbols in 2n-dimensions, where n is the block length. To explain the properties of the 2n-dimensional designs, we utilize various metrics like minimum Euclidean distance, normalized second-order and fourth-order moments, and constellation figures of merit. We show that both these AE frameworks obtain similar spherical coded-modulation designs in 2n-dimensions, and bit-wise AE that inherently obtains the optimal bit-labeling outperforms symbol-wise AE (with faster convergence under low SNR) and the conventional AF relay network with a considerable SNR margin.

On the Performance Analysis of Higher Order QAM Schemes Over Mixed RF/FSO Systems

In this work, the performance of a dual-hop variable gain amplify-and-forward (AF) mixed radio frequency (RF)/free space optics (FSO) system is analyzed in details. As variable gain AF relay network is considered, processing delay results in outdated channel state information (CSI) during amplification at the relay. For general applicability, the RF link is modeled with the generalized Nakagami-m fading. The FSO link is modeled with the Gamma-Gamma distribution which is affected with the atmospheric turbulence and pointing error impairments, and both the intensity modulation with direct detection (IM/DD) and heterodyne detection are employed at the FSO receiver. In this context, analytical expressions of outage probability and ergodic capacity are derived in terms of Meijer-G function and extended generalized bivariate Meijer-G function. For diversity order, asymptotic outage probability expression is also derived. Further, cumulative distribution function based generalized average symbol error rate expressions for various quadrature amplitude modulation (QAM) schemes such as hexagonal QAM, rectangular QAM, and cross QAM are derived in terms of Meijer-G function. Furthermore, a detailed comparative study of various modulation schemes is presented and the impact of pointing error, atmospheric turbulence, outdated CSI, and Nakagami-m parameter are highlighted on the system performance. Finally, all the analytical results are verified through Monte-Carlo simulations.

Second-Order Statistics of MRC Reception With a Transparent Amplify-and-Forward Relay

Achievable spatial diversity supported by a single transparent amplify-and-forward (AF) relay relies on disintegrated channel state information (CSI) that can be acquired at the destination. This paper studies the impact of the quantization of the source-relay (SR) CSI in terms of the first- and second-order statistics of maximal-ratio combining (MRC) reception with the incomplete SR CSI at the destination. Probability density functions (PDFs) of the upper and lower bounds of the signal-to-noise ratio (SNR) achieved at the destination are derived. Corresponding level-crossing rate (LCR) and average fade-duration (AFD), which are undoubtedly required to choose parameters of forward error correcting (FEC) mechanisms across the transparent AF relay network, are evaluated via Monte Carlo simulations. The simulations show that the SNR PDF, LCR and AFD highly depends not only on the accuracy of SR CSI at the destination but also on the location of the AF relay.

Joint Power Splitting and Relay Selection in Energy-Harvesting Communications for IoT Networks

In this paper, we consider an energy-harvesting (EH) relay system consisting of a source, a destination, and multiple EH decode-and-forward (DF) relays that can harvest the energy from their received radio signals. A power-splitting ratio is employed at an EH DF relay to characterize a trade-off between an energy used for decoding the source signal received at the relay and the remaining energy harvested for retransmitting the decode outcome. We propose an optimal power splitting and relay selection (OPS-RS) framework and also consider the conventional equal power splitting and relay selection (EPS-RS) for comparison purposes. We derive closed-form expressions of outage probability for both the OPS-RS and EPS-RS schemes and characterize their diversity gains through an asymptotic outage analysis in the high signal-to-noise ratio region. We further examine an extension of our OPS-RS framework to an energy-harvesting battery (EHB) enabled cooperative relay scenario, where the EH relays are equipped with batteries used to store their harvested energies. We propose an amplify-and-forward (AF) based EHB-OPS-RS and a DF based EHB-OPS-RS schemes for AF and DF relay networks, respectively. Numerical results show that the proposed OPS-RS always outperforms the EPS-RS in terms of outage probability. Moreover, the outage probabilities of AF and DF based EHB-OPS-RS schemes are much smaller than that of OPS-RS and EPS-RS methods, demonstrating the benefit of exploiting the batteries in EH relays. Additionally, the DF based EHB-OPS-RS substantially outperforms the AF based EHB-OPS-RS and such an outage advantage becomes more significant, as the number of EH relays increases.

Physical layer security based on NOMA and AJ for MISOSE channels with an untrusted relay

Physical layer security based on non-orthogonal multiple access (NOMA) and artificial jamming (AJ) is considered in a one-way amplify-and-forward (AF) relay network with an untrusted relay. In the first phase of the two-phase operation of the untrusted AF relay network, a source node transmits the first information and AJ symbols, and the destination decodes the AJ symbol first and waits for the relayed replica of the first information symbol, which is forwarded by the untrusted relay. In the second phase, the source sends the second information symbol and the relay amplifies and forwards the received signal in the first phase with a fixed gain. In such an operation scenario, an untrusted relay tries to eavesdrop on the information signal while relaying the received signal properly. To decode the information symbol, the destination cancels out the AJ signal and then decodes the first information symbol by combining the signals received during the two phases. Finally, the second information symbol is decoded with the second-phase signal after cancelling out all the other symbols, i.e., the first information and AJ symbols. The eavesdropper and relay try to eavesdrop on the information signal with all possible orders of interference cancellation, i.e., NOMA receive processing. In this study, an ergodic secrecy rate is derived according to the operation scenario during the two phases. The behaviours of the ergodic secrecy rate with respect to power allocation to two information symbols as well as an AJ symbol are investigated. It is shown that the expected secrecy rate can be maximized by selecting the transmit power and rates for the three symbols properly. It is also demonstrated that the proposed physical layer security scheme achieves a higher secrecy rate than a secure beamformed transmission based on NOMA and artificial noise.

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.

Multi-User AF Relay Networks with Power Allocation and Transfer: A Joint Approach

The Internet-of-Things (IoT) framework has been considered as an enabler of the smart world where all devices will be deployed with extra-sensory power in order to sense the world as well as communicate with other sensor nodes. As a result, smart devices require more energy. Therefore, energy harvesting (EH) and wireless power transfer (WPT) emerge as a remedy for relieving the battery limitations of wireless devices. In this work, we consider a multi-user amplify-and-forward (AF)-assisted network, wherein multiple source nodes communicate with destination nodes with the help of a relay node. All the source nodes and the relay node have the capability of EH. In addition, to cope with a single point of failure i.e., failure of the relay node due to the lack of transmit power, we consider the WPT from the source nodes to the relay node. For WPT, a dedicated energy control channel is utilized by the source nodes. To maximize the sum rate using a deadline, we adopt a joint approach of power allocation and WPT and formulate an optimization problem under the constraints of the battery as well as energy causality. The formulated problem is non-convex and intractable. In order to make the problem solvable, we utilize a successive convex approximation method. Furthermore, an iterative algorithm based on the dual decomposition technique is investigated to get the optimal power allocation and transfer. Numerical examples are used to illustrate the performance of the proposed iterative algorithm.

Time-Switching EH-Based Joint Relay Selection and Resource Allocation Algorithms for Multi-User Multi-Carrier AF Relay Networks

In this paper, an energy efficiency maximization (EEM) optimization problem for the multi-user multi-carrier energy-constrained amplify-and-forward (AF) multi-relay network is formulated under the total source transmit power budget and energy-causality constraints. We consider that each relay node is solely powered by the source nodes, employing energy harvesting time-switching (EHTS) protocol to harvest the energy through the ambient radio-frequency (RF) signal transmitted from the source nodes under the simultaneous wireless information and power transfer (SWIPT) paradigm. First, we propose a subcarrier and energy causality-based multi-relay selection policy. Second, we jointly optimize the parameters that control the energy efficiency (EE) of the system namely multi-relay selection, subcarrier pairing, user allocation, power allocation, and RF EHTS time block, that renders the problem to be a mixed integer non-linear programming problem (MINLP) which remains NP-hard to solve. Hence, we remodel the problem to a tractable quasi-concave form by applying a string of convex transformations. Later, we propose an iterative EEM algorithm to optimize the multi-parameter problem. Further, a suboptimal and best relay selection algorithm is studied by trading-off between complexity and performance. The effectiveness of the proposed algorithms is demonstrated by simulation results.

Delay constrained throughput optimization in multi-hop AF relay networks, using limited quantized CSI

In this paper, we analyze the throughput of multi-hop amplify and forward (AF) relay networks in delay-constrained scenario. Using quantized channel state information (CSI), the transmission rates and powers are discretely adapted with individual average power constraint on each node. A sub-gradient projection-based algorithm is utilized, by which there is no need for probability density functions (PDFs) to solve the optimization problem. Our numerical evaluations show that the sub-gradient projection-based algorithm results in a comparable performance with an analytical approach using PDFs. As shown, a considerably better performance obtained by the designed scheme compared to previous schemes with constant power transmission. More than 70% throughput improvement is achieved by our scheme compared to constant power transmission with just two more feedback bits and a short training time required at the beginning of the transmission.

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.

Precoding Design for Correlated MIMO-AF Relay Networks With Statistical Channel State Information

An iterative precoding design of a two-hop amplify-and-forward (AF) multiple-input multiple-output relay network with one source, multiple relays, and one destination is presented. To provide a solution for general scenarios, the source-to-destination direct link and double correlated Kronecker Rician fading channels are considered. Statistical channel state information is used for the average capacity formulation for the sake of its robustness and infrequent update. The source and relay precoders are optimized to maximize a closed-form upper bound of the average capacity giving a suboptimal design. The non-convex design problem is divided into three sub-problems: source precoder, relay beamforming, and relay power allocation (PA). For optimizing the source precoder subject to multiple power constraints, rather than using computationally expensive penalty type algorithms, an efficient design procedure as a type of water-filling with multiple water levels is developed. Its negative PA is handled by a simple method of determining the eigen-modes of positive power. Using the Riemannian steepest descent method and a newly proposed power adaptation to optimize the relay beamforming and relay PA, respectively, the constrained optimization problems become unconstrained. Simulations show that the developed design procedure with trivial initialization provides nearly global optimum performance with fast convergence and efficient computation. The developed methods for the source precoder and relay PA outperform upon the augmented Lagrangian method with respect to convergence and computing time. Furthermore, the generality of the proposed scheme makes the design procedure applicable to AF relay networks with different simplified Kronecker channel models and with/without the direct link.

Secure Communication for Amplify-and-Forward Relay Networks With Finite Alphabet Input

This paper considers secure communication for amplify-and-forward (AF) relay networks with finite alphabet input. The joint optimization of power selection and beamforming design for improving the physical layer security of AF relay networks with single and multiple eavesdroppers is investigated. For the case with one eavesdropper, we transform the problem of multi-variable beamforming design into a single-variable optimization problem through semi-definite programming and solve it with one-dimensional optimization techniques. Moreover, the corresponding source power is obtained by utilizing the relation between the mutual information and minimum mean square error. Then, an iterative two-step algorithm is proposed to maximize the achievable secrecy rate. In the presence of multiple eavesdroppers, a zero-forcing beamforming scheme, where the confidential signal is nulled out in the direction of all eavesdroppers, is proposed to enhance the physical layer security. We decouple the source power and the beamforming vector by transforming the achievable secrecy rate into a single-variable function of the source power. Then, the suboptimal source power and the corresponding beamforming vector with low-complexity are derived. Numerical examples show that the proposed schemes significantly enhance the secrecy performance of the AF relay networks.

A novel enhanced bat optimization based energy efficiency and imperfect channel state information in cooperative MIMO‐AF systems

SummaryEnergy Efficiency (EE) is a vital design standard for the future generation of communication systems. Similarly, cooperative communication is extremely efficient for improving the performance of such systems. Current research presents a relay precoding optimization algorithm in order to resolve EE problem in the Multiple‐Input‐Multiple‐Output (MIMO) Amplify‐And‐Forward (AF) Relay Networks containing correct Channel State Information (CSI) only. With the intension of focus on imperfect, this work presents a novel design of MIMO AF Relay Networks under Imperfect CSI (ICSI) by taking Channel Estimation (CE) errors and feedback delay errors, deprived of taking the straight link from source to destination. For this reason, we present a Hidden Semi Markov Model (HSMM) under ICSI, in which the source and destination based relay links are identified through destination. After that, we implement an Enhanced Bat Optimization (EBO) algorithm to enhance the EE of MIMO relay‐based non‐regenerative cooperative communication systems by means of improving the source and relay precoders by taking relay and direct links into consideration. Simulation outcomes prove that the EE‐ EBO optimization is capable of enhancing the outcomes of MIMO‐AF systems while matched up with direct/relay link with EE precoding optimization and precoding optimization algorithms.

Cognitive AF Relay Networks over Asymmetric Shadowing/Fading Channels in the Presence of Low-Rate Feedback

DOI: 10.26650/electrica.2018.65047 This study investigates the performance of a cognitive amplify-and-forward (AF) relay network over composite asymmetric multipath/shadowing fading channels, whereby a new power allocation method is adopted at the secondary source and relay, assuming the mean-value interference channel. To quantify the performance of the proposed structure, closed-form outage probability and ergodic capacity expressions are derived. Moreover, asymptotic ergodic capacity analysis is performed to observe the effects of limited feedback and fading/shadowing severity in the system. The analytical results are validated with Monte-Carlo simulations, and they show that the proposed structure can be a realistic scenario for next-generation wireless systems, and a system designer can test the overall performance of the proposed system without dealing with complex prototypes.

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.

An Improved Variational Inference Approach to Iterative OFDM Receiver Design for Superimposed Training-Based AF Relay Networks

Using variational Bayesian approximation (VBA), we propose a general framework for joint channel estimation, demodulation, and decoding in an orthogonal frequency-division multiplexing (OFDM) amplify-and-forward (AF) relay network. AF relaying is adopted due to its simplicity and ease of implementation, and both cases of fixed- and variable-gain AF protocols are addressed. Unlike the classical approach where a number of subcarriers are solely dedicated to pilots, partial data-dependent superimposed training is considered here, which preserves the spectral efficiency. Assuming a bit-interleaved coded modulation OFDM system at the source, a modified formulation of VBA is proposed, which is, in fact, a Bayesian framework of turbo data detection of OFDM under channel estimation errors. More precisely, by an appropriate exploitation of the inherent “soft” information on channel and data available from the VBA formalism, we derive a modified iterative receiver, which reduces the impact of channel uncertainty by averaging the “soft data decision” over the posterior distribution of the unknown channel at each decoding iteration. The proposed modified VBA approach is contrasted to the conventional VBA and to the mismatched VBA approach, where, in the latter, the unknown channel is just replaced by its imperfect estimate. We show that conventional and mismatched VBA are suboptimal and can be viewed as a particular case of the proposed VBA method. In addition, we show that the VBA approach makes a nice connection between the classical techniques such as pilot-only channel estimation and the expectation–maximization algorithm, which can be viewed as a special case of VBA. By comparison with state-of-the-art VBA-based estimators through numerical analysis, we highlight the superiority of our modified VBA method and demonstrate a notable performance improvement in terms of the bit error rate.

Optimal beamforming for dual‐hop MIMO AF relay networks with imperfect CSI

In this study, the authors take into account the imperfect channel state information for beamforming (BF) scheme in a dual-hop multiple-input multiple-output (MIMO) amplify-and-forward (AF) relay network. Since the overall performance has been decided by the signal-to-interference-plus-noise ratio (SINR) at the destination, the authors derive the optimal BF weights that maximise the SINR at the desination. To evaluate the performance of the relay network, the authors also derive closed-form expressions for the outage probability and probability density function of the received SINR. Computer simulations are carried out, which show the superiority of the designed optimal BF scheme, the impacts of channel errors and antenna configurations on the performance of the MIMO AF relay systems, and the validity of the analytical expressions. It is shown that due to the channel errors, the performance of the relay network is bounded no matter how much power is injected into the system.

Dynamic Power Splitting Strategy for SWIPT Based Two‐Way Multiplicative AF Relay Networks with Nonlinear Energy Harvesting Model

This paper investigates an energy‐constrained two‐way multiplicative amplify‐and‐forward (AF) relay network, where a practical nonlinear energy harvesting (NLEH) model is equipped at the relay to realize simultaneous wireless information and power transfer (SWIPT). We focus on the design of dynamic power splitting (DPS) strategy, in which the PS ratio is able to adjust itself according to the instantaneous channel state information (CSI). Specifically, we first formulate an optimization problem to maximize the outage throughput, subject to the NLEH. Since this formulated problem is nonconvex and difficult to solve, we further transfer it into an equivalent problem and develop a Dinkelbach iterative method to obtain the corresponding solution. Numerical results are given to verify the quick convergence of the proposed iterative method and show the superior outage throughput of the designed DPS strategy by comparing with two peer strategies designed for the linear energy harvesting (LEH) model.

On the Optimal Power Allocation for Two-Way Full-Duplex AF Relay Networks

This paper investigates the optimal power allocation that maximizes the system utility for a full-duplex (FD) amplify-and-forward (AF) two-way relay network (TWRN) with a rate outage and a power constraint. Both cases of an individual and a sum power constraint are considered. To formulate the corresponding optimization problem, closed-form expressions of outage probabilities are needed. With FD transceivers, the derivation of such closed-form expressions become too involved. Thus, approximate closed-form expressions were derived instead. The resulting optimization problem is still nonconvex and difficult to solve. Via solving a series of approximate convex problems, a successive convex approximation (SCA) algorithm was proposed. Our simulation results demonstrate the accuracy of the approximate closed-form expressions of outage probabilities and that the proposed SCA algorithm achieves near-optimal performance and significantly outperforms the full power allocation under the individual power constraint and uniform power allocation under the sum power constraint both in system utility and in power consumption. Our results further show that simultaneous power transmission for all relay nodes with judicious power allocation generated by the SCA algorithm achieves $174\%$ of performance gain under the individual power constraint, and $85 \%$ of performance gain under the sum power constraint over the relay selection scheme. A tradeoff between the FD system and the half-duplex (HD) system with respect to the residual interference was also observed. We can also observe that not only the residual self-interference but also the cross-link interference is a factor that degrades the system performance for an FD system.

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.