Multiple Relay Systems Research Articles

Examining the efficiency of D2D communication employing DF-enabled multiple relay systems amid co-channel interference

Device-to-device (D2D) communication is emerging as a potential paradigm in contemporary wireless communication systems. Enabling D2D communication in the mmWave range has numerous challenges that must be overcome. The biggest concern is the introduction of interference from several sources. This study investigates the impact of co-channel interference (CCI) on D2D communication when energy harvesting (EH) and decode-and-forward (DF) techniques are used across several relay nodes. It includes mathematical equations for the cumulative distribution function (CDF) of the Signal-to-Interference-Plus-Noise ratio (SINR), as well as formulas for calculating the network's outage probability (OP), throughput (TP), and availability rate (AR). Furthermore, it produces an asymptotic expression for analyzing the probability density function (PDF) of the instantaneous SINR, providing a simple and complete approach to understanding its OP, TP, and AR properties. The analytical results are supported by Monte Carlo simulations and MATLAB implementation.

On Covert Communication Performance in Multi-relay Systems with Outdated CSI

Communication performance significantly depends on the availability of Channel State Information (CSI). This paper investigates the impact of outdated CSI on achievable covert communication performance in a multiple-relay system under a power control scheme. Considering the feedback delay of all links, we first develop an accurate characterization of outdated CSI. Based on this, we formulate theoretical models to depict the inherent relationship between outdated CSI and fundamental covert performance metrics, namely detection error probability (DEP) and covert rate (CR). Utilizing these models, we delve into optimizing CR subject to the DEP constraint, unveiling the maximal CR performance achievable with outdated CSI. Extensive numerical results illustrate the impact of outdated CSI on covert communication performance, also indicating that an increase in the number of relays can mitigate the negative effects of outdated CSI.

Energy-Efficient Power Allocation in Non-Linear Energy Harvesting Multiple Relay Systems

In this paper, to maximize the energy efficiency (EE) in the two-hop multi-relay cooperative decoding and forwarding (DF) system for simultaneous wireless information and power transmission (SWIPT), an optimal power allocation algorithm is proposed, in which the relay energy harvesting (EH) adopts a nonlinear model. Under the constraints, including energy causality, the minimum transmission quality of information and the total transmission power at the relays, an optimization problem is constructed to jointly optimize the transmit power and power-splitting (PS) ratios of multiple relays. Although this problem is a nonlinear fractional programming problem, an iterative algorithm is developed to obtain the optimal power allocation. In particular, the joint power allocation at multiple relays is first decoupled into a single relay power allocation, and then single-relay power allocation is performed by the Dinkelbach iteration algorithm, which can be proven that it is a convex programming problem. Its closed form solutions for different polylines of EH models are obtained by using mathematical methods, such as monotonicity, Lagrange multipliers, the KKT condition and the Cardan formula. The simulation results show the superiority of the power allocation algorithm proposed in this paper in terms of EE.

Two-Timescale Hybrid Analog-Digital Beamforming for mmWave Full-Duplex MIMO Multiple-Relay Aided Systems

Due to the severe pathloss experienced by electromagnetic waves in the millimeter wave (mmWave) band, a substantial challenge in their design is to have an adequate coverage area. With the objective of improving the coverage area and the sum rate attained, we conceive new full-duplex (FD) mmWave multiple-input multiple-output (MIMO) multiple-relay systems. Specifically, we propose a novel two-timescale analog-digital hybrid beamforming scheme for maximizing the sum rate, while reducing the system's complexity and the channel state information (CSI) signalling overhead, as well as mitigating both the effects of self-interference and that of outdated CSIs caused by the associated delays. In the proposed scheme, the long-timescale analog beamforming matrices are designed based on the available channel statistics and updated in a frame-based manner, where a frame contains a fixed number of time slots. By contrast, the short-timescale digital beamforming matrices are optimized more frequently - namely for each time slot - based on the low-dimensional effective CSI matrices available on a real-time basis. We develop both an efficient analog beamforming algorithm based on the cut-set bound as well as on stochastic successive convex approximation (SSCA) and an innovative digital beamforming algorithm that relies on the theory of penalty dual decomposition (PDD), where our design objective is to maximize the system's sum rate. Both the convergence properties and the computational complexity of the proposed algorithms are also examined. Our simulation results show that the proposed two-timescale hybrid beamforming design significantly outperforms the conventional beamformers both in terms of requiring a lower CSI-signalling overhead and a higher sum rate in the face of realistic outdated CSIs.

Power Allocation for SWIPT in Full-Duplex AF Relay Interference Channels Using Game Theory

A full-duplex, amplify-and-forward multiple relay system employing simultaneous wireless information and power transfer receivers operating in interference channels is studied. Since all links want to maximize their own achievable rate, a power allocation problem under transmit power and energy harvesting constraints is developed. Through alternative optimization, a distributed iterative water-filling algorithm based on game theory with provable convergence is devised. The existence and uniqueness of a Nash equilibrium point are both guaranteed and the convergence of the proposed algorithm is examined using a diagonally strict concavity condition. Numerical results show that the proposed algorithm is convergent and can achieve a higher sum rate than previous schemes.

Decentralized WSEE Optimization for Massive MIMO Two-Way Half-Duplex AF Relaying

Design of energy-efficient wireless systems has recently attracted attention to reduce their carbon footprint. This paper optimizes non-convex weighted sum energy efficiency (WSEE) of a multi-pair two-way amplify-and-forward half-duplex massive multiple-input multiple output relay system. We optimize it by developing a two-layer decentralized successive convex approximation optimization framework. The first layer approximates the non-convex WSEE either as a generic convex program (GCP) or as a second order cone program (SOCP). The second layer decentrally solves the approximated problem using alternating direction method of multipliers. We show that the proposed iterative algorithm yields a Karush-Kuhn-Tucker point of the original WSEE problem. We numerically analyze the effect of weights on the energy efficiency (EE) of individual users, and show that the proposed framework enable us to meet the heterogeneous EE requirements. We also analytically and numerically show that the decentralized algorithm has lesser complexity than its centralized counterpart, but yields the same WSEE.

Precoding design for space-time codes and relay selection with a novel scheme for multiple relay systems

In this paper, we consider the joint design of precoding matrices at both the source and relay nodes in a multi-relay system based on perfect and imperfect channel information, and propose the novel relay selection scheme based on log-likelihood ratio (LLR). Moreover, the symbol error rate (SER) for relay selection system based on proposed scheme is analyzed. At first, we design the combined precoding matrices based on respectively the maximum signal-to-noise ratio (SNR) with perfect channel state information (CSI) and the minimum SER of the single-relay system with imperfect CSI. Using decomposition of matrices, the joint design problems are solved with a two-step method, i.e., the first step is to determine the optimal direction of the precoding matrices, and the second step is to transform the optimization problem into two kinds of independent sub-problems which can be solved in lower complexity. Then, different from traditional relay selection based on signal-to-noise ratio, the relay node with the maximum LLR is chosen. Simulation results show the proposed selection scheme based on LLR is superior to the scheme based on SNR in the SER performance. Furthermore, the multi-relay system using the precoding matrices joint space-time coding technology can improve SER performance of the system effectively compared with only space-time coding or only precoding system.

Influence of Relays Location and Propagation Environment on the BER of Multiple Relay Systems

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Outage Analysis and Power Allocation Optimization for Multiple Energy-Harvesting Relay System Using SWIPT

Energy harvesting (EH) combined with cooperative relying plays a promising role in future wireless communication systems. We consider a wireless multiple EH relay system. All relays are assumed to be EH nodes with simultaneous wireless and information transfer (SWIPT) capabilities, which means the relays are wirelessly powered by harvesting energy from the received signal. Each EH node separates the input RF signal into two parts which are, respectively, for EH and information transmission using the power splitting (PS) protocol. In this paper, a closed-form outage probability expression is derived for the cooperative relaying system based on the characteristic function of the system’s probability density function (PDF) with only one relay. With the approximation of the outage probability expression, three optimization problems are built to minimize the outage probability under different constraints. We use the Lagrange method and Karush–Kuhn–Tucker (KKT) condition to solve the optimization problems to jointly optimize the relay’s PS factors and the transmit power. Numerical results show that our derived expression of the outage probability is accuracy and gives insights into the effect of various system parameters on the performance of protocols. Meanwhile, compared with the no optimal condition, our proposed optimization algorithms can all offer superior performance under different system constraints.

Multi‐relay cooperative transmission based on rateless codes and adaptive demodulation

A rate adaption scheme is given at the receiver using rateless codes and log-likelihood ratio (LLR) threshold-based adaptive demodulation (ADM). The received bits with LLR absolute values higher than the preset threshold are demodulated by the receiver, otherwise, deleted. Through the theoretical analysis of the average mutual information (MI) of the demodulated bits, the method is obtained to calculate the LLR demodulation threshold under the required error performance after decoding and the constraint of codeword length for decoding. Then, the rate adaption scheme is applied in a parallel multiple relay wireless communication system. The LLR threshold is set according to the instantaneous SNR of the received signals in order to keep the average MI per demodulated bit of each relay link the same. The demodulated bits coming from all links are combined for decoding. The 256-QAM constellation and Raptor code are then considered as a special case to design a sample scheme. Simulation results prove the correctness of the theoretical analysis and the feasibility of the proposed scheme, and when it is employed by a multi-relay transmission system, the diversity gain can be obtained, and the anti-fading and the anti-jamming abilities of the system are promoted.

Optimal Power Splitting for Simultaneous Wireless Information and Power Transfer in Amplify-and-Forward Multiple-Relay Systems

In this paper, we investigate simultaneous wireless information and power transfer (SWIPT) amplify-and-forward relay systems, in which multiple relay nodes support communication between a source node and a destination node. Relay node transceivers are equipped with radio frequency energy harvesters for a power source to retransmit the signals from the source to the destination node. Both the power splitting (PS) ratio and adaptive power control are jointly optimized for SWIPT multiple-relay systems. We prove that the optimal power allocation strategy in our joint solution is to fully use the harvested power, which is contrary to conventional non-SWIPT multiple-relay systems. Based on this result, we propose an optimal centralized PS scheme and suboptimal distributed PS methods. Simulation results demonstrate that the proposed schemes outperform the naive PS schemes in terms of the average rate and the bit-error rate.

RF Energy Harvesting Based Multiple Access Relay Systems: A DMT Perspective

A multiple-access relay system, where the relay node is powered by radio frequency radiation is analyzed in this paper. Specifically, the focus is on the time-switching-based scheme in which the intermediate relay switches between the energy harvesting (EH), information decoding (ID), and the information re-transmission (TX). For this system, we have characterized the diversity-multiplexing trade-off (DMT) for two variants of the EH-based dynamic decode-and-forward (DDF) protocols: without feedback (EH-DDF) and with limited feedback (EH-DDF-LF). Analysis of the protocols reveals that the diversity gain of EH-DDF scheme is inferior to that of the traditional non-EH-based DDF protocol. Furthermore, the impact of energy harvesting duration on the DMT performance has been extensively investigated. Consequently, it is observed that the achievable diversity gain of the EH-DDF improves with the reduction in energy harvesting interval. However, there exists a performance difference between the classical non-EH-based DDF and EH-DDF even for the minute harvest duration. On the other hand, in the case of EH-DDF-LF, the performance approaches the diversity upper bound in the high multiplexing gain regime. Finally, a detailed comparison of the proposed EH-based schemes has been presented.

Resource allocation in multiple-relay systems exploiting opportunistic energy harvesting

Resource allocation in multiple-relay systems exploiting opportunistic energy harvesting

Power‐constrained, spectral efficiency‐optimal, green cooperative device‐to‐device communication systems

The author consider a relay-assisted, two hop, cooperative device-to-device (D2D) communication system where a source device S transmits data to a destination device D using a non-regenerative cooperative relay whose average transmit power is constrained. For the cooperative D2D system, the author consider the problem of optimally adapting the relay gain as a function of fading gains of S–R and R–D links to maximise fading-averaged spectral efficiency. The author derive the spectral efficiency-optimal relay gain adaptation policy (SERGAP), which determines optimal gain for the relay, and, analyse the fading-averaged spectral efficiency of SERGAP. To gain more insights, the author derive upper bounds on the average spectral efficiency, and, also investigate its asymptotic behaviour using an insightful analysis. Furthermore, the author extend the fading-averaged analysis to a system having multiple relays. The author also present numerical results for single relay and multiple relay systems and benchmark the proposed policy's performance with conventional and suboptimal relaying policies. The author show that SERGAP delivers higher average spectral efficiency than conventional relaying policies. Finally, spectral efficiency-optimal relay placement for the proposed policy is also investigated via simulations, and, the author find that it is different from the suboptimal relaying policies.

MIMO-STBC Based Multiple Relay Cooperative Communication Over Time-Selective Rayleigh Fading Links With Imperfect Channel Estimates

This paper analyzes the effect of time-selective fading arising due to node mobility and imperfect channel estimates on the end-to-end performance of multiple-input multiple-output space-time block coded multiple relay cooperative communication systems. Both dual-phase and multi-phase selective decode-and-forward relaying protocols are considered for the end-to-end communication in a multiple relay cooperative system, followed by presentation of complete analyses for the same. For each protocol, closed-form expressions are derived for the per-frame average pair-wise error probability and asymptotic error floor over independent and nonidentical time-selective Rayleigh fading links. A framework is also developed for obtaining the optimal source relay power factors for each of the above protocols, which significantly improve the end-to-end reliability of the system for a given power budget. It is shown that both the multirelay systems achieve the full diversity order (DO) when all the nodes are static and perfect channel estimates are available at each receiving node. The DO of the system reduces to that of the direct source–destination link for a scenario when only the relays are mobile. Interestingly, however, in other mobile scenarios, both the systems are limited by an asymptotic error floor with increasing signal to noise ratio. Further, the impact of DO of the source–relay and relay–destination links on the optimal source–relay power allocation is also explicitly demonstrated. Simulation results yield several important insights into the end-to-end error performance for different mobility conditions and also validate the derived analytical results.

Bidirectional AF Relaying With Underlay Spectrum Sharing in Cognitive Radio Networks

This paper investigates the impact of primary transmissions on the performance of a dual-hop bidirectional cognitive radio system. The secondary users (SUs) communicate with each other in an underlay mode with the assistance of amplify-and-forward (AF) relays in the presence of primary users (PUs). Depending on whether there exists interference at the secondary transceivers, originating from the primary transmissions, or there is a possibility of employing the best relay selection technique at the secondary side, two operating cases are considered for the secondary network (SN). For both cases, tight lower bounds on the outage probability (OP) and the average symbol error probability (SEP) are derived in closed form. Moreover, a novel and general closed-form expression for the bit error rate (BER) of $M$ -ary square quadrature amplitude modulation (QAM) for both single- and multiple-relay systems, under additive white Gaussian noise (AWGN) when Gray coded bit mapping is employed, is presented. In addition, we provide an upper bound and closed-form approximate expression for the ergodic capacity (EC). Numerical results provide important insights into the impact of system parameters on performance; for instance, it is demonstrated that, in both cases, under consideration of power constraints on the secondary nodes as dictated by the underlay mode of operation, the SN always achieves the full diversity order similar to the noncognitive counterpart.

Impact of Non-Linear High Power Amplifiers on Cooperative Relaying Systems

In this paper, we investigate the impact of the high-power amplifier non-linear distortion on multiple relay systems by introducing the soft envelope limiter, traveling wave tube amplifier, and solid-state power amplifier to the relays. The system employs amplify-and-forward either fixed or variable gain relaying and uses the opportunistic relay selection with outdated channel state information to select the best relay. The results show that the performance loss is small at low rates; however, it is significant for high rates. In particular, the outage probability and the bit error rate are saturated by an irreducible floor at high rates. The same analysis is pursued for the capacity and shows that it is saturated by a detrimental ceiling as the average signal-to-noise ratio becomes higher. This result contrasts the case of the ideal hardware where the capacity grows indefinitely. Moreover, the results show that the capacity ceiling is proportional to the impairment’s parameter and for some special cases the impaired systems practically operate in acceptable conditions. Closed-forms and high SNR asymptotes of the outage probability, the bit error rate, and the capacity are derived. Finally, analytical expressions are validated by the Monte Carlo simulation.

Co-channel interference cancellation using precoding for bi-direction multiple hops MIMO relay systems

In order to increase performance of a system while saving power consumption, multiple hop MIMO relay systems (MHMRSs) have been considered. There are many researches on the physical (PHY) layer, medium access control (MAC) layer, and MAC-PHY cross-layer to avoid a co-channel interference, such as the matched/orthogonal weight algorithm, TDMA-based smart antenna and so on. The matched/orthogonal algorithm is available for bi-directional communications; however, it requests at least three antenna elements at every relay. Consequently, it is unavailable for small wireless devices that are being demanded. In this paper, we propose an algorithm to cancel the co-channel interference of bi-directional communication MHMRSs by signal processing at receivers using precoding at transmitters. The proposal algorithm can perform with only two antenna elements while maintaining character of MIMO. The proposal algorithm is compared to the TDMA-based smart antenna algorithm which also can perform with two antenna elements, in both perfect and imperfect channel state information (CSI) schemes. Numerical calculation results indicate that a channel capacity of proposal algorithm is much higher than that of TDMA-based smart antenna algorithm in the perfect CSI scheme due to complete cancellation of co-channel interference and viability of bi-directional communications of proposal algorithm. In the imperfect CSI scheme, the channel capacity of the TDMA-based smart antenna algorithm is more robust when channel estimation errors increase; however, the channel capacity of proposal algorithm is still higher when the channel estimation error is large.

A Linear Combining Scheme to Suppress Interference in Multiple Relay Systems

A Linear Combining Scheme to Suppress Interference in Multiple Relay Systems

Performance Analysis of OFDM-Based Nonlinear AF Multiple-Relay Systems

We derive closed-form expressions of outage probability with asymptotic analysis for orthogonal frequency division multiplexing-based nonlinear amplify-and-forward multiple-relay systems using best-relay selection over independent and non-identically distributed Nakagami- ${m}$ fading channels for integer values of fading parameter. We then investigate a novel closed-form expression of average symbol error rate for a general order rectangular quadrature amplitude modulation scheme by using the well-known cumulative distribution function-based approach. Numerically evaluated results are compared with Monte Carlo simulations and the accuracy of the derived expressions is verified.