Amplify-and-forward Relay Research Articles

Performance Analysis of Dual-Hop MIMO AF Relaying Network With Multiple Interferences

In this paper, we investigate the performance of a dual-hop multiple-input–multiple-output (MIMO) amplify-and-forward (AF) relay network, where the source, relay, and destination are all equipped with multiple antennas. By using maximum ratio transmission (MRT) at the transmitter and maximum ratio combining (MRC) at the receiver, we first obtain the output signal-to-interference-plus-noise ratio (SINR) of the dual-hop AF relay system, considering multiple cochannel interferences (CCIs), as well as noise at the relay. Then, we derive an exact closed-form expression for the outage probability (OP), and the asymptotic result of OP at high SNR, which can be used to calculate the array gain and diversity order. Finally, computer simulations are conducted to validate the performance analysis. Our new analytical expressions not only provide a fast and efficient method to evaluate the system performance but enable us to gain valuable insights into the effects of key parameters on the MIMO AF relaying network performance that benefits from implementing multiple antennas at each of the three nodes as well.

Approximation of Multi-Hop Relay to Dual-Hop Relay and Its Error Performance Analysis

In this letter, we develop a novel analytical framework in order to derive average symbol error rate (ASER) as a tractable form in multi-hop amplify-and-forward (AF) relay systems with cooperative diversity. In the proposed analytical approach, we modify multi-hop relay systems to dual-hop schemes over Rayleigh fading channels. The received signal in the $l$ th relay can be expressed as a single signal from the source, and the probability density function (pdf) of its signal-to-noise ratio (SNR) can be equivalently modeled as a summation of the pdfs of the SNRs among the source and $(l-1)$ relays. Based on this, the ASERs are then analyzed as approximated bounds, which are verified by comparison with simulation results. The derived ASER expressions show that the diversity order of multi-hop AF relay systems with $L$ relays is $(L+1)$ , which is identical to that of dual-hop systems.

Destination Assisted Jamming and Beamforming for Improving the Security of AF Relay Systems

In this paper, we propose a destination-assisted jamming and beamforming (DAJB) scheme for physical layer security in a one-way cooperative amplify-and-forward (AF) relay communication system. The system model consists of one source, one destination, one eavesdropper, and N relay nodes, with the individual power constraint of each relay node and the destination-assisted jamming node as well as unknown instantaneous channel state information (CSI) of the eavesdropper. Due to the half-duplex constraint of the relay nodes, there are two phases in our proposed DAJB scheme. In the first phase, the source node broadcasts information signal and all N relay nodes listen simultaneously. In the meantime, the destination node transmits the jamming signal to confuse the potential eavesdropper. In the second phase, all N relay nodes amplify and forward the received signals, covered by the artificial noise (AN), to the destination using the distributed beamforming technology. The optimal beamformer weights and power allocation are obtained by solving the second-order convex cone programming (SOCP) together with a linear programming (LP) problem. Furthermore, the performance of the DAJB scheme is analyzed in terms of the achievable secrecy rate. Compared with the scheme that selects a relay node as the jammer, we obtain larger power gain to achieve higher secrecy rates. Finally, the simulation results verify that the DAJB scheme greatly improves the secrecy rate of a one-way cooperative AF relay communication system.

Beamforming for Dual-Hop MIMO AF Relay Networks With Channel Estimation Error and Feedback Delay

This paper concerns the beamforming (BF) design for a dual-hop multiple-input multiple-output (MIMO) amplify-and-forward (AF) relay network. Both a general antenna configuration and imperfect channel state information are taking into consideration, where multiple antennas are deployed at the source, relay, and destination, channel impairments exist at the source-relay and relay-destination hops. The BF scheme is optimized to maximize the received signal-to-noise ratio (SNR). In order to evaluate the performance of the relay network, asymptotic average symbol error rate (ASER) at high SNR is derived. Computer simulations are conducted to show the superiority of the designed BF scheme and the impacts of channel impairments and antenna configurations on the performance of the MIMO AF relay systems. It is shown that the diversity order of the relay network can be reduced to one due to the channel impairments.

Transceiver Optimization for Two-Hop MIMO Relay Systems With Direct Link and MSE Constraints

In this paper, we investigate the transceiver design in a two-hop amplify-and-forward (AF) multiple-input multiple-output (MIMO) relay system with the direct link and quality-of-service (QoS) constraint. The QoS criterion is specified by the upper bound of the mean-squared error of the signal waveform estimation at the destination node. To minimize the total system transmission power, we apply a new AF relay protocol where the source node transmits signals during both time slots. Two iterative algorithms are proposed to jointly optimize the source and relay precoding matrices for the general case with multiple concurrent data streams, and the special case where a single data stream is transmitted, respectively. Simulation results show the effectiveness of both proposed algorithms. Interestingly, for the single data stream case, the second algorithm converges faster than the first algorithm. Compared with conventional two-hop MIMO relay systems where the source node is silent at the second time slot, the new protocol reduces the system transmission power. Under a given system transmission power, the proposed algorithms yield a higher system mutual information thanks to a better utilization of the direct link. Simulation results in this paper shed lights on some fundamental questions in relay system design such as when direct communication between source and destination (without any relay nodes) is optimal, and when the new AF relay protocol provides a larger gain compared with the conventional single phase source power allocation.

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.

ROC Analysis of BLM Detector in AF Relays Based Cooperative Wireless Networks

In this paper, receiver operating characteristics (ROC) of Bayesian linear model (BLM) detector in amplify and forward (AF) relays network is investigated. Cooperative communication with relay strategy is considered in this paper for its role of mitigating channel impairments such as multipath fading effects, shadowing, etc. Even though, the problem of channel impairments can be addressed, signal detection is still needed at the receiver for recovering the original transmitted signal from noise and other interference signals. Therefore, BLM detector is proposed for the sake of improving the signal detection performance at the receiver and to reduce the implementation complexity of the system. Performance analysis of the considered system is analyzed in terms of ROC (probability of detection against the probability of false alarm). Simulation results showed that the proposed method is effective and can improve the detection performance in AF based multiple relays networks.

Channel capacity analysis of a mixed dual‐hop radio‐frequency–free space optical transmission system with Málaga distribution

In this study, the channel capacity performance of a dual-hop asymmetric radio-frequency–free space optical (RF–FSO) communication system in the presence of pointing errors is presented. Here, both fixed-gain amplify and forward (AF) and decode and forward (DF) relays are considered. The RF link experiences Rayleigh fading and the FSO link experiences Malaga distributed turbulence channel. For this mixed RF–FSO cooperative system, novel mathematical expressions for cumulative distributive function (CDF) and the channel capacity are derived and performance is analysed with both fixed-gain AF and DF relays in the presence of pointing errors. In addition, the authors derive the asymptotic expressions for the CDF and the channel capacity derived earlier in terms of Meijer's G function in the high signal-to-noise ratio regime.

Amplify-and-Forward Relay Networks With Variable-Length Limited Feedback

We study the channel quantization problem for amplify-and-forward (AF) relay networks and our target is to design a quantizer to minimize the outage probability. It is priorly known that any fixed-length quantizer with a finite-cardinality codebook cannot attain the same minimum outage probability as the case where all nodes in the AF relay networks have access to perfect channel state information (CSI). We propose variable-length quantizers with random infinite-cardinality codebooks for the sum and individual power constraints. We provide theoretical proofs and numerical simulations to validate that the proposed quantizers can achieve the full-CSI outage probabilities with finite average feedback rates.

Asymptotic Capacity Analysis of Large-Scale MIMO AF Relay Networks in a Composite Fading Environment

Large-scale multiple-input–multiple-output (MIMO) networks, together with relay technology, have received considerable attention due to their remarkable capacity potential. Nevertheless, the majority of recent research studies on the asymptotic capacity of large-scale MIMO amplify-and-forward (AF) relay networks are limited to a fundamental assumption of small-scale fading, where the effect of large-scale fading, including shadow fading and path loss, is ignored. Motivated by this observation, in this paper, we present an extended model for the asymptotic capacity analysis in a composite fading environment, where Rayleigh fading, shadow fading, and path loss effect are incorporated altogether. Moreover, a realistic relay distribution is considered for real-world application of our capacity analysis. The proposed model consists of one source and one destination that are both equipped with $M$ antennas, which communicate through $K$ relays, each having $N$ antennas. We first employ random matrix theory to derive the empirical cumulative distribution of the channel covariance matrix and analyze the asymptotic capacity per source–destination antenna pair as both $M$ and $NK$ tend to infinity, but their ratio remains as a constant. We then consider the asymptotic capacity under two asymptotic cases for a finite and an infinite number of relays, respectively. It is shown through both theoretical analysis and Monte Carlo simulations that increasing the shadowing standard deviation can improve asymptotic capacity, whereas increasing the path loss exponent would lead to a capacity reduction. Our simulation results also reveal the effects of the relay distribution, as well as the source and relay transmission powers, on the asymptotic capacity.

Energy‐efficient cooperative two‐hop amplify‐and‐forward relay protocol in cognitive radio networks

It has been shown that amplify-and-forward (AF) transmission is a viable transmission protocol for wireless networks incorporating distributed spatial diversity. However, a drawback of this relatively simple protocol is identified, the destination node is only to combine a part of the signal, while the other part of the signal has been regarded as interference for delay, leading to the lower utilisation of the resource inevitably, which manifests in the bigger noise, lower signal-to-noise ratio, and higher bit error rate. A revised AF relay protocol has been proposed for it could fully combine signal and eliminate delay at destination node through caching signal. A multi-user single-relay transmission model could demonstrate the superior performance of this protocol, which is in a hotspots region of a cognitive radio network. The closed-form solution of the channel transmission rate is obtained with the form of matrix multiplication, and it can ensure that even if without any interference cancellation operation it still can improve the transmission rate. Analytical expression of downlink transmission energy efficiency (DLEE) has been derived. Numerical simulation results show that the transmission performances and DLEE have been improved by proposed protocol compared with the conventional AF relay protocol and direct transmission.

Secure Multiple Amplify-and-Forward Relaying With Cochannel Interference

We investigate the impact of cochannel interference on the security performance of multiple amplify-and-forward (AF) relaying networks, where $N$ intermediate AF relays assist the data transmission from the source to the destination. The relays are corrupted by multiple cochannel interferers, and the information transmitted from the relays to the destination can be overheard by the eavesdropper. In order to deal with the interference and wiretap, the best out of $N$ relays is selected for security enhancement. To this end, we derive a novel lower bound on the secrecy outage probability (SOP), which is then utilized to present two best relay selection criteria, based on the instantaneous and statistical channel information of the interfering links. For these criteria and the conventional max–min criterion, we quantify the impact of cochannel interference and relay selection by deriving the lower bound on the SOP. Furthermore, we derive the asymptotic SOP for each criterion, to explicitly reveal the impact of transmit power allocation among interferers on the secrecy performance, which offers valuable insights into practical design. We demonstrate that the all selection criteria achieve full secrecy diversity order $N$ , while the proposed two criteria in this paper outperform the conventional max–min scheme.

Combined Effect of RF Impairment and CEE on the Performance of Dual-Hop Fixed-Gain AF Relaying

We study the performance of dual-hop fixed-gain (FG) amplify-and-forward (AF) relaying systems in the presence of both radio frequency impairments (RFI) and channel estimation error (CEE). The expression for end-to-end signal-to-noise plus distortion-and-error ratio is derived along with exact analytical expressions of outage probability (OP) over independent but non-identically distributed Nakagami- $ m_{i}$ fading channel. Then, we perform an asymptotic analysis of OP at high SNR and find that there is an error floor on OP due to the effects of CEE. Although there is no direct effect of RFI on the error floor, the way in which it affects the value of CEE at high SNR and thus takes part in indirectly elevating the error floor is also looked into. The analytical results are validated through Monte Carlo simulation. Finally, the dominance of RFI and CEE at different transmission rates and average SNRs is also discussed.

Secrecy Rate and Optimal Power Allocation of the Amplify-and-Forward Relay Wire-Tap System

In this research work, we investigate the secrecy rate and optimal power allocation schemes for a half-duplex (HD) wire-tap Rayleigh fading channel in which a source wishes to communicate securely to a destination in the presence of an eavesdropper and under the aid of an amplify-and-forward (AF) relay. The secrecy capacity and the corresponding optimal power allocation schemes are examined under both individual and joint power constraints. Due to the absence of an insightful expression of the secrecy rate for a given power allocation scheme, determining such secrecy capacity is challenging. To overcome this issue, we first propose a novel method to calculate the expectation of an exponentially distributed random variable using the exponential integral function. By exploiting this calculation, we then establish the average secrecy rate of the considered AF relay channel in closed-form. By examining the quasi-concavity of the optimal power allocation problem, it is then concluded that the problem is quasi-concave. As such, the globally optimal solution exists and is unique for both individual and joint power constraints. A simple root finding method then can be applied into the derived close-formed formula to approximately calculate the optimal power allocation scheme to achieve the secrecy capacity. Numerical results are then provided to confirm the accuracy of the derived formula and the optimality of the proposed power allocation.

A novel LMS-BLM algorithm for AF relays based cooperative wireless networks

Wireless communication networks are usually affected by channel impairments such as multi-path fading effects, shadowing, noise, etc. Therefore, techniques to mitigate wireless channel impairments, to improve the quality and spectral efficiency of communication over wireless channels are indispensable. Thus, amplify and forward (AF) relays based cooperative wireless networks are considered in this study for their capability to reduce the effects of fading caused by multipath propagation. Moreover, most studies on relay networks assume perfect channel state information at the receiver (CSIR), but in reality, due to the nature of wireless channels, little information is known on both the channel state information (CSI) and original transmitted signal at the receiver. Therefore, our main contribution is based on proposing a novel algorithm that combines the least mean square (LMS) algorithm and Bayesian linear model (BLM) detector for their low implementation complexity and feasibility. Analytical and theoretical simulations on receiver operating characteristics (ROC), complementary ROC, mean square errors (MSE) learning curves, optimum threshold and probability of error are presented. The results have shown that the proposed algorithm is effective and can provide higher detection performance in the current and next generation wireless networks where multiple relays strategy is applied.

On the Effective Capacity of Amplify-and-Forward Multihop Transmission Over Arbitrary and Correlated Fading Channels

This letter presents a novel approach for analyzing, in a unified way, the effective capacity performance of multihop transmission with channel state information assisted amplify-andforward relay systems over arbitrary and correlated fading channels under a maximum delay constraint. Using a moment generating function based approach, an exact single integral expression for the effective capacity is deduced. This expression can be easily evaluated by means of standard numerical integration techniques for a great deal of fading distributions, such as the Nakagami-m, Generalized-K, and Generealized Gamma. Several case studies, including uncorrelated and correlated fading environments, are employed to demonstrate the versatility of the proposed analytical approach. Extensive numerically evaluated results accompanied with complimentary Monte-Carlo simulations are used to substantiate the analytical derivations.

Joint Power Allocation in Wireless Relay Networks: the Case of Hybrid Digital-Analog Transmission

In conventional digital communication systems, the quality of the received signal does not improve beyond a certain level as the channel quality increases. Such kind of quality saturation effect is caused by the unrecoverable quantization errors produced by source coding. The Hybrid Digital-Analog (HDA) transmission, where the quantization errors are transmitted in an analog mode along with the quantized data in a digital mode, has been recognized as an effective technique to combat the quality saturation effect. In this paper, we introduce HDA transmission in Wireless Relay Networks (WRNs) over Rayleigh slow-fading channels to eliminate the quality saturation effect and achieve graceful improvement for the better channel quality. Our goal is to minimize the end-to-end distortion by optimal power allocation. We note that digital-analog power allocation involved in HDA transmission is coupled with source-relay power allocation in WRNs. Therefore, the joint power allocation problem should be considered. We investigate this problem for two kinds of relays in WRNs, i.e., Amplify-and-Forward (AF) relays and Decode-and-Forward (DF) relays. In the case of AF relays, we find that the joint power problem is concave and thus derive the explicit expressions of the optimal solution. In the case of DF relays, we formulate the joint power allocation problem as a nonlinear fractional programming problem and then propose an efficient algorithm to search the optimal solution. Simulation results show that the proposed joint power allocation schemes outperform existing schemes in terms of end-to-end distortion in both WRNs with AF relays and that with DF relays under various channel conditions.

Optimal Power Allocation Schemes for the Single AF Relay and Jammer Wiretap Channels

This paper considers the wiretap channel in which a source node communicates with a destination node with the aid of a single helper and in the presence of an eavesdropper. The helper can apply either amplify-and-forward (AF) relaying or jamming. The secrecy capacity and respective optimal power allocation schemes at the source and the helper are investigated under both individual and joint power constraints. Given that the links among the nodes might not always be available for transmission (e.g., due to heavy shadowing), several network topologies are considered for relaying. To deal with the related nonconcave optimization problems in solving the optimal power allocation schemes, we first propose an analytical approach based on Descartes' rule of signs. Using this approach, optimal power allocation strategies are derived for some relay topologies and for the jamming system. Insights into the proposed schemes for different transmission power ranges and comparisons to the optimal information rate power allocations are also discussed. Simulation results are finally provided to quantify the optimality of the proposed schemes.

Performance of a Cognitive Relay Network under AF Relay Selection Scheme with Imperfect Channel Estimation

In this paper outage performance of a secondary user (SU) is evaluated under an amplify and forward (AF) relay selection scheme with an imperfect channel state information (CSI) while the SU shares spectrum in an underlay cognitive radio network (CRN). In underlay, the SU coexists with primary user (PU) in the same band pro- vided the interference produced by SU at the PU receiver is below an interference threshold of PU. This limits the transmission power of SU and coverage area. Relays help to improve the performance of SU in such underlay sce- nario. However relays are also constrained in their trans- mit power due to interference constraint imposed by PU. Closed form expression of the outage probability of SU with maximum transmit power constraint of relay under imperfect CSI is derived. A scaling factor based power control is used for the SU transmitter and the relay in or- der to maintain the interference constraint at the PU re- ceiver due to imperfect CSI. The impact of several param- eters viz. correlation coefficient, channel estimation error, tolerable interference threshold, number of relays and the maximum transmit power constraint of relay on SU per- formance is investigated. A MATLAB based test bed has also been developed to carry out simulation in order to validate the theoretical results.

Secrecy Outage Probability of AF Relay Transmission with MRC/TAS in Presence of Eavesdropper

In this paper, we offer the secrecy outage probability of the amplify-and-forward (AF) transmission, which consists of one source, one destination, one relay, and one passive eavesdropper. Particularly, we consider that the relay is equipped with multiple antennas while other terminals is utilized with single antenna and apply diversity techniques (for both the reception and the transmission) at the relay to achieve gains in a secrecy outage performance. Additionally, we analyze the exact secrecy outage probability of the proposed systems in a one-integral form. Finally, some numerical examples are given to verify our provided analytical results for different system conditions.