Amplify-and-forward Relay Systems Research Articles

Joint Hybrid Beamforming Design for Millimeter Wave Amplify-and-Forward Relay Communication Systems

Hybrid beamforming (HBF) has been regarded as one of the most promising technologies in millimeter Wave (mmWave) communication systems. In order to guarantee the communication quality in non-line-of-sight (NLOS) scenarios, joint HBF design for the mmWave amplify-and-forward (AF) relay communication system is studied in this paper. The ideal case is first considered where the mmWave half-duplex (HD) AF relay system operates with channel state information (CSI) accurately known. In order to tackle the non-convex problem, a manifold optimization (MO)-based alternating optimization algorithm is proposed, where an optimization problem containing only constant modulus constraints in Euclidean space can be converted to an unconstrained optimization problem in a Riemann manifold. Furthermore, considering more practical cases with estimation errors of CSI, we investigate the robust joint HBF design with the system operating in full-duplex (FD) mode to obtain higher spectral efficiency (SE). A null-space projection (NP) based self-interference cancellation (SIC) algorithm is developed to attenuate the self-interference (SI). Different from the traditional SI suppression algorithm, there’s no limit on the number of RF chains. Numerical results reveal that our proposed algorithms has a good convergence and can effectively deal with the influence of different CSI estimation errors. A significant performance improvement can be achieved in contrast with other approaches.

Performance Comparison of Relay-Based Covert Communications: DF, CF and AF.

In this paper, we investigate the performance of covert communications in different types of a relay system: decode-and-forward (DF), compress-and-forward (CF) and amplify-and-forward (AF). We consider a source node that attempts to send both public and covert messages to a destination node through a relay on which a covert message detector is embedded. By taking the minimum detection error probability (DEP) at the relay into account, we optimize the power distribution between the public and covert messages to achieve the maximum covert rate. We further make a delay-aware comparison among DF, CF and AF relay systems with the obtained closed-form covert rates and conduct an extensive examination on the asymptotic behaviors in different limits. Our analyses reveal that CF or AF tend to outperform DF for high source transmit power or low relay transmit power, while various system parameters such as the processing delay, minimum required quality of service for public messages and DEP threshold lead to different performance relationships among DF, CF and AF for high relay transmit power. Numerical results verify our investigation into the performance comparison in various channel models.

Joint Optimization for Multi-Antenna AF-Relay Aided Over-the-Air Computation

Benefiting from exploiting the waveform superposition property in the multi-access channels, over-the-air computation (AirComp) has emerged as a promising technique to swiftly compute functions of data from a large number of sensors. To enlarge the wireless coverage area, a two-phase multi-antenna amplify-and-forward (AF)-relay aided AirComp system is considered, where all the sensors transmit sensing data during both two phases in a half-duplex AF relay system with direct links. We present efficient designs for optimizing the transmit scalar vectors at the sensors, the AF matrix at the relay, and the aggregation vector at the access point, which aims to minimize the mean-square-error (MSE) subject to the transmit power budgets at the relay and the sensors, respectively. To solve the resultant multiple variables coupled non-convex optimization problem efficiently, we develop an alternating optimization-based algorithm to obtain locally optimal solutions. Specifically, in each iteration, closed-form expressions are derived for each optimizing variable. Finally, the computation distortion improvement of our proposed design over baseline schemes is demonstrated via simulations.

Millimeter Wave Communications With Reconfigurable Intelligent Surfaces: Performance Analysis and Optimization

Reconfigurable Intelligent Surface (RIS) can create favorable multipath to establish strong links that are useful in millimeter wave (mmWave) communications. While previous works assumed Rayleigh or Rician fading, we use the fluctuating two-ray (FTR) distribution to model the small-scale fading in mmWave frequency. First, we obtain the statistical characterizations of the product of independent FTR random variables (RVs) and the sum of product of FTR RVs. For the RIS-aided and amplify-and-forward (AF) relay systems, we derive exact end-to-end signal-to-noise ratio (SNR) expressions. To maximize the end-to-end SNR, we propose a novel and simple way to obtain the optimal phase shifts at the RIS elements. The optimal power allocation scheme for the AF relay system is also proposed. Furthermore, we evaluate important performance metrics including the outage probability and the average bit-error probability. To validate the accuracy of our analytical results, Monte-Carlo simulations are subsequently conducted to provide interesting insights. It is found that the RIS-aided system can attain the same performance as the AF relay system with low transmit power. More interestingly, as the channel conditions improve, the RIS-aided system can outperform the AF relay system using a smaller number of reflecting elements.

Joint Power Allocation and Relay Beamforming Optimization for Weighted Sum-Rate Maximization in NOMA AF Relay System

This letter introduces a novel joint power-allocation (PA) and relay beamforming optimization (JPBO) algorithm for non-orthogonal multiple-access (NOMA) amplify-and-forward (AF) relay systems to achieve the maximum weighted sum-rate (WSR). In our proposed new framework, the WSR maximization problem is transformed into a tractable weighted-sum minimum mean-square-error (WSMMSE) problem. Then, the PA and the relay beamforming-matrix (BM) are alternately optimized by use of successive convex approximation (SCA) and Lagrange-multiplier (LM) algorithm. Simulation results demonstrate that our proposed new algorithm can significantly improve the WSR with a faster convergence than the existing method.

Transceiver Design for AF MIMO Relay Systems With a Power Splitting Based Energy Harvesting Relay Node

In this article, a dual-hop amplify-and-forward (AF) multiple-input multiple-output (MIMO) relay communication system is studied. With a splitting (PS) protocol, the relay node harvests the radio frequency (RF) energy in the signals sent by the source node and utilizes the harvested energy to forward signals from the source node to the destination node. We aim at maximizing the source-destination mutual information (MI) through a joint design of the source matrix, the relay matrix, and the PS ratios under the source node power constraint and the relay node harvested energy constraint. We consider a general sum energy constraint at the relay node with different PS ratios across relay antennas, which includes existing works based on uniform PS or per data stream energy constraint as special cases. Moreover, a practical nonlinear energy harvesting (EH) model is adopted, where the harvested energy is bounded as the incident RF signal power increases. We establish the structure of the source matrix and the relay matrix, which simplifies the complicated transceiver design problem with matrix variables to a power distribution problem with scalar variables. Three approaches are proposed to efficiently solve the optimal power distribution problem. In particular, the first proposed algorithm solves the original nonconvex power allocation problem using the sequential quadratic programming, while the other two algorithms convert the original problem to convex problems by exploiting a tight upper bound and a tight lower bound of the objective function, respectively. Numerical simulations demonstrate that when the EH circuit works in the linear region, the proposed algorithms have a larger system MI than existing PS and TS based MIMO AF relay systems. The peak harvest power constraint plays an important role in choosing the location of the relay node.

A Unified Performance Analysis of Relaying Communication System for IoT Application With Hybrid Fading

Power line and wireless hybrid communication address the problem that wireless and power line cannot communicate with each other in the Internet of Things (IoT). However, the theoretical performance of amplify-and-forward (AF) relay communication based on hybrid fading condition has no closed expression. This article takes a relay system model of wireless and power line hybrid media as a representative and investigates a unified performance analysis method for AF relay systems with hybrid fading. The mixture lognormal (LogN) approximate algorithm based on the moment-generating function (MGF) is applied to approximate a wireless fading coefficient to mixture LogN distribution. Moreover, we propose a joint optimization algorithm for determining the key parameters given that the adjustable variables in the MGF equations evidently affect the approximation accuracy. Importantly, this article is then extended to other fading models, taking general gamma (GG) as an example. The effectiveness and reliability of the algorithm are verified by the Monte Carlo simulation. Finally, closed analytic expressions of the system performance, such as bit error rate (BER), outage probability, and average channel capacity, are derived. The effects of hybrid fading factor, impulse noise parameter, and power allocation on system performance are analyzed using the theoretical formulas.

Optimal power allocation in NOMA-based two-path successive AF relay systems

Due to the characteristic of transmitting multiplexed signals in superposed mode over the same spectrum, non-orthogonal multiple access (NOMA) technology is deemed as a promising way to improve spectral efficiency in fifth generation (5G) networks. In this paper, we develop a NOMA cooperative system based on the two-path successive relaying concept, in which the data at the source node is divided into two parallel parts and is transmitted to the destination in superposed mode via the assistance of two amplify-and-forward (AF) relays. On the condition that the transmit power of the individual nodes and the entire system are all constrained, the maximization of achievable rate is formulated as an optimization problem. Following the guidelines of Karush-Kuhn-Tucher (KKT) conditions, the dual decomposition method is adopted to obtain the closed-form expressions of the optimal power allocation. Moreover, to balance the achievable rate between two superposed signals, which is equivalent to minimizing the required spectrum bandwidth, a power allocation scheme between the superposed signals is proposed. In order to verify the effectiveness and efficiency of the proposed power allocation scheme, we conduct extensive numerical simulation on some realistic system setup. The results demonstrate that our analytical insights about the optimal power allocation are aligned with the simulation outcome.

Outage probability of power splitting SWIPT two-way relay networks in Nakagami-m fading

This paper investigates the outage probability of an energy harvesting (EH) relay-aided cooperative network, where a source node transmits information to its destination node with the help of an energy harvesting cooperative node. For such a system, we derive an explicit closed-form expression of outage probability over Nakagami-m fading channels for both amplify-and-forward (AF) and decode-and-forward (DF) relay protocols, and we verify the explicit closed-form expressions of outage probability with the Monte Carlo method. It is shown that the simulation results match well with the numerical ones. From the numerical analysis and simulation results, it can be observed that the system parameters have great impact on both AF and DF relay systems. For the DF system, with the increment of the power splitting ratio, the system outage probability decreases, while for the AF system, with the increment of the power splitting ratio, it first increases and then decreases. Besides, for both DF and AF systems, when the relay is placed relatively closer to the source, better outage performance will be achieved.

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.

Ergodic Capacity Analysis of AF DH MIMO Relay Systems With Residual Transceiver Hardware Impairments: Conventional and Large System Limits

Despite the inevitable presence of transceiver impairments, most prior work on multiple-input multiple-output (MIMO) wireless systems assumes perfect transceiver hardware, which is unrealistic in practice. In this direction, motivated by the increasing interest in MIMO relay systems due to their improved spectral efficiency and coverage, this paper investigates the impact of residual hardware impairments on the ergodic capacity of dual-hop (DH) amplify-and-forward (AF) MIMO relay systems. Specifically, a thorough characterization of the ergodic channel capacity of DH AF relay systems in the presence of hardware impairments is presented herein for both the finite and large antenna regimes by employing results from finite-dimensional and large random matrix theory, respectively. Regarding the former setting, we derive the exact ergodic capacity as well as closed-form expressions for tight upper and lower bounds. Furthermore, we provide an insightful study for the low signal-to-noise ratio regimes. Next, the application of the free probability theory allows us to study the effects of the hardware impairments in future 5G deployments including a large number of antennas. While these results are obtained for the large system limit, simulations show that the asymptotic results are quite precise even for conventional system dimensions.

Optimal Beamforming for Dual-Hop MIMO AF Relay Networks With Cochannel Interferences

In this paper, we investigate a beamforming (BF) scheme for a dual-hop multiple-input multiple-output (MIMO) amplify-and-forward (AF) relay network in the presence of multiple cochannel interferences (CCIs) at both the relay and the destination nodes. In order to maximize the signal-to-interference-plus-noise ratio at the destination node, the optimal BF weights for the relay network in the presence of CCIs are derived. A tight lower bound on the outage probability (OP) is derived in a closed form by assuming that multiple CCIs have equal power at the relay and destination nodes. Through computer simulations, it is shown that the proposed BF scheme can outperform the existing schemes. Furthermore, the impacts of antenna configurations, CCIs, and power allocation on the outage performance of the MIMO AF relay systems have been demonstrated with simulations.

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.

An Equivalence Principle for OFDM-Based Combined Bulk/Per-Subcarrier Relay Selection over Equally Spatially Correlated Channels

In this paper, we propose a novel relay selection scheme for orthogonal frequency-division multiplexing systems by combining conventional bulk and per-subcarrier selection schemes and analyze its outage performance over equally spatially correlated channels. Specifically, the combined selection scheme selects only two relays at the first attempt and performs per-subcarrier selection over these two relays. We analyze the asymptotic outage performance of the combined selection scheme in the high signal-to-noise ratio (SNR) region and prove a generalized theorem. This theorem states that the combined selection can achieve an optimal outage probability equivalent to the per-subcarrier selection at a high SNR without using the full set of available relays for selection. This unique property is termed the equivalence principle , and it holds for all correlation conditions. To explore this principle, we consider three examples: decode-and-forward, fixed-gain amplify-and-forward (AF), and variable-gain AF relay systems. Furthermore, two extended applications, i.e., antenna selection and branch selection, are also considered to reveal the feasibility and the expandability of the equivalence principle. Our analysis is verified by Monte Carlo simulations. The proposed combined selection and the proved theorem provide a general and feasible solution to the tradeoff between system complexity and outage performance when relay selection is applied.

Joint Cooperative Beamforming, Jamming, and Power Allocation to Secure AF Relay Systems

The idea of multiuser (nodes) cooperation is an efficient way to improve the physical-layer security of a wireless transmission in the presence of passive eavesdroppers. However, due to the half-duplex constraint of the practical transceivers, two phases are required for one round of data transmission, which grants the eavesdroppers two opportunities to wiretap the information. Therefore, protecting the data transmissions in both phases is critical. Toward this end, we propose a joint cooperative beamforming, jamming, and power-allocation scheme to enhance the security of an amplify-and-forward (AF) cooperative relay network in this paper. Different from the existing works assuming that the source node always uses its total power, we show that the secrecy rate is a quasi-concave function of the power of the source node so that allocating its total power may not be optimal. The beamformer design and power optimization problem can be solved by a bisection method together with a generalized eigenvalue decomposition, which has a semiclosed form and is computationally very convenient. Simulations show that the joint scheme greatly improves the security.

Performance of OFDM AF relay system with subcarrier mapping in the presence of carrier frequency offsets

This article deals with the performance analysis of orthogonal frequency division multiplexing (OFDM) amplify-and-forward (AF) relay system with subcarrier mapping (SCM) in the presence of carrier frequency offset (CFO). Although SCM in an OFDM system has been investigated extensively, nevertheless, the bit error rate (BER) of the system with CFO is not yet available in the literature. This paper presents the BER analysis of a dual hop OFDM AF relay system with ordered subcarrier paring schemes, i.e., best-to-worst (BTW) SCM and best-to-best (BTB) SCM. Accurate close-form expressions are derived for end-to-end BER while considering a dual-hop fixed gain AF relaying system with CFO in Rayleigh fading channel. To provide more insights, their closed-form asymptotic expressions are then obtained. It is shown that the presence of CFO causes the BER of system maintain a fixed level even while signal-to noise ratio (SNR) is in high regime. The simulation results verify that the derived average BER expressions are accurate in Rayleigh fading channel.

Spectrum and Energy Efficiencies for Multiuser Pairs Massive MIMO Systems With Full-Duplex Amplify-and-Forward Relay

To achieve insights about the impact of amplified loop interference, we consider a dual-hop full-duplex (FD) massive multiple-input multiple-output (MIMO) amplify-and-forward (AF) relaying system in terms of achievable ergodic rates for each user pair as well as spectrum and energy efficiencies. It is assumed that the base station (or relay) is equipped with $M_{Rx}$ receive antennas and $M_{Tx}$ transmit antennas, while all sources and destinations have a single antenna. For such FD massive MIMO AF relaying systems, the closed-form expressions of the lower bounds of achievable ergodic rates are derived first with a finite number of receive and transmit antennas at base station. Then, the asymptotic performance analysis is performed by considering three different power-scaling schemes: 1) $P_{S} =E_{S} /M_{Rx} $ and $P_{R} =E_{R} $ ; 2) $P_{S} =E_{S} $ and $P_{R} =E_{R} /M_{Tx} $ ; and 3) $P_{S} =E_{S} /M_{Rx} $ and $P_{R} =E_{R} /M_{Tx} $ , where $E_{S} $ and $E_{R} $ are fixed, and $P_{S} $ and $P_{R} $ denote the transmit powers of each source and relay, respectively. Our results show that only when the power-scaling 2) is utilized, do the FD massive MIMO AF relay systems have the ability to restrict the loop interference, so that the system performance is free of loop interference when the number of antennas at the relay is large enough. On the contrary, with the power-scaling cases 1) and 3), the systems have no ability to cancel the loop interference even if $M_{Rx} $ or $M_{Tx} $ (or both) goes to infinity. The insight is different from the results in the FD massive MIMO decode-and-forward relaying systems where the loop interference can be entirely eliminated for the three power-scaling cases.