Non-orthogonal Amplify-and-forward Research Articles

Relay Power Allocation for NAF Cooperation Assisted NOMA Network

In this letter, a power allocation problem at secondary users (SUs) to maximize the overall system throughput is addressed in a non-orthogonal amplify-and-forward (NAF) cooperation assisted non-orthogonal multiple access (NOMA) network. Due to the nonlinearity of optimization problem, a cooperative multi-agent Q-Learning based power allocation algorithm (CQPA) is proposed under both sum and individual power constraints of SUs with relay function. To further reduce the computational complexity, a neighboring strategy searching based power allocation algorithm (NSPA) is additionally proposed. Simulation results demonstrate the efficiency of proposed algorithms, where a valuable trade-off between throughput and computational complexity can be achieved by the NSPA.

Secrecy Rate Maximization for Untrusted Relay Networks With Nonorthogonal Cooperative Transmission Protocols

In this paper, a relay based network is considered where the source transmits confidential message to the destination via a nonregenerative relay. Due to the fact that the relay is unidentified, and thus may wiretap the relayed message from source to destination. In this regard, two new half-duplex nonorthogonal amplify-and-forward (NAF) secure communication protocols are proposed, with different assumptions on the transmission ability of the destination, i.e., NAF-I for destination without transmission ability and NAF-II for destination with transmission ability. We separately derive the sufficient and necessary conditions to yield positive secrecy rate for these protocols under fixed source/destination transmission power, and discuss their joint power allocation that maximizes the system secrecy rate. Despite the nonconvexity of the considered power allocation problems, alternative optimization approach is proved useful in dealing with these problems, and the corresponding algorithms are proposed. We further prove the convergence of the proposed algorithms and analyze their complexity. The discussion is also extended to the orthogonal amplify-and-forward (OAF) based protocols, i.e., OAF-I or OAF-II, for comparison purpose. Our numerical results demonstrate the gain of the secrecy rate performance of the proposed NAF protocols over existing transmission protocols, and also verify the effectiveness of the designed alternative optimization algorithms.

Perbandingan Kinerja Non-Orthogonal dan Orthogonal Amplify and Forward pada Two-Way Cooperative WLAN

Nowadays, the advancement of Wireless Local Area Network (WLAN) technology has developed very rapidly because it is very practical and has effective mobility level. In practice, there is a major problem in wireless communications systems, which is fading. Fading can cause information signal power decreasing. Fading can be overcome using a cooperative communication system, which is a method that utilizes antenna from other users (relays), using principle of diversity, hence the performance of wireless communication system is improved. A relay has several protocols on cooperative communication system, such as Amplify and Forward (AF), Decode and Forward (DF), and Compress and Forward (CF). The AF protocol is divided into two types: Non-Orthogonal Amplify and Forward (NAF) and Orthogonal Amplify and Forward (OAF). In this paper, the performance comparison of two-way NAF and OAF in terms of outage probability, throughput, and spectral efficiency is investigated. The method used is computer simulation with system modeling and performance analysis. The simulation results show that OAF protocol can minimize outage probability and increase throughput and spectral efficiency, compared to NAF protocol on two-way WLAN cooperative network.

Fast-Decodable Space–Time Codes for the -Relay and Multiple-Access MIMO Channel

In this article, the first general constructions of fast-decodable, more specifically (conditionally) $g$-group decodable, space-time block codes for the Nonorthogonal Amplify and Forward (NAF) Multiple-Input Multiple-Output (MIMO) relay channel under the half-duplex constraint are proposed. In this scenario, the source and the intermediate relays used for data amplification are allowed to employ multiple antennas for data transmission and reception. The worst-case decoding complexity of the obtained codes is reduced by up to $75%$. In addition to being fast-decodable, the proposed codes achieve full-diversity and have nonvanishing determinants, which has been shown to be useful for achieving the optimal Diversity-Multiplexing Tradeoff (DMT) of the NAF channel. Further, it is shown that the same techniques as in the cooperative scenario can be utilized to achieve fast-decodability for $K$-user MIMO Multiple-Access Channel (MAC) space-time block codes. The resulting codes in addition exhibit the conditional nonvanishing determinant property which, for its part, has been shown to be useful for achieving the optimal MAC-DMT.

Non-orthogonal Amplify and Forward Relay Selection Systems with Distributed Space–Time Trellis Coded Continuous Phase Modulation

Most of the works on cooperative systems with or without relay selection have focused on linear modulations such as phase shift keying and quadrature amplitude modulation. Whereas, continuous phase modulation (CPM) is a good alternative to these modulations due to its constant envelope property which enables us to use inexpensive and energy-efficient non-linear power amplifiers. In the literature, a few works are based on relaying systems with CPM. To the best of our knowledge, none exists with relay selection. In this paper, we propose single and multiple relay selection CPM schemes based on a new generalized relay selection criterion for non-orthogonal amplify and forward (AF) systems operating with various time sharing protocols. In particular, using the proposed criterion, the best relay or the best two relays over a set of four available relays is/are selected. Error performances of the non-orthogonal AF relay selection systems and their counterparts are compared over frequency non-selective quasi-static Rayleigh fading channels using Viterbi algorithm at the destination terminal. Our numerical results present superiority of the proposed non-orthogonal relay selection systems.

Distributed Space-Time Codes for Full-Duplex IR-UWB Amplify-and-Forward Cooperation

In this paper, we consider the problem of full-duplex (FD) relaying in the context of impulse-radio ultra-wideband (IR-UWB) communications. In particular, we propose two novel distributed space-time block codes (STBCs) suitable for the amplify-and-forward (AF) cooperation protocol with one and two relays. Despite the fact that FD relaying results in significant levels of interference between the transmit and receive antennas of each relay, it introduces new concepts to the problem of distributed STBC design. Compared to half-duplex (HD) STBC, FD-STBC is subject to an additional constraint that imposes the structure of the codewords while it offers the predominant advantage that resides in the possibility of including a smaller number of information symbols per codeword for achieving a full rate. We take advantage of this potential for constructing fully-diverse, full-rate and totally-real IR-UWB FD-STBCs that outperform the existing HD-STBCs for all practical levels of the residual self loop interference. In fact, for the sake of transmitting at full rate, the best known distributed HD-STBCs for the non-orthogonal AF protocol require the joint encoding/decoding of $4N_{r}$ symbols where $N_{r} $ is the number of relays. On the other hand, the proposed FD-STBCs require embedding only $N_{r} +2$ symbols per codeword for transmitting at full rate. Following from this fact, not only the decoding complexity is reduced, but also the coding gains are improved resulting in enhanced performance levels.

On Achievable Rate and Ergodic Capacity of NAF Multi-Relay Networks with CSI

This paper investigates the achievable rate and ergodic capacity of a non-orthogonal amplify-and-forward (NAF) half-duplex multi-relay network where multiple relays exploit channel state information (CSI) to cooperate with a pair of source and destination. In the first step, for a given input covariance matrix at the source, we derive an optimal power allocation scheme among the relays via optimal instantaneous power amplification coefficients to maximize the achievable rate. Given the nature of broadcasting and receiving collisions in NAF, the considered problem in this step is non-convex. To overcome this drawback, we propose a novel method by evaluating the achievable rate in different sub-domains of the vector channels. It is then demonstrated that the globally optimal solution can be derived in closed-form. In the next step, we establish the ergodic channel capacity by jointly optimizing the input covariance matrix at the source and the power allocation among the relays. We show that this is a bi-level non-convex problem and solve it using Tammer decomposition method. This approach allows us to transform the original optimization problem into an equivalent master problem and a set of sub-problems having closed-form solutions derived in the first step. The channel capacity is then obtained using an iterative water-filling-based algorithm. Finally, we analyze the capacity-achieving input covariance matrix at the source in high and low signal-to-noise ratio (SNR) regimes. At sufficiently high SNRs, it is shown that the transmit power at the source should be equally distributed in all broadcasting and cooperative phases. On the other hand, in low SNR regions, the source should spend all its power in the broadcasting phase associated with a relay having the strongest cascaded source-relay and relay-destination channels.

Achievable Rate and Power Allocation for Single-Relay AF Systems Over Rayleigh Fading Channels at High and Low SNRs

In this paper, we propose a general method to analyze the achievable rate and to characterize the optimal power-allocation (PA) scheme for a wide range of half-duplex single-relay amplify-and-forward (AF) protocols over Rayleigh fading channels in high and low signal-to-noise-ratio (SNR) regimes. These include one-way (OW) dual-hop AF (DHAF) systems, OW nonorthogonal AF (NAF) systems, and two-phase two-way AF (2P TWAF) systems using either fixed-gain (FG) or variable-gain (VG) amplification coefficients. At high-SNR regimes, our main idea is to exploit the capacity of a two-branch maximal-ratio combining (MRC) system to obtain tight yet simple approximations to the achievable rates. In low-SNR regions, we use a simple approximation to the logarithm to compute the asymptotic achievable rates. For all considered AF protocols, the closed-form approximations are tight and easy to analyze since they involve only the exponential integral. Then, using the derived approximations, we analytically quantify the asymptotic PA schemes among the nodes to achieve the maximum rate and the sum rate for OW and TW schemes, respectively. The OW and TW protocols of interest are finally compared with the direct transmission (DT) scheme. Although OW relaying is inferior in terms of capacity in high- and low-SNR regimes, the 2P TW system might become advantageous in terms of sum-rate performance at high SNRs under the right channel conditions.

Linear Transceiver Design for Nonorthogonal Amplify-and-Forward Protocol Using a Bit Error Rate Criterion

The ever growing demand of higher data rates can now be addressed by exploiting cooperative diversity. This form of diversity has become a fundamental technique for achieving spatial diversity by exploiting the presence of idle users in the network. This has led to new challenges in terms of designing new protocols and detectors for cooperative communications. Among various amplify-and-forward (AF) protocols, the half duplex non-orthogonal amplify-and-forward (NAF) protocol is superior to other AF schemes in terms of error performance and capacity. However, this superiority is achieved at the cost of higher receiver complexity. Furthermore, in order to exploit the full diversity of the system an optimal precoder is required. In this paper, an optimal joint linear transceiver is proposed for the NAF protocol. This transceiver operates on the principles of minimum bit error rate (BER), and is referred as joint bit error rate (JBER) detector. The BER performance of JBER detector is superior to all the proposed linear detectors such as channel inversion, the maximal ratio combining, the biased maximum likelihood detectors, and the minimum mean square error. The proposed transceiver also outperforms previous precoders designed for the NAF protocol.

On the Capacity of the Static Half-Duplex Non-Orthogonal AF Relay Channel

In this paper, we analyze the capacity of the static half-duplex single-relay amplify-and-forward (AF) system under both per-node and joint power constraints. Different from multiple-input multiple-output systems, the channel matrix of the cooperative AF system is a function of the parameters to be optimized and hence water-filling over the square of the singular values is no longer optimal. Furthermore, given that the mutual information of the AF system is not a concave function, conventional optimization methods cannot be applied. Instead, by deriving and comparing all local solutions, we characterize the optimal input covariance matrix at the source and the optimal power allocation scheme at the relay that maximize the achievable rate. First, for the individual power constraint scenario, it is shown that the capacity of the AF system is achieved by either a direct transmission (DT) scheme, a non-orthogonal AF (NAF) beamforming (BF) protocol with a unit-rank covariance matrix, or a NAF system using a specific full-rank covariance matrix. Then, for the global power constraint scenario, it is shown that only a DT or a NAF-BF protocol can achieve the capacity. In both cases, orthogonal transmission is strictly suboptimal. The capacity of the AF system is finally analyzed for some concrete examples, such as under asymptotically high and low transmission powers and for several network models.

Optimal Power Adaptation for Cooperative AF Relaying With Channel Side Information

In this paper, we develop optimal power adaptation schemes by means of power amplification coefficients at the relay for half-duplex single-relay amplify-and-forward (AF) cooperative systems with channel side information (CSI) available at the relay. We consider both the orthogonal AF (OAF) and the nonorthogonal AF (NAF) transmission protocols. In particular, assuming that the relay has full knowledge of the channel gains, optimal power adaptation schemes under a long-term average power constraint are established in closed form using the mutual information (MI) and pairwise error probability (PEP) criteria with Gaussian inputs at the source. The proposed solutions can be understood as multidimensional (multi-D) distributed water filling in time and space. Numerical results show that the proposed power amplification methods provide a significant improvement over conventional schemes using either channel distribution information (CDI) or channel inversion (CI). The gain is observed with regard to the MI with Gaussian inputs and the bit-error-rate (BER) performance using finite constellations for both coded and uncoded systems.

Precoding and Symbol Grouping for NAF Relaying in BICM Systems

This paper considers the precoder design for a bandwidth-efficient bit-interleaved coded modulation (BICM) system over nonorthogonal amplify-and-forward (NAF) single-relay channels with an arbitrary length of cooperative frame 2N. Based on the tight union bound to the bit error probability (BEP), we first derive an asymptotic design criterion with regard to a general 2N × 2N rotation matrix. This expression allows us to develop a class of precoders that not only achieves full cooperative diversity but optimizes the asymptotic error performance as well. Interestingly, the developed class of optimal precoders indicates that the source should keep silent in the cooperative phase. In the broadcasting phase, it is shown that power is equally distributed to 2N information symbols at the source. By further examining the structure of the optimal class of 2N × 2N precoders, it is then revealed that precoding over a group of at least two information symbols is sufficient to fully exploit diversity and coding advantages. Such a precoding technique, which is referred to as symbol grouping, therefore significantly reduces the system complexity without sacrificing the error performance. Among the pool of optimal precoders with respect to the asymptotic performance, the design of a precoder that provides a good convergence property is also discussed. Numerical examples show that the proposed precoder greatly improves the error performance of the cooperative system with low complexity.

Diversity-Multiplexing Tradeoff in Multiantenna Multirelay Networks: Improvements and Some Optimality Results

This paper investigates the benefits of amplify-and-forward (AF) relaying in the setup of multiantenna wireless networks. For this purpose, random sequential (RS) relaying is studied. It is shown that random unitary matrix multiplication at the relay nodes empowers the RS scheme to achieve a better diversity-multiplexing tradeoff (DMT) as compared to the traditional AF relaying. First, the RS scheme is proved to achieve the optimum DMT for a multiantenna full-duplex single-relay two-hop network. Applying this result, a new achievable DMT is derived for the case of multiantenna half-duplex parallel relay network. Interestingly, it turns out that the DMT of the RS scheme is optimum for the case of multiantenna two parallel noninterfering half-duplex relays. Furthermore, random unitary matrix multiplication is shown to also improve the DMT of the nonorthogonal AF relaying scheme for the case of a multiantenna single relay channel. Finally, the general case of multiantenna full-duplex relay networks is studied. First, a new lower-bound is derived on its DMT using the RS scheme. Furthermore, maximum multiplexing gain of the network is also shown to be achievable by traditional amplify-forward relaying. The gain value is equal to the minimum vertex cut-set of the underlying graph of the network, which can be computed in polynomial time in terms of the number of network nodes.

단일 노드에서 다중 안테나를 사용하는 HD DDF Relay 프로토콜에 대한 DMT 분석

The diversity-multiplexing tradeoff (DMT) functions of three special half-duplex (HD) dynamic decode-and-forward (DDF) protocols with multiple antennas only at the source node, only at the destination node, and only at the relay node are analytically derived. The DMT functions of these three relay protocols are compared with one another and with those of the nonorthogonal amplify and forward (NAF) protocols.

Performance Comparison of Orthogonal and Non-orthogonal AF Protocols in Cooperative Relay Systems

For a single relay channel, we compare the capacity of two different amplify-and-forward (AF) protocols, which are orthogonal AF (OAF) and non-orthogonal AF (NAF). The NAF protocol has been proposed to overcome a significant loss of performance of OAF in the high spectral efficiency region, and it was also theoretically proved that NAF performs better than OAF in terms of the diversity-multiplexing tradeoff. However, existing results have been evaluated at the asymptotically high signal to noise ratio (SNR), thus the power allocation problem between the source and the relay was neglected. We examine which protocol has better performance in a practical system operating at a finite SNR. We also study where a relay should be located if we consider the power allocation problem. A notable conclusion is that the capacity performance depends on both SNR and power allocation ratio, which indicates OAF may perform better than NAF in a certain environment.

Multiple-Frame Precoding for NAF Relaying Over Rayleigh Fading Channels

This paper proposes a precoding scheme over multiple cooperative frames to exploit time and cooperative diversities over a non-orthogonal amplify-and-forward (NAF) half-duplex single-relay Rayleigh fading channel. Focusing on a coded system under the framework of bit interleaved coded modulation (BICM), we first derive a union bound on the bit error probability (BEP) of the proposed system. It is shown that the diversity gain function is the (Nf ·dH)th power of that of uncoded cooperative systems, where Nf is the number of precoded cooperative frames, and dH is the minimum Hamming distance of the outer code. An optimal class of precoders is then derived to optimize the asymptotic coding gain. It is then shown that the source should transmit a superposition of all symbols in the broadcasting phases while being silent in all cooperative phases for the best asymptotic performance. By further analyzing the first iteration performance, a design criterion is then developed to find optimal superposition angles for good convergence behavior. A pragmatic approach is then proposed to find good rotation angles. Analytical and simulation results show that the proposed scheme provides a significantly higher order of time and cooperative diversities and better coding gains than previous precoding schemes.

Multiple‐frame precoding and multi‐D mapping for BICM over ergodic NAF relay channels

ABSTRACTThis paper proposes the idea of precoding over multiple cooperative frames with multi‐dimensional (multi‐D) mapping for a bit interleaved coded modulation system over an ergodic non‐orthogonal amplify‐and‐forward (NAF) half‐duplex single‐relay channel. The benefits of multiple‐frame precoding and multi‐D labeling are analyzed in two different regions: the error‐floor region to exploit diversity and the turbo pinch‐off region for near‐capacity performance. In the error‐floor area, it is shown that the diversity gain function of the considered system is th power of that of uncoded cooperative systems, where Nf is the number of precoded cooperative frames and dH is the minimum Hamming distance of the outer code. To optimize the asymptotic coding gain, it is then shown that the source and relay must transmit orthogonally for best asymptotic performance. In the turbo pinch‐off region, we demonstrate that the proposed system concatenated with a simple outer binary code can be employed to achieve near‐capacity performance. Using union bounding techniques, we show that the optimal multi‐D labeling for NAF relaying shall maximize the average Euclidean distance between all pairs in the multi‐D rotated constellation whose labels differ in only 1 bit. The extrinsic information transfer charts are then used to match the outer code, the multi‐D mapping, and the precoder. It is demonstrated that the proposed system is also promising for NAF relaying in the turbo pinch‐off region, in the sense that it can operate below the achievable rate achieved by a conventional coded modulation scheme. Copyright © 2011 John Wiley & Sons, Ltd.

Bandwidth-Efficient Bit-Interleaved Coded Modulation Over NAF Relay Channels: Error Performance and Precoder Design

This paper investigates the error performance and precoder design for a bandwidth-efficient bit-interleaved coded modulation (BICM) system over a nonorthogonal amplify-and-forward (NAF) half-duplex single-relay channel. A tight union bound on the asymptotic bit error probability (BEP) is first derived for an arbitrary block length of 2 <i xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">N</i> , which corresponds to the case of using a 2 <i xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">N</i> × 2 <i xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">N</i> precoder. This bound provides a useful tool for predicting the error performance. Attention is then paid to the coded NAF system that uses a 2 × 2 precoder, where a closed-form expression of the bound is obtained. Based on this expression, an optimal class of 2 × 2 precoders with respect to the asymptotic performance is then developed. Unlike the optimal precoders that are designed for uncoded systems, the derived precoder indicates that the source only needs to send the superposition of the first symbol and the rotated version of the second symbol in the first time slot while being silent in the remaining slot to achieve the best asymptotic performance. For good convergence property, it is further shown that a rotation angle that maximizes the minimum Euclidean distance of the superposition constellation should be used. An optimal rotation angle is then analytically determined for various modulation schemes. Both analytical and simulation results show that the proposed precoders not only exploit full cooperative diversity but offer a significant coding gain over the optimal precoders for uncoded NAF systems as well.

Optimal Beamforming with Combining for the Non-Orthogonal Amplify-and-Forward (NAF) Protocol in Cooperative Communication Systems

This paper expands optimal beamforming with combining from the amplify-and-forward (AF) protocol to the non-orthogonal AF (NAF) protocol for environments with perfect channel state information (CSI) and a sum power constraint. After formulating an optimization problem for maximizing the signal-to-noise ratio (SNR), we propose optimal beamforming and combining vectors. After exhaustive comparison of the optimal beamforming weights with those for the previous results in and the characteristics of the beamforming weights are analyzed according to the protocols and the power constraints. Moreover, it is shown that the optimal combining vector is given succinctly with reduced computational complexity, and that the optimal beamforming could be accomplished using partial CSI. Simulation results verify that the proposed schemes enhance performance.

Jointly Optimal Precoder and Power Allocation for an Amplify-and-Forward Half-Duplex Relay System

This paper investigates the optimal precoder design and power allocation between the source and relay for a half-duplex single-relay non-orthogonal amplify-and-forward (NAF) system. Based on the pair-wise error probability (PEP) analysis, an optimal class of 2 × 2 precoders is first derived for the traditional power allocation scheme, where one-third of the system power is spent at the relay node, while two-thirds are spent at the source node. Different from optimal unitary precoders proposed earlier, the derived class of precoders indicates that the source should spend all its power transmitting a superposition of the symbols in the broadcast phase, while being silent in the cooperative phase, for optimal asymptotic performance. We then further address the problem of jointly optimal precoder and power allocation for the system under consideration. It is shown that the total power should be equally distributed to the source and the relay, and the source should again spend no power during the cooperative phase for the best asymptotic performance. Analytical and simulation results reveal that the proposed precoders not only exploit full cooperative diversity, but also provide significant coding gain over the optimal unitary precoders. For instance, a coding gain of around 1dB can be attained at the practical BER level of 10 − 5 for various modulation schemes.