Multiple Relay Systems Research Articles

Performance analysis of multiple relay cooperative communication over generalized κ–μ and η–μ fading channels

In this paper, we derive the closed form expressions for symbol error rate (SER) of a multiple relay cooperative communication system using selective decode-and-forward protocol over generalized κ–μ and η–μ independent identically distributed fading channels for different modulation schemes. We also derive the exact expression of SER for non-coherent detection and an approximate expression of SER for coherent detection. At the destination, we employ the maximal ratio combining to provide diversity. The final expressions of SER are represented in terms of moment generating function which is a combination of elementary functions. We also perform the Monte Carlo simulations by assuming different channels and by varying the number of relays to validate the analytical results.

Linear Relaying Design for Spectrum Sharing Non-regenerative MIMO Cognitive Multiple-Relay Systems

In this paper, we study optimal precoding matrix for spectrum sharing multiple-input multiple-output (MIMO) cognitive multiple-relay systems. Our aim is to maximize the system capacity subject to the total relay transmit power constraint and the interference power constraint at the primary user. For general case, all the nodes have multiple antennas. The precoder design problem is a non-convex problem. Currently there is no global optimal solution for it. We propose a suboptimal algorithm in which we first transform the original precoder design problem to a unitary matrix constrained problem. And then, we develop a modified Riemannian steepest descent algorithm (MRSDA) to solve it. For the special case that the secondary user has a single antenna and other nodes have multi-antennas, we propose an optimal solution based on rank-one decomposition theorem to transform the original problem into a semidefinite programming. Simulation results demonstrate the effectiveness of the proposed precoding matrix design algorithms.

The Diversity Gains of Amplify-and-Forward Relay System with Frequency Selective Channels

The diversity gains of amplify-and-forward (AF) relay system with frequency selective channels are discussed. The orthogonal frequency division multiplexing (OFDM) is applied to overcome the inter-symbol interference. The diversity gains are presented for single and multiple relay systems with detailed derivations.

Interference-Constrained Optimal Power-Adaptive Amplify-and-Forward Relaying and Selection for Underlay Cognitive Radios

In an underlay cognitive radio (CR) system, a secondary user can transmit when the primary is transmitting but is subject to tight constraints on the interference it causes to the primary receiver. Amplify-and-forward (AF) relaying is an effective technique that significantly improves the performance of a CR by providing an alternate path for the secondary transmitter's signal to reach the secondary receiver. We present and analyze a novel optimal relay gain adaptation policy (ORGAP) in which the relay is interference aware and optimally adapts both its gain and transmit power as a function of its local channel gains. ORGAP minimizes the symbol error probability at the secondary receiver subject to constraints on the average relay transmit power and on the average interference caused to the primary. It is different from ad hoc AF relaying policies and serves as a new and fundamental theoretical benchmark for relaying in an underlay CR. We also develop a near-optimal and simpler relay gain adaptation policy that is easy to implement. An extension to a multirelay scenario with selection is also developed. Our extensive numerical results for single and multiple relay systems quantify the power savings achieved over several ad hoc policies for both MPSK and MQAM constellations.

Optimal diversity multiplexing tradeoff for opportunistic relaying coded cooperation protocols with quantised channel state information feedback

A cooperative multiple relay system is considered in this study which exploit opportunistic relaying (OR)-based protocol with coded cooperation approach. For the considered system, the optimal diversity multiplexing tradeoff (DMT) is determined in different scenarios including either considering the source node as a potential relay or not. The study is then extended to the case where the quantised channel state information (QCSI) feedback is considered. In particular, an OR-based protocol with QCSI at the source node is presented. It is shown that the QCSI feedback linearly improves the DMT performance. In addition, it is proved that the role of QCSI feedback to improve DMT performance is higher than that of cooperative relays.

Robust joint optimization for MIMO AF multiple-relay systems with correlated channel uncertainties

In the paper, robust joint optimization of the source/relays precoders and destination equalizer is proposed for non-regenerative dual-hop multiple-input multiple-output (MIMO) amplify-and-forward (AF) multiple-relay systems with correlated channel uncertainties. By taking the imperfect channel state information (CSI) into consideration, the robust transceiver/relays joint optimization is developed based on the minimum mean-squared error (MMSE) criterion under individual power constraints at the source and relays. The optimization problem of precoding and amplifying matrices under power constraints belongs to neither concave nor convex so that a nonlinear matrix-form conjugate gradient (MCG) algorithm is applied to explore local optimal solutions. Simulation results illustrate that the robust transceiver/relays joint architecture for an AF-MIMO multiple-relay system outperforms the non-robust transceiver/relays design.

Multiple Relay Selection for Delay-Limited Applications

A multiple relay selection system model that implements the decode-and-forward mode is investigated. All communication nodes are assumed to be equipped by multiple antennas. Furthermore, lattices space-time coded multiple-input multiple-output half duplex channel is applied. The main goal is to increase the throughput of the system by selecting multiple number of relays. The selection criteria depends on the maximum decoding delay at relays where the system implements a decoding time-out algorithm at each relay. This leads to a significant saving in the overall system power consumptions and attempts to solve the relays synchronization problem. All results are presented using numerical simulations.

Precoding Design of MIMO AF Two-Way Multiple-Relay Systems

The precoding joint optimization is proposed for multiple-input multiple-output (MIMO) two-way multiple-relay systems with amplify-and-forward (AF) strategy in correlated fading channels. The terminal transceivers and relay precoding matrices are designed based on the minimum mean square error (MMSE) criterion. This combined design of precoding matrices and equalizers under power constraints belongs to neither concave nor convex so that the nonlinear matrix-form conjugate gradient (MCG) algorithm is developed to acquire the local optimal solutions. Simulation results demonstrate that the proposed precoding joint architecture possesses a superior bit-error-rate (BER) performance and a faster convergence rate.

Diversity Analysis of Randomized Linear Dispersion Codes in a Half-Duplex Amplify-and-Forward Multiple-Relay System

A point-to-point multiple-relay communication system with half-duplex constraints is considered. The relays operate under the amplify-and-forward paradigm and implement a linear dispersion distributed space-time code with randomized dispersion matrices of independent and identically distributed entries. The large-signal-to-noise-ratio behavior of the asymptotically large deterministic system is studied for both the optimum (maximum likelihood) receiver and the linear minimum mean squared error (LMMSE) receiver. The diversity order of the system is shown to have a strong dependence on the aspect ratio of the linear dispersion matrices. More specifically, when the linear dispersion matrices are sufficiently tall, both receivers achieve the maximum diversity order, i.e., the total number of relays plus one. Conversely, when the linear dispersion matrices are fat (in the sense that relays linearly compress the information received from the source), the optimum receiver is shown to achieve an asymptotic diversity order of two, whereas the LMMSE receiver is totally unable to exploit the available spatial diversity.

다중 안테나 다중 중계 시스템을 위한 가중치 대각화 기반의 저 복잡도 전력 할당 기법

본 논문에서는 증폭 후 재전송 프로토콜 기반의 다중 안테나 다중 중계 시스템에서 저 복잡도의 전력 할당 기법을 제안한다. 기존의 다중 안테나 전처리 기법이 복소수로 구성 된 꽉 찬 행렬을 전처리 필터로 사용하였다면, 제안 하는 기법은 각 중계 노드에서 안테나 별 전력으로 구성 된 실수 대각 행렬을 전처리 필터로 사용한다고 볼 수 있다. 추가적으로 복소수 꽉 찬 행렬로 유효 채널을 대각화 하지 못함에서 발생하는 오차를 감소시키기 위해 가중치 벡터를 각 스트림에 적용시켜 안테나 수와 상관없이 낮은 복잡도로 최적 성능에 근접한 성능을 얻을 수 있다. 마지막으로 모의실험을 통해 제안하는 기법이 상호정보량 측면에서 기존의 기법들보다 우수함을 보인다.

Source/relays/destination combined MMSE-based optimization for AF-MIMO multiple-relay systems with correlated channel uncertainties

In this paper, source/relays-precoders and destination-equalizer combined optimization are proposed as a dual-hop amplify-and-forward (AF) multiple-input multiple-output (MIMO) multiple-relay system with Gaussian random and correlated channel uncertainties in both hops. Taking correlated channel uncertainties into account, a robust transceiver joint optimization design is developed based on the minimum mean-squared error (MMSE) criterion under individual power constraints at the source and the relays. Simulation results illustrate that the robust multiple relays/transceiver joint design architecture for an AF-MIMO system equipped with multiple relays substantially outperforms a nonrobust transceiver design that assumes estimated channels as actual channels.

Joint Network-Channel Coding with Rateless Code over Multiple Access Relay System

In this paper, we consider an asymmetric time-division multiple access relay system consisting of two sources, one relay and one destination, where the channel conditions and message lengths of the two sources are allowed to be different. To enhance the link robustness and the system throughput, joint network-channel coding (JNCC) is employed with a specially designed rateless code which conducts both the channel coding and network coding simultaneously. In particular, at the sources, messages are rateless coded and then broadcasted to the relay and destination. While at the relay, a novel two-dimensional (2-D) LT code is proposed, which jointly encodes the precoded message bits of the two sources using a 2-D degree profile and at the meantime completes the network coding inherently. Interestingly, the proposed scheme can be degraded to several conventional JNCC schemes based on rateless coding. To further approach the theoretical limit, the corresponding degree profiles implemented at both sources and the relay are jointly designed based on the extrinsic information transfer (EXIT) function analysis. Simulations show that our proposed JNCC scheme with the optimized degree profiles outperforms other JNCC schemes with the conventional profiles both on the BER and throughput performances.

Cooperative Demodulation for Multiple Access Relay Systems with Network Coding

Cooperative Demodulation for Multiple Access Relay Systems with Network Coding

Modified K-best breadth-first assisted antenna selection for dual-hop MIMO AF multiple-relay systems in correlated channels

An efficient antenna-pair selection scheme is proposed for a non-regenerative dual-hop amplify-and-forward (AF) multiple-input multiple-output (MIMO) multiple-relay system in which multiple antennas are placed at each node over correlated fading channels in the paper. The design of multiple-relay antenna-pair selection can be transformed into a modified K-best tree search structure based on the signal-to-noise ratio (SNR) maximization criterion. This two-level antenna selection strategy selects a subset of antenna pairs from available relays based on the concept of the K-best breadth-first search mechanism in conjunction with the harmonic mean and norm metrics subject to (s.t.) either optimal- or equal-power allocation constraints across the activated antenna pairs. Consequently, the use of the proposed antenna selection achieves a substantial saving in system hardware complexity of the multiple radio frequency (RF) chains associated with multiple antennas without compromising the symbol-error-rate (SER) performance when compared to existing antenna selection schemes for half-duplex AF MIMO relay networks.

Superposition Coding and Analysis for Cooperative Multiple Access Relay System

The conventional straightforward relaying scheme named decode-and-forward (DF) protocol is used at relay to decode the data received from source and forward the decoded data to the destination to improve the spatial diversity gain. Although it is a simple scheme, the total resource efficiency is low for multiple sources. Superposition coding has been known as a spectral efficient technique in wireless networks. However, when it is applied to the uplink multiple access relay systems, it suffers from performance degradation caused by the power allocation between the symbols of multiple sources. In this paper, we propose to remedy this problem by using hierarchical modulation at the source node and superposition coding at the relay node to enhance the bit energy. We investigate how hierarchical modulation can be incorporated and optimized with superposition coding. Specially, we discuss the capacity behavior of the proposed scheme and compare with the baseline, namely the capacity behavior of the existing DF scheme and the capacity behavior of the superposition coding. Our results are encouraging in that superposed hierarchical modulation significantly improves the better block error rate and capacity performance in multiple access relay channels.

Precoding and decoding design for two-way MIMO AF multiple-relay system

In this paper, a joint precoding and decoding design scheme is proposed for two-way Multiple-Input Multiple-Output (MIMO) multiple-relay system. The precoding and decoding matrices are jointly optimized based on Minimum Mean-Square-Error (MMSE) criteria under transmit power constraints. The optimization problem is solved by using a convergent iterative algorithm which includes four sub-problems. It is shown that due to the difficulty of the block diagonal nature of the relay precoding matrix, sub-problem two cannot be solved with existing methods. It is then solved by converting sub-problem two into a convex optimization problem and a simplified method is proposed to reduce the computational complexity. Simulation results show that the proposed scheme can achieve lower Bit Error Rate (BER) and larger sum rate than other schemes. Furthermore, the BER and the sum rate performance can be improved by increasing the number of antennas for the same number of relays or increasing the number of relays for the same number of antennas.

Weighted-Sum-Rate Maximization in Certain Half-Duplex Cooperative Systems

In half-duplex cooperative systems the problem of finding the jointly optimal power and channel resource allocation that maximizes the weighted sum rate (WSR) can be difficult to solve. Algorithms to solve that problem are provided herein for two classes of orthogonal half-duplex systems. For a class of systems in which the set of rates that can be achieved without time sharing is convex, the WSR problem is decomposed into a direct search in which a target rate problem is solved at each step. The target rate problem involves maximizing one of the rates subject to target values for the others, and can often be efficiently solved. For a subclass of those systems, the notion of perspective is used to transform the WSR problem into an efficiently-solvable convex optimization problem. Numerical examples involving a multiple access relay system and a pairwise cooperation scheme show that joint optimization can result in significantly larger weighted sum rates than optimization over the powers alone with a fixed channel resource allocation.

Cooperative multiple relay system for frequency selective environment: outage analysis and power allocation

AbstractIn this paper, we propose a novel cooperative relaying scheme with multiple relays for frequency selective wireless environment. In our proposed scheme, the frequency selective wireless channel is divided into flat fading sub‐channels. Cooperative relaying is then employed over each sub‐channel to improve the system diversity order. We then investigate the asymptotic behavior of the outage probability and show that the proposed scheme achieves full diversity order in both amplify and forward (AF) and adaptive decode and forward (ADF) relaying scenarios. Furthermore, we propose a power allocation strategy to minimize the system outage probability. Simulation results confirm our analysis and show that the proposed power allocation method outperforms uniform power allocation. Copyright © 2010 John Wiley & Sons, Ltd.

Differentially Amplitude- and Phase-Encoded QAM for Amplify-and-Forward Multiple-Relay Systems

This paper studies the differentially amplitude- and phase-encoded quadrature amplitude modulation (DAPE QAM) transmission for the amplify-and-forward multiple-relay system using the fixed-relay-gain mechanism over independent Rician and Nakagami- <i xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">m</i> fading links. In the multiple-relay system, the destination collects signals from the source and multiple relays in distinct phases. Operating over two successively received symbols, an equal-gain combining (EGC) receiver and a weighted-gain combining (WGC) receiver are developed to noncoherently combine received signals from direct and multiple-relay links and thereby achieve cooperative diversity. The EGC receiver operates without any link-side information, whereas the knowledge of average signal-to-noise ratios (SNRs) on source-relay and relay-destination links is required for realizing the WGC receiver. Based on Beaulieu's convergent series approach, efficient computation formulas of the bit error probability (BEP) upper bounds are derived for both receivers. Numerical and simulation results on 16- and 64-point signal constellations show that the WGC receiver exhibits better BEP performance than the EGC receiver when link SNR estimates are not significantly large in error. The WGC receiver for DAPE QAM is also shown to outperform, in terms of BEP, the conventional receiver for differentially detecting the differential phase-shift keying modulation signal with the same constellation size.

Layered Capacity-Based Relay-and-Antenna Joint Selection for MIMO-AF-Multiple-Relay Systems in Correlated Channels

A computationally efficient two-stage greedy capacity maximization (GCM) relay-and-antenna joint selection is proposed for a dual-hop nonregenerative amplify-and-forward (AF) multiple-input multiple-output (MIMO) multiple-relay system with multiple antennas equipped at each node in correlated fading channels. This modified GCM (MGCM) antenna selection strategy selects a subset of antenna pairs from available relays based on the concept of channel capacity maximization subject to an optimal power allocation constraint across the activated antenna pairs. In order to reduce system hardware complexity, antenna selection schemes are performed at the destination node as well. Finally, simulations are conducted to compare the channel capacity of the proposed two-layered antenna selection technique with other existing antenna selection algorithms for half-duplex AF-MIMO multiple-relay systems.