Full Cooperative Diversity Research Articles

Cooperative communications with relay selection for wireless networks: design issues and applications

ABSTRACTRelay selection schemes for cooperative communications to achieve full cooperative diversity gains while maintaining spectral and energy efficiency have been extensively studied in a recent research. These schemes select only the best relay from multiple relaying candidates to cooperate with a communication link. In the present paper, we reviewed recently proposed cooperative communication protocols that integrate with relay selection mechanisms. The key design issues for relay selection mechanisms, for example, relaying candidate selection, optimal relay assignment, and cooperative transmission, were identified. We further discussed the challenges of optimal relay assignment in multi‐hop wireless sensor networks and presented the potential applications of cooperative communications with a relay selection in such networks. Future research directions were outlined, for example, the issues of service differentiation and system fairness in cooperative communication systems and the joint use of game theory and adaptive learning techniques in relaying candidate selection and optimal‐relay assignment mechanisms for efficient allocation of network resources. Copyright © 2011 John Wiley & Sons, Ltd.

Relay Selection Schemes for Precoded Cooperative OFDM and Their Achievable Diversity Orders

We investigate two different relay selection (RS) methods for precoded decode-and-forward (DF) cooperative OFDM systems: one scheme is to select the best relays for individual precoding groups (IPG-RS), and the other is to choose a single relay for the entire precoding groups (EPG-RS). We derive their diversity performances from the pairwise error probability (PEP) analysis, indicating that both schemes can achieve the full frequency and cooperative diversity with a proper choice of precoding size. Numerical results also show that IPG-RS can either reduce the decoding complexity or improve the error performance significantly as compared to existing solutions whereas EPG-RS has some performance loss as a result of less communication overhead.

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.

A General Diversity Gain Function and Its Application in Amplify-and-Forward Cooperative Networks

The diversity gain function is a unified metric for the asymptotic error performance of wireless communication systems. In this correspondence, we propose a theorem that relates the diversity gain function and the coding gain to the probability density function of the instantaneous signal-to-noise ratio (SNR) at the origin. It provides a general framework for analyzing the asymptotic reliability of wireless communication systems in the presence of fading. As two applications of the proposed theorem, we evaluate two relay selection schemes in fixed-gain amplify-and-forward (AF) cooperative networks. The results show that even if not all channel state information is available at the destination, fixed-gain AF relay selection schemes can still achieve full cooperative diversity and near optimal error performance. This is an outstanding merit that instantaneous-gain AF relay selection schemes do not possess [Y. Jing and H. Jafarkhani, “Single and multiple relay selection schemes and their achievable diversity orders,” IEEE Trans. WIRELESS COMMUN., vol. 8, no. 3, pp. 1414-1423, Mar. 2009].

Full Diversity Space-Frequency Codes for Frequency Asynchronous Cooperative Relay Networks with Linear Receivers

In this paper, we propose a family of distributed space-frequency codes (SFCs) for frequency asynchronous cooperative relay networks with multiple carrier frequency offsets (CFOs) and flat fading channels. The codes have the special structures that the columns of each code matrix can be divided into several orthogonal groups and each group is stacked by several sub-blocks with Toeplitz structure. These codes possess two interesting properties: a) Even under the frequency-asynchronous scenario, the codes can , namely, if R relay nodes participate the cooperation adopting the proposed SFCs, then at the destination node, the achievable diversity order is R; b) Only , such as zero-forcing (ZF) and minimum mean square error (MMSE) receivers, are required to collect the full cooperative diversity, instead of the maximum likelihood (ML) detector as utilized in most existing STC (SFC) schemes. The codes in this family have different symbol rates, orthogonality and performances for different numbers of relay nodes, which can be adjusted by choosing different design parameters. It is shown that frequency-reversal SFC (FR-SFC), and frequency-shift SFC (FS-SFC) proposed in previous papers are only two special members of the code family, and new SFCs outperforming both of them are proposed.

A Linear Analog Network Coding for Asynchronous Two-Way Relay Networks

Time asynchronism is a practical issue need to be addressed for a general distributed two-way relay network, where two terminal nodes exchange information through multiple spatial-separated relay nodes. In this letter, we propose an analog network coding (ANC) scheme for a time asynchronous two-way relay network. In the proposed scheme, each relay node linearly transforms the received mixed asynchronous signals in the first time-slot by a Toeplitz matrix, and then broadcasts them back to the terminals in the second time-slot. A sufficient condition is derived for the proposed ANC to achieve full cooperative diversity using only linear receivers at the terminal nodes, such as zero-forcing (ZF), or minimum mean square error (MMSE) receivers, with any delay profiles of the timing errors. The decoding of the proposed ANC scheme is computationally efficient and the symbol rate can approach 1, when the coding block length is sufficiently large compared to the number of relay nodes R and the timing errors.

Fast Kalman Equalization for Time-Frequency Asynchronous Cooperative Relay Networks With Distributed Space-Time Codes

Cooperative relay networks are inherently time and frequency asynchronous due to their distributed nature. In this correspondence, we propose a transceiver scheme to combat both time and frequency offsets for cooperative relay networks with multiple relay nodes. At the relay nodes, a distributed linear convolutive space-time coding is adopted, which has the following advantages: 1) Full cooperative diversity can be achieved using a minimum mean square error (MMSE) or MMSE decision feedback equalizer (MMSE-DFE) detector, instead of a maximum-likelihood receiver when only time asynchronism exists. 2) The resultant equivalent channel possesses some special structure, which can be exploited to reduce the equalization complexity at the destination node. By taking full advantage of such a special structure, fast Kalman equalizations based on linear MMSE and MMSE-DFE are proposed for the receiver, where the estimation of the state vector (information symbols) can be recursively taken and become very computationally efficient, compared with direct equalization. The proposed scheme can achieve considerable diversity gain with both time and frequency offsets and applies to frequency-selective fading channels.

Multigroup ML Decodable Collocated and Distributed Space-Time Block Codes

In this paper, collocated and distributed space-time block codes (DSTBCs) which admit multigroup maximum-likelihood (ML) decoding are studied. First, the collocated case is considered and the problem of constructing space-time block codes (STBCs) which optimally tradeoff rate and ML decoding complexity is posed. Recently, sufficient conditions for multigroup ML decodability have been provided in the literature and codes meeting these sufficient conditions were called Clifford unitary weight (CUW) STBCs. An algebraic framework based on extended Clifford algebras (ECAs) is proposed to study CUW STBCs and using this framework, the optimal tradeoff between rate and ML decoding complexity of CUW STBCs is obtained for few specific cases. Code constructions meeting this tradeoff optimally are also provided. The paper then focuses on multigroup ML decodable DSTBCs for application in synchronous wireless relay networks and three constructions of four-group ML decodable DSTBCs are provided. Finally, the orthogonal frequency-division multiplexing (OFDM)-based Alamouti space-time coded scheme proposed by Li-Xia for a 2-relay asynchronous relay network is extended to a more general transmission scheme that can achieve full asynchronous cooperative diversity for arbitrary number of relays. It is then shown how differential encoding at the source can be combined with the proposed transmission scheme to arrive at a new transmission scheme that can achieve full cooperative diversity in asynchronous wireless relay networks with no channel information and also no timing error knowledge at the destination node. Four-group decodable DSTBCs applicable in the proposed OFDM-based transmission scheme are also given.

Shift-orthogonal space-time block codes

In this paper, we present a new class of spacetime block code, called shift-orthogonal space-time block codes (SOSTBC), which can maintain orthogonality (hence symbolwise linear decoding) in asynchronous wireless relay networks, under both amplify-and-forward (AF) and decode-and-forward (DF) relaying schemes. The definitions, systematic constructions and properties of SOSTBC are presented. We also present some simulation results to illustrate its effectiveness in achieving full asynchronous cooperative diversity.

Decorrelate-and-forward relaying scheme for multiuser wireless code division multiple access networks

Decorrelate-and-forward relaying scheme for wireless synchronous code division multiple access (CDMA) networks where multiple sources communicate with a destination supported by multiple relays in flat Rayleigh fading channels is considered. By exploiting equicorrelated spreading sequences, a simple near–far resistant decorrelator together with a beamforming scheme at each relay and the maximal ratio combiner (MRC) at the destination are developed in order to achieve the full cooperative diversity for every source. Different from the case with a single source, the beamforming design in multiple-source networks needs to take into account the amount of transmit power each relay spends to forward the signals from the sources. As such, the authors also propose a novel power allocation scheme to improve the fairness among the sources in terms of the instantaneous signal-to-noise ratio. Simulation results demonstrate the effectiveness of the proposed solution.

Regenerative cooperative diversity with path selection and equal power consumption in wireless networks

Recently developed cooperative protocol with distributed path selection provides a simple and practical means of achieving full cooperative diversity in wireless networks. While the best path selection method can significantly improve bit error rate (BER) performance, it may cause unequal power consumption among relay nodes, which may reduce the lifetime of energy-constrained networks. A path selection method under the equal power constraint has been developed for the amplifyand- forward (AF) protocol, but there is no such method for the decode-and-forward (DF) protocol. In this paper, we develop a distributed path selection method with an equal power constraint for the DF protocol. We also analyze the BER performance of our path-selection method. Numerical results demonstrate that the proposed method can guarantee equal power consumption, while achieving full diversity as the best path selection method and providing significant performance gain relative to noncooperative communication.

Space-time cooperative diversity scheme using full feedback

This article proposes a new space-time cooperative diversity scheme called full feedback-based cooperative diversity scheme (FFBCD). In contrast to the conventional adaptive space-time cooperative diversity schemes that utilize the feedback from only the destination node, the new scheme utilizes the feedback from both the destination node and the cooperation node. With the feedback from the destination node, the occasional successful reception of the destination node in the information distribution stage can be detected, thus avoiding unnecessary retransmissions in the information delivery stage. The feedback from the cooperation node indicates the receiving state of the cooperation node in the information distribution stage, and the source node and the cooperation node will not perform cooperative retransmission during the information delivery stage unless the cooperation node is received successfully in the information distribution stage. In this way the new scheme can reduce the number of transmission attempt and improve the channel utilization. The expressions of the average number of transmission attempt are given. Numerical approximations and simulation results both show that the new scheme performs better than the non-cooperative scheme and the conventional adaptive space-time cooperative diversity scheme.

Distributed space-frequency codes for cooperative communication systems with multiple carrier frequency offsets

In cooperative communications, due to the distributed nature, multiple different carrier frequency offsets (CFOs) may occur and make the channel time-varying. It is hard for the receiver to compensate multiple CFOs from multiple relay nodes simultaneously. Thus, the conventional space-time codes to collect cooperative diversity for co-located multi-input multi-output (MIMO) systems may not be applied directly. In this paper, we consider the cooperative transmission with multiple CFOs when the channels from relay nodes to destination node are flat (frequency-non-selective) fading. We approximate a flat fading channel with CFO as a block time-invariant intersymbol-interference (ISI) channel in the frequency domain. We then propose two distributed space-frequency codes (SFC) for such ISI channels in the frequency domain to achieve the cooperative full spatial diversity, where the space-frequency coding concept is different from the one in the literature and also has a different role. One is called frequency-reversal SFC and the other is called frequency-domain linear convolutive SFC. Furthermore, we show that, with only linear receivers, such as zero-forcing (ZF) and minimum mean square error (MMSE) receivers, our codes achieve the full cooperative diversity.

Computationally efficient equalization for asynchronous cooperative communications with multiple frequency offsets

In cooperative communications, time and frequency synchronization is an important issue needed to be addressed in practice. Due to the nature of cooperative communications, multiple frequency offsets may occur and the traditional frequency offset compensations may not apply. For this problem, equalization for the time-varying channel has been used in the literature, where the equalization matrix inverse needs to be retaken every symbol. In this paper, we propose computationally efficient minimum mean square error (MMSE) and MMSE decision feedback equalizers (MMSE-DFE) when multiple frequency offsets are present, where the equalization matrix inverses do not need to be retaken every symbol. Our proposed equalization methods apply to linear convolutively coded cooperative systems, where linear convolutive space-time coding is used to achieve the full cooperative diversity when there are timing errors from the cooperative users or relay nodes, i.e., asynchronous cooperative communication systems.

Distributive High-Rate Space–Frequency Codes Achieving Full Cooperative and Multipath Diversities for Asynchronous Cooperative Communications

In user-cooperative communications, relay nodes are usually asynchronous. By realizing that the processing in the frequency domain is insensitive to the errors in the time domain, Mei and Shin recently applied the space-time-coded orthogonal frequency-division multiplexing (OFDM) technique to achieve full cooperative diversity for asynchronous cooperative communications, where orthogonal space-time block codes (particularly the Alamouti code) were used for relay nodes. In this paper, we consider asynchronous cooperative communications, and the channels from one node to another node are frequency-selective fading. We propose a high-rate space-frequency coding method and prove that it can achieve both cooperative and multipath diversities. Simulation results are shown to verify the performance of the constructed codes.

Algebraic distributed differential space-time codes with low decoding complexity

The differential encoding/decoding setup introduced by Kiran et al, Oggier-Hassibi and Jing-Jafarkhani for wireless relay networks that use codebooks consisting of unitary matrices is extended to allow codebooks consisting of scaled unitary matrices. For such codebooks to be usable in the Jing-Hassibi protocol for cooperative diversity, the conditions involving the relay matrices and the codebook that need to be satisfied are identified. Using the algebraic framework of extended Clifford algebras, a new class of Distributed Differential Space-Time Codes satisfying these conditions for power of two number of relays and also achieving full cooperative diversity with a low complexity sub-optimal receiver is proposed. Simulation results indicate that the proposed codes outperform both the cyclic codes as well as the circulant codes. Furthermore, these codes can also be applied as Differential Space-Time codes for noncoherent communication in classical point to point multiple antenna systems.

Full-rate distributed space-time codes for cooperative communications

A full-rate distributed space-time (ST) code design is proposed for amplify-and-forward cooperative wireless channels. By employing a signal space diversity technique at the source node and a unique signature vector at each relay node, the proposed distributed ST codes can achieve full cooperative diversity and full rate. The achievable diversity gain is shown to be M + 1, where M is the number of relay nodes. Optimal power allocation is also proposed to maximize the coding gain under a total power constraint.

Space-time trellis codes with asynchronous full diversity up to fractional symbol delays

A family of space-time trellis codes that are associated with shift-full-rank (SFR) generator matrices and thus achieve asynchronous full cooperative diversity order has been recently proposed, where it is assumed that the delays occurring at the relays must be integer multiples of the symbol duration. In this letter, we consider a cooperative communication system in which the delays can be fractional (rational) symbol durations and, correspondingly, multiple sampling per symbol interval is used at the destination. We show that the previously proposed space-time trellis codes can still achieve asynchronous full diversity in fractional symbol delay scenarios if their generator matrices satisfy a relaxed definition of SFR matrices, namely, q-shift-full-rank (q-SFR) matrices, and therefore, more designs for their generator matrices than the SFR ones become available. Furthermore, compared with the applications in the system with integer symbol delays, the decoding complexity of the optimal Viterbi algorithm for the codes does not increase and some performance gains can be observed in the system with fractional symbol delays.

A Family of Distributed Space-Time Trellis Codes With Asynchronous Cooperative Diversity

In current cooperative communication schemes, to achieve cooperative diversity, synchronization between terminals is usually assumed, which may not be practical since each terminal has its own local oscillator. In this paper, based on the stack construction proposed by Hammons and El Gamal, we first construct a family of space-time trellis codes for BPSK modulation scheme that is characterized to possess the full cooperative diversity order without the synchronization assumption. We then generalize this family of the space-time trellis codes from BPSK to higher order QAM and PSK modulation schemes based on the unified construction proposed by Lu and Kumar. Some diversity product properties of space-time trellis codes are studied and simplified decoding methods are discussed. Simulation results are given to illustrate the performance of the newly proposed codes

Shift-full-rank matrices and applications in space-time trellis codes for relay networks with asynchronous cooperative diversity

To achieve full cooperative diversity in a relay network, most of the existing space-time coding schemes require the synchronization between terminals. A family of space-time trellis codes that achieve full cooperative diversity order without the assumption of synchronization has been recently proposed. The family is based on the stack construction by Hammons and El Gamal and its generalizations by Lu and Kumar. It has been shown that the construction of such a family is equivalent to the construction of binary matrices that have full row rank no matter how their rows are shifted, where a row corresponds to a terminal (or transmit antenna) and its length corresponds to the memory size of the trellis code on that terminal. We call such matrices as shift-full-rank (SFR) matrices. A family of SFR matrices has been also constructed, but the memory sizes of the corresponding space-time trellis codes (the number of columns of SFR matrices) grow exponentially in terms of the number of terminals (the number of rows of SFR matrices), which may cause a high decoding complexity when the number of terminals is not small. In this paper, we systematically study and construct SFR matrices of any sizes for any number of terminals. Furthermore, we construct shortest (square) SFR (SSFR) matrices that correspond to space-time trellis codes with the smallest memory sizes and asynchronous full cooperative diversity. We also present some simulation results to illustrate the performances of the space-time trellis codes associated with SFR matrices in asynchronous cooperative communications.