Distributed Space-time Coding Research Articles

Physical layer network coding for wireless multi-way relaying with finite signal sets

In this survey article, we consider the wireless multi-way relaying scenario, in which there is no direct link connecting the nodes and multiple nodes exchange information with the help of a relay node. In a multi-way relaying scenario, if several nodes transmit simultaneously, due to the superposition nature of the wireless channel, multiple access interference results at the relay node, which can potentially degrade the performance. However, recent results on physical layer network coding for the two-way relay channel with finite signal sets have shown that the multiple access interference can be effectively tackled by a proper choice of transmission schemes at the nodes. The effect of the multiple access interference is the presence of signal set dependent deep channel fade conditions. For the two-way relay channel, the harmful effect of the deep channel fade conditions have been shown to be avoidable using two techniques: (i) adaptively changing the network coding maps used at the relay node, a process called denoising, which eliminates the harmful effect of the additive noise when a deep channel fade condition occurs (ii) eliminating the occurrence of the deep channel fade conditions at the transmitting nodes itself without any CSIT by Distributed Space Time Coding. We survey the results based on these two schemes for the two-way and three way relaying scenarios and point out some problems which remain unsolved. Towards the end, we discuss about the extension of the schemes developed for the two-way relaying scenario to the multi-way relaying scenario.

Diversity Analysis of Analog Network Coding with Multi-User Interferences

Network coding can improve the bandwidth efficiency by letting multiple users share the relay channels. However, the multi-user interferences (MUI) at the intended receiver may degrade the diversity performances. So in this work, we study several diversity strategies for the multiple-access relay channel and analyze the impact of MUI on the diversity performances. Both the variable gain relaying (VGR) and the fixed gain relaying (FGR) are considered, where the relay nodes are subject to instantaneous power constraints and long-term power constraints, respectively. We first develop a Min-Max relay selection strategy and prove that full diversity can be achieved. Next, the distributed space-time block coding (DSTBC) and the diagonal distributed space-time coding (DDSTC) are studied. For DSTBC, we show that full diversity can be achieved by FGR, but the diversity of VGR is upper bounded by \min (L+1, K+1), where L and K are the number of relays and users, respectively. For single-user systems, we then develop a selective DSTBC-VGR scheme to recover the diversity loss by adaptively allocating the relay power. Finally for DDSTC, we show that both FGR and VGR can achieve full diversity, and the optimum code design criterion is to maximize the minimum product distance.

Non-coherent distributed space–time coding techniques for two-way wireless relay networks

To overcome the overhead involved with channel estimation, several non-coherent distributed space–time coding (DSTC) strategies for two-way wireless relay networks (TWRNs) using the amplify-and-forward and the decode-and-forward protocol have been recently proposed that do not require channel state information (CSI) at any node to decode the information symbols. In this paper, novel differential DSTC strategies for TWRNs using the two- and three-phase protocol are proposed. In our transmission schemes, the relays do not waste power to transmit information known at the respective destination nodes. This is achieved by combining the symbols from both terminals received at the relays into a single symbol of the unaltered constellation. Furthermore, in our strategies, the direct link between the communicating terminals can be naturally incorporated to further improve the diversity gain. Simulations show a substantially improved performance in terms of bit error rate (BER) of the proposed strategies as compared to the existing strategies.

Two- and four-relay selection schemes for application in interference limited legacy networks

The limiting effect of multi-user interference from an adjacent cell upon the relays used for cooperative transmission is considered in the context of legacy networks which adopt max(min(·,·)) type relay selection policies. We extend previous work which considered single relay selection to the selection of two or four such relays, as is required in distributed space–time coding. We obtain new analytical expressions for outage probability over Rayleigh frequency flat fading channels for two signal-to-noise ratio regimes. We confirm by simulation that such a relay selection scheme has robustness to relay selection feedback error and outperforms a single relay selection scheme.

Distributed Space-Time Coding for Full-Duplex Asynchronous Cooperative Communications

In this paper, we propose two distributed linear convolutional space-time coding (DLC-STC) schemes for full-duplex (FD) asynchronous cooperative communications. The DLC-STC Scheme 1 is for the case of the complete loop channel cancellation, which achieves the full asynchronous cooperative diversity. The DLC-STC Scheme 2 is for the case of the partial loop channel cancellation and amplifying, where some loop signals are used as the self-coding instead of treated as interference to be directly cancelled. We show this scheme can achieve full asynchronous cooperative diversity. We then evaluate the performance of the two schemes when loop channel information is not accurate and present an amplifying factor control method for the DLC-STC Scheme 2 to improve its performance with inaccurate loop channel information. Simulation results show that the DLC-STC Scheme 1 outperforms the DLC-STC Scheme 2 and the delay diversity scheme if perfect or high quality loop channel information is available at the relay, while the DLC-STC Scheme 2 achieves better performance if the loop channel information is imperfect.

Training and Decodings for Cooperative Network with Multiple Relays and Receive Antennas

In this paper, channel training and coherent decodings under channel estimation error are investigated for relay networks with one single-antenna transmitter, R single-antenna relays, and one R-antenna receiver. A two-stage training scheme is proposed to estimate both the relay-receiver and the transmitter-relay channels at the receiver, which are commonly required in amplify-and-forward (AF) relay networks. We use distributed space-time coding (DSTC) for data transmission and investigate the effect of channel estimation errors on network performance. Two coherent decodings are considered: mismatched decoding in which channel estimations are treated as if perfect, and matched decoding in which estimation error is taken into consideration. We show that for full diversity, with mismatched decoding, at least 3R symbol intervals are required for training; while with matched decoding, R+2 symbol intervals for training are enough. The complexities of the decoding schemes are investigated. To achieve a balance between performance and complexity, an adaptive decoding scheme is proposed. Simulated error rates are shown to justify the analytical results.

Distributed Space Time Coding for Wireless Two-Way Relaying

We consider the wireless two-way relay channel, in which two-way data transfer takes place between the end nodes with the help of a relay. For the Denoise-And-Forward (DNF) protocol, it was shown by Koike-Akino et. al. that adaptively changing the network coding map used at the relay greatly reduces the impact of Multiple Access interference at the relay. The harmful effect of the deep channel fade conditions can be effectively mitigated by proper choice of these network coding maps at the relay. Alternatively, in this paper we propose a Distributed Space Time Coding (DSTC) scheme, which effectively removes most of the deep fade channel conditions at the transmitting nodes itself without any CSIT and without any need to adaptively change the network coding map used at the relay. It is shown that the deep fades occur when the channel fade coefficient vector falls in a finite number of vector subspaces of $\mathbb{C}^2$, which are referred to as the singular fade subspaces. DSTC design criterion referred to as the \textit{singularity minimization criterion} under which the number of such vector subspaces are minimized is obtained. Also, a criterion to maximize the coding gain of the DSTC is obtained. Explicit low decoding complexity DSTC designs which satisfy the singularity minimization criterion and maximize the coding gain for QAM and PSK signal sets are provided. Simulation results show that at high Signal to Noise Ratio, the DSTC scheme provides large gains when compared to the conventional Exclusive OR network code and performs slightly better than the adaptive network coding scheme proposed by Koike-Akino et. al.

Iterative Channel Estimation and Data Detection for Amplify-and-Forward Relay Networks

We consider channel estimation in amplify-and-forward wireless relay networks when non-orthogonal coherent distributed space-time coding is done at relays. We propose to perform iterative channel estimation and data detection based on parallel interference cancelation (PIC) at the receiver. The schemes that we propose are based on soft or hard estimates of the transmitted data symbols. We illustrate the performance improvement compared to the classical approach of pilot-only-based channel estimation and minimum mean-square-error detection. Also, we show that semi-blind channel estimation together with PIC detection is particularly promising for large signal constellations. Moreover, we show that the use of hard estimates of symbols in the proposed iterative receiver provides satisfying results, while requiring a lower computational complexity.

Throughput performance of parallel and repetition coding in incremental decode-and-forward relaying

The throughput performance of cooperative repetition and parallel coding in incremental decode-and-forward is investigated. Four transmission methods are considered: parallel coding with and without distributed space-time coding (PC-ST and PC, respectively); and repetition coding with and without Chase combining at the destination (RC and SC, respectively). The analysis is based on the mutual information seen at the receiver for each scheme. Exact expressions for the outage probability and throughput for all methods are derived. Both ad-hoc and infra-structured relaying scenarios are investigated. Results show that SC can perform very close to RC, PC and PC-ST in terms of throughput, specially in the case of infra-structured relaying or adequate power and rate allocation. The conclusion is that SC would be a better option in practice, since it requires a simpler receiver than PC-ST, PC, and RC.

Opportunistic Distributed Space-Time Coding for Decode-and-Forward Cooperation Systems

In this paper, we consider a decode-and-forward (DF) cooperation system consisting of two cooperative users in sending their information to a common destination, for which the distributed space-time coding (DSTC) is applied in an opportunistic manner, called opportunistic DSTC (O-DSTC), depending on whether the two users succeed in decoding each other's information or not. We propose two O-DSTC schemes for the full-duplex and half-duplex relaying scenarios, which are, respectively, referred to as the full-duplex and half-duplex-based O-DSTC. We evaluate the outage performance of the proposed O-DSTC as well as the conventional selective DF (S-DF) cooperation and fixed DSTC (F-DSTC) schemes. Numerical results show that the O-DSTC outperforms the conventional S-DF and F-DSTC schemes considering both full-duplex and half-duplex. In addition, we develop the diversity-multiplexing tradeoff (DMT) of the proposed O-DSTC, conventional S-DF and F-DSTC schemes by considering the two cooperative users with different data rates (also known as different multiplexing gains). We show that, for both the full-duplex and half-duplex modes, the proposed O-DSTC strictly outperforms the conventional S-DF and F-DSTC in terms of DMT. It is also shown that, in the full-duplex-based O-DSTC scheme, the diversity gain obtained by any of the two cooperative users not only depends on its own multiplexing gain, but also relates to its partner's multiplexing gain. By jointly considering the two users' DMT, the full-duplex-based O-DSTC scheme can achieve the optimal diversity gain when the two users are with the same multiplexing gain. For the half-duplex-based O-DSTC scheme, the DMT performance of the two users are independent of each other, which differs from the full-duplex-based O-DSTC scheme where mutual dependence exists between the cooperative users in terms of DMT.

A Simple Distributed Space-Time Coded Strategy for Two-Way Relay Channels

For two-way wireless relay networks (TWRNs), the simultaneous bidirectional transmission has been shown to outperform other strategies using decode-and-forward (DF) distributed space-time coding (DSTC), thanks to its high spectral efficiency. However, it has a rather high relay decoding complexity and cannot use the direct link between the communicating terminals. In this letter, we propose a simple DSTC transmission scheme for TWRNs that avoids the latter disadvantages at the same symbol rate and with a performance advantage at high powers. Our strategy allows the communicating terminals to use the direct link between them to achieve a higher diversity gain. An extension of the proposed strategy to the differential case is also discussed.

STiCMAC: A MAC Protocol for Robust Space-Time Coding in Cooperative Wireless LANs

Relay-assisted cooperative wireless communication has been shown to have significant performance gains over the legacy direct transmission scheme. Compared with single relay based cooperation schemes, utilizing multiple relays further improves the reliability and rate of transmissions. Distributed space-time coding (DSTC), as one of the schemes to utilize multiple relays, requires tight coordination between relays and does not perform well in a distributed environment with mobility. In this paper, a cooperative medium access control (MAC) layer protocol, called STiCMAC, is designed to allow multiple relays to transmit at the same time in an IEEE 802.11 network. The transmission is based on a novel DSTC scheme called randomized distributed space-time coding (R-DSTC), which requires minimum coordination. Unlike conventional cooperation schemes that pick nodes with good links, STiCMAC picks a transmission mode that could most improve the end-to-end data rate. Any station that correctly receives from the source can act as a relay and participate in forwarding. The MAC protocol is implemented in a fully decentralized manner and is able to opportunistically recruit relays on the fly, thus making it robust to channel variations and user mobility. Simulation results show that the network capacity and delay performance are greatly improved, especially in a mobile environment.

Joint Power Allocation for Differentially Modulated Wireless Relay Networks

This paper deals with the power allocation problem in a wireless relay network employing differential modulation technique and Alamouti distributed space-time code, where signals from both the direct and relay paths are taken into account in the detection process. We propose a sub-optimal power allocation scheme based on the maximization of an approximate receive covariance expression. The proposed scheme jointly allocates the transmit power of both the source and relay nodes under a total transmit power and per-node transmit power constraints. We can increase the effectiveness of the proposed power allocation algorithm by grouping the relays with respect to their individual covariances. Numerical experiments show that the proposed covariance maximization algorithm combined with the relay grouping algorithm offers a respectable BER performance improvement, compared to the conventional schemes. Finally, we demonstrate that the proposed scheme requires only a small number of iterations to achieve convergence, making it attractive to practical systems.

Delay tolerant (delto) distributed TAST codes for cooperative wireless networks

In a distributed cooperative communication system, as the distances between different relay nodes and the receiving nodes may be different, so the performances of distributed space time codes at receiving nodes may badly be degraded if timing synchronization is not assured. In this article, extending the work of Damen et al. we introduce the design of distributed threaded algebraic space-time (TAST) codes offering resistance to timing delay off-set. We present some new and useful techniques of constructing delay tolerant TAST code for distributed cooperative networks, which, like their brethren codes, are delay tolerant for any delay profile and achieve full diversity for arbitrary number of relays, transmit/receive antennas, and input alphabet size. Our proposed codes with minimum lengths achieve better performances than the existing codes retaining full rate and full diversity with or without use of guard bands. Simulations results confirm our claim of obtaining better performances.

A Unified Matching Framework for Multi-Flow Decode-and-Forward Cooperative Networks

Recent works have shown that cooperative diversity can be achieved by using relay selection (RS), distributed space-time coding (DSTC), and distributed beam-forming (DBF) in narrow-band decode-and-forward (DF) cooperative networks with one source-and-destination (s-d) pair. However, the joint resource allocation for broadband DF cooperative networks with multiple s-d flows has not received much attention yet. In this paper, a random hypergraph based unified matching framework is proposed, under which five feasible types of multi-flow DF cooperative networks will be considered. In each type, the maximum matching method will be applied to RS, DSTC, and DBF schemes so as to achieve the optimal channel allocation and relay selection with fairness assurance. By analyzing the properties of maximum matching, the outage probability of each s-d pair after resource allocation will be obtained. The results of diversity-multiplexing tradeoff will show that the proposed framework is capable of achieving the full frequency diversity and cooperative diversity for each s-d pair simultaneously, while the frequency multiplexing is equally shared. Based on the unified framework, the random rotation based parallel Hopcroft-Karp (R <sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">2</sup> PHK) algorithm will then be designed, which can work in each destination node independently, and shall enjoy a poly-logarithmic complexity O(log <sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">2l</sup> <sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">o</sup> N), where N is the number of channels and l <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">o</sub> is a constant.

Opportunistic Relaying for MIMO Amplify-and-Forward Cooperative Networks

We consider a wireless relay network with multiple antenna terminals over Rayleigh fading channels, and apply distributed space-time coding (DSTC) in amplify-and-forward (A&F) mode. The A&F scheme is used in a way that each relay transmits a scaled version of the linear combination of the received symbols. It turns out that, combined with power allocation in the relays, A&F DSTC results in an opportunistic relaying scheme, in which only the best relay is selected to retransmit the source's space-time coded signal. Furthermore, assuming the knowledge of source-relay CSI at the source node, we design an efficient power allocation which outperforms uniform power allocation across the source antennas. Next, assuming M-PSK or M-QAM modulations, we analyze the performance of the proposed cooperative diversity transmission schemes in a wireless relay networks with the multiple-antenna source and destination. We derive the probability density function (PDF) of the received SNR at the destination. Then, the PDF is used to determine the symbol error rate (SER) in Rayleigh fading channels. We derived closed-form approximations of the average SER in the high SNR scenario, from which we find the diversity order of system R min{N s , N d }, where R, N s , and N d are the number of the relays, source antennas, and destination antennas, respectively. Simulation results show that the proposed system obtain more than 6 dB gain in SNR over A&F MIMO DSTC for BER 10?4, when R = 2, N s = 2, and N d = 1.

Outage probability in distributed transmission based on best relay pair selection

Cooperative diversity has been recently proposed as a way to form virtual antenna arrays and thereby mitigate the deleterious effect of fading channels in transmission. In an environment where multiple relays are available, selection of a subset of such relays may be required as, for example, in distributed space-time coding. In this study, the authors therefore use local measurements of the instantaneous channel conditions to select the best relay pair from a set of N available relays, which both come from the same cluster or different clusters, and then use these best relays for cooperation between the source and the destination. The authors also show that the best relay pair selection scheme has robustness against feedback error and outperforms a scheme based on selecting only the best single relay. The authors obtain analytical expressions for the probability density function, cumulative density function and the moment generating function of the received signal-to-noise ratio to derive closed-form expressions for outage probability over Rayleigh frequency flat-fading channels. The analytical results are supported by simulation studies.

Energy-Efficient Space-Time Coded Cooperation in Outage-Restricted Multihop Wireless Networks

Due to the limited energy supplies of nodes in many applications such as wireless sensor networks, energy efficiency is crucial for extending the lifetime of these networks. This paper addresses the cooperative transmission for outage-restricted multihop wireless ad hoc networks. The source node wants to transmit messages to a single destination. Other nodes in the network may operate as relay nodes. In this paper, new multihop cooperative protocol is proposed using the space-time codes for the purpose of energy savings, subject to a required outage probability at the destination. We restrict the cooperation to nodes along a chosen route. Two efficient power allocation schemes are derived, which depend only on the statistics of the channels. Furthermore, three efficient cooperative multihop transmissions are proposed when arbitrary distributed space-time codes are used. The proposed cooperative protocols offer different degrees of energy efficiency, spectral efficiency, complexity, and signalling overhead. Compared to non-cooperative multihop routing, an energy saving of up to 72% is achievable in line networks with 3 relays and an outage probability constraint of 10-3 at the destination.

Channel Training Design in Amplify-and-Forward MIMO Relay Networks

This paper is on the channel training design for distributed space-time coding (DSTC) in multi-antenna relay networks. DSTC is shown to achieve full diversity in relay networks. To use DSTC, the receiver has to know both the channels between the relays and the receiver (Relay-Rx channels), and the channels between the transmitter and the relays (Tx-Relay channels). For the Relay-Rx channels, by sending pilot signals from the relays, the training problem can be solved using multi-input-multi-output (MIMO) training schemes. Given the knowledge of the Relay-Rx channels, to obtain estimations of the Tx-Relay channels at the receiver, DSTC is used. The linear minimum-mean-square-error (LMMSE) estimation at the receiver and the optimal pilot design that minimizes the estimation error are derived. We also investigate the requirement on the training time that can lead to full diversity in data transmission. An upper bound and a lower bound on the training time are provided. A novel training design whose training time length is adaptive to the quality of the Relay-Rx channels is also proposed. Simulations are exhibited to justify our analytical results and to show advantages of the proposed scheme over others.

Cooperative Layered Video Multicast Using Randomized Distributed Space Time Codes

With the increased popularity of mobile multimedia services, efficient and robust video multicast strategies are of critical importance. Cooperative communications has been shown to improve the robustness and the data rates for point-to-point transmission. In this paper, a two-hop cooperative transmission scheme for multicast in infrastructure-based networks is used, where multiple relays forward the data simultaneously using randomized distributed space time codes (RDSTC). This randomized cooperative transmission is further integrated with layered video coding and packet level forward error correction (FEC) to enable efficient and robust video multicast. Three different schemes are proposed to find the system operating parameters based on the availability of the channel information at the source station: RDSTC with full channel information, RDSTC with limited channel information, and RDSTC with node count. The performance of these three schemes are compared with rate adaptive direct transmission and conventional multicast that does not use rate adaptation. The results show that while rate-adaptive direct transmission provides better video quality than conventional multicast, all three proposed randomized cooperative schemes outperform both strategies significantly as long as the network has enough nodes. Furthermore, the performance gap between RDSTC with full channel information and RDSTC with limited channel information or node count is relatively small, indicating the robustness of the proposed cooperative multicast system using RDSTC.