Synchronization of relay nodes is an important and critical issue in exploiting cooperative diversity in wireless networks. In this paper, two asynchronous cooperative diversity schemes are proposed, namely, distributed delay diversity and asynchronous space-time coded cooperative diversity schemes. In terms of the overall diversity-multiplexing (DM) tradeoff function, we show that the proposed independent coding based distributed delay diversity and asynchronous space-time coded cooperative diversity schemes achieve the same performance as the synchronous space-time coded approach which requires an accurate symbol-level timing synchronization to ensure signals arriving at the destination from different relay nodes are perfectly synchronized. This demonstrates diversity order is maintained even at the presence of asynchronism between relay node. Moreover, when all relay nodes succeed in decoding the source information, the asynchronous space-time coded approach is capable of achieving better DM-tradeoff than synchronous schemes and performs equivalently to transmitting information through a parallel fading channel as far as the DM-tradeoff is concerned. Our results suggest the benefits of fully exploiting the space-time degrees of freedom in multiple antenna systems by employing asynchronous space-time codes even in a frequency flat fading channel. In addition, it is shown asynchronous space-time coded systems are able to achieve higher mutual information than synchronous space-time coded systems for any finite signal-to-noise-ratio (SNR) when properly selected baseband waveforms are employed.
In wireless networks, treating intermediate nodes between the source and its destination as potential relays and utilizing these relay nodes to improve the diversity gain has attracted considerable attention lately and re-kindled interests in relay channels after this problem was first tackled from the perspective of Shannon capacity in the 70's [1], [2]. One school of works [3], [4], [5] follow the footsteps of [2], where they employ block Markov superposition encoding, random binning and successive decoding as coding strategy. Another line of work adopts the idea of cooperative diversity which was first proposed in [6], [7] for CDMA networks, and then extended to wireless networks with multiple sources and relays [8], [9], [10], [11], [12], [13], [14]. We are not attempting to provide a comprehensive review of all related works on relay channels here [3], but instead divert our attentions to those work related with cooperative diversity.
In this paper, we mainly focus on two well received relaying strategies, namely, decode-and-forward (DF) and amplify-andforward (AF) schemes. Decision on which relaying strategy is adopted is subject to constraints imposed upon relay nodes. If nodes cannot transmit and receive at the same time and thus work in a half-duplex mode [15], the communication link in a relay channel with a single level of relay nodes consists of two phases. In the first phase, the source broadcasts its information to relays and its destination. During the second phase, relays forward either re-encoded source transmissions (decode-and-forward) or a scaled version of received source signals (amplify-and-forward) [10]. At the destination, signals arriving over two phases are jointly processed to improve the overall performance. Variations of these schemes include allowing source nodes to continuously send packets over two phases to increase the spectral efficiency [12], [16]. As for coding strategies through which cooperative diversity is achieved, [11] proposes to encode the source information over two independent blocks from source to destination and relays to destination, respectively. In [13], without requiring relay nodes to provide feedback messages to the source, rate compatible punctured convolutional codes (RCPC) and turbo codes are proposed to encode over two independent blocks. Also, an extension is made by putting multiple antennas at relay nodes to further improve the diversity and multiplexing gain. If multiple relay nodes are considered as virtual antennas, a space-time-coded cooperative diversity approach is proposed in [9] to jointly encode the source signals across successful relay nodes during the second phase.
As noted in [17], synchronization of relay nodes is an important and critical issue in exploiting cooperative diversity in wireless ad hoc and sensor networks. However, in the existing works, e.g., [18], [9], it has been assumed that relay nodes are perfectly synchronized such that signals arriving at the destination node from distinct relay nodes are aligned perfectly with respect to their symbol epochs. Under this assumption, distributed space-time-coded cooperative diversity approach achieves diversity gains in the order of the number of available transmitting nodes in a relay network [9].
Perfect synchronization is, however, hard, if not impossible, to be achieved in infra-structureless wireless ad-hoc and sensor networks. In [19], the issue of carrier asynchronism between the source and relay node is addressed in terms of its impact on the lower and upper bounds of the outage and ergodic capacity of a three-node wireless relay channel. At the presence of time delays between relay nodes, an extension of Alamouti space-time-block-codes (STBC) [20] is proposed in [21] to exploit spatial diversity when time delay is only an integer number of symbol periods. And in [22], [23], macroscopic space-time codes are designed to perform robust against uncertainties of relative delays between different basestations. Without requiring the symbol synchronization, we propose a repetition coding based distributed delay diversity scheme in [24], [25] which achieves the same order of diversity promised by distributed space-time codes. Unlike the extension of other approaches to the synchronization problem in distributed space-time coding [22], the proposed system also admits a robust and easily trainable receiver when synchronization is not present in the system.
In [26], relay nodes perform adaptive decode-and-forward or amplify-and-forward schemes allowing them to transmit or remain silent depending on the received signal-to-noiseratio (SNR). However, their proposed schemes require intentionally increasing data symbol period to avoid inter-symbolinterference (ISI) caused by the asynchronous transmission of the same source signal to different receivers, which limits efficiency. In [27], asynchronism caused by phase error of channel fading variables is studied in terms of its impact
