Wireless networks, diversity and space-time codes

We apply the idea of space-time coding devised for multiple-antenna systems to the problem of communications over wireless relay networks. A two-stage protocol is used, where in one stage the transmitter sends information and in the other, the relay nodes encode their received signals into a "distributed" linear dispersion code, and then transmit the coded signals to the receiver. We show that for high SNR the proposed system has a diversity of order α_0 min{T, R}, with T the coherence interval, R the number of relay nodes, and α0 the solution to the equation α + (log α)/(log P) = 1 - (log log P)/(log P), where P is the total transmit power in the network. In particular, we show that the pairwise error probability (PEP) decays no slower than ((log P)/P)^(min{T,R}). Thus, apart from the log P factor and assuming T ≥ R, the system has the same diversity as a multiple-antenna system with R transmit antennas and one receive antenna, which is the same as assuming that the R relay nodes can fully cooperate and have full knowledge of the transmit signal. We further show that for a fixed total transmit power across the entire network, the optimal power allocation is for the transmitter to expend half the power and for the relays to collectively expend the other half. We also show that at low and high SNR, the coding gain is the same as that of multiple-antenna systems. However, at intermediate SNR, it can be quite different. We discuss some of the ramifications of using different space-time codes and finally verify our analysis through the simulation or randomly generated distributed space-time 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 non-coherent communication in classical point to point multiple antenna systems.Comment: To appear in IEEE Transactions on Wireless Communications. 10 pages, 5 figure

OFDM based Distributed Space Time Coding for Asynchronous Relay Networks

Recently Li and Xia have proposed a transmission scheme for wireless relay networks based on the Alamouti space time code and orthogonal frequency division multiplexing to combat the effect of timing errors at the relay nodes. This transmission scheme is amazingly simple and achieves a diversity order of two for any number of relays. Motivated by its simplicity, this scheme is extended to a more general transmission scheme that can achieve full cooperative diversity for any number of relays. The conditions on the distributed space time block code (DSTBC) structure that admit its application in the proposed transmission scheme are identified and it is pointed out that the recently proposed full diversity four group decodable DSTBCs from precoded co-ordinate interleaved orthogonal designs and extended Clifford algebras satisfy these conditions. 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. Finally, four group decodable distributed differential space time block codes applicable in this new transmission scheme for power of two number of relays are also provided.Comment: 5 pages, 2 figures, to appear in IEEE International Conference on Communications, Beijing, China, May 19-23, 200

Diversity-Multiplexing Tradeoff of Asynchronous Cooperative Diversity in Wireless Networks

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

Orthogonal Code Design for MIMO Amplify-and-Forward Cooperative Networks

This paper is on the design of practical distributed space-time codes for wireless relay networks with multiple antennas terminals. The amplify-and-forward scheme is used in a way that each relay transmits a scaled version of the linear combination of the received symbols. We propose distributed orthogonal space-time codes which are distributed among the source node's antennas and relays. Using linear orthogonal decoding in the destination makes it feasible to employ large number of potential relays to improve the diversity order. Assuming multiple amplitude modulation, we derive a formula for the symbol error probability of the investigated scheme over Rayleigh fading channels. Our analytical results have been confirmed by simulation results, using full-rate, full-diversity distributed codes

Space-Time Block Coding for Wireless Communications

Abstract Wireless designers constantly seek to improve the spectrum efficiency/capacity, coverage of wireless networks, and link reliability. Space-time wireless technology that uses multiple antennas along with appropriate signalling and receiver techniques offers a powerful tool for improving wireless performance. Some aspects of this technology have already been incorporated into various wireless network and cellular mobile standards. More advanced MIMO techniques are planned for future mobile networks, wireless local area network (LANs) and wide area network (WANs). Multiple antennas when used with appropriate space-time coding (STC) techniques can achieve huge performance gains in multipath fading wireless links. The fundamentals of space-time coding were established in the context of space-time Trellis coding by Tarokh, Seshadri and Calderbank. Alamouti then proposed a simple transmit diversity coding scheme and based on this scheme, general space-time block codes were further introduced by Tarokh, Jafarkhani and Calderbank. Since then space-time coding has soon evolved into a most vibrant research area in wireless communications. Recently, space-time block coding has been adopted in the third generation mobile communication standard which aims to deliver true multimedia capability. Space-time block codes have a most attractive feature of the linear decoding/detection algorithms and thus become the most popular among different STC techniques. The decoding of space-time block codes, however, requires knowledge of channels at the receiver and in most publications, channel parameters are assumed known, which is not practical due to the changing channel conditions in real communication systems. This thesis is mainly concerned with space-time block codes and their performances. The focus is on signal detection and channel estimation for wireless communication systems using space-time block codes. We first present the required background materials, discuss different implementations of space-time block codes using different numbers of transmit and receive antennas, and evaluate the performances of space-time block codes using binary phase-shift keying (BPSK), quadrature phase-shift keying (QPSK), and quadrature amplitude modulation (QAM). Then, we investigate Tarokh’s joint detection scheme with no channel state information thoroughly, and also propose a new general joint channel estimation and data detection scheme that works with QPSK and 16-QAM and different numbers of antennas. Next, we further study Yang’s channel estimation scheme, and expand this channel estimation scheme to work with 16-QAM modulation. After dealing with complex signal constellations, we subsequently develop the equations and algorithms of both channel estimation schemes to further test their performances when real signals are used (BPSK modulation). Then, we simulate and compare the performances of the two new channel estimation schemes when employing different number of transmit and receive antennas and when employing different modulation methods. Finally, conclusions are drawn and further research areas are discussed

Cooperative diversity using MIMO systems

Multipath fading is one of the primary factors for degrading the performance in a wireless network. Information theoretic and past research suggest the use various diversity techniques to combat fading in wireless networks. Antenna diversity, a form of diversity technique, when incorporated in a wireless transceiver increases the system capacity and is one of the effective methods to combat fading in wireless systems. Also, recent research by Laneman et.al., Sendonaris et.al. suggests that cooperation among users in a wireless networks is an effective approach for a better signal reception in multipath fading environments. The diversity gains obtained by cooperation among the users of a wireless network is termed as cooperative diversity . Although, prior research in cooperative diversity considers users equipped with single antenna, in practical scenarios users may be able to accommodate multiple antennas due to the recent advanced research in semiconductor industry. Hence, the primary purpose of this thesis is to design, simulate and analyze an end-end performance of multi-antenna wireless systems employing cooperative multi antenna relay nodes so as to exploit the cooperative diversity and antenna diversity simultaneously in a wireless networks. Three main contributions to the area of cooperative multiple-input multiple-output (MIMO) wireless systems is presented in this thesis. First, we perform information theoretic analysis to study the impact of antenna arrays on cooperative wireless networks and propose the best possible distribution of antenna arrays among the three terminals of a simple three terminal cooperative relay network. Second, we design, simulate, and analyze a cooperative multiple-input multiple-output (MIMO) wireless systems employing orthogonal space-time block codes as proposed by Alamouti in 1998 with a decode-and-forward (DF) relay terminal. We implement a maximal ratio combining receiver that provides almost twice the diversity gain with respect to point-point multiple input multiple output link. Finally, we implement a practical receiver for cooperative reception using multiple antennas at all nodes based on Bell-Labs Layered Space Time architecture (BLAST). We incorporate a practical adaptive decode-and-forward (DF) relaying technique for reliable signal retransmission for both Alamouti space-time coding and the BLAST schemes. Results presented in terms of bit error rates and throughput show that remarkable performance gains are achievable by combining the concepts drawn from space-time coding, cooperative relaying and array processing