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

Noncoherent Low-Decoding-Complexity Space-Time Codes for Wireless Relay Networks

The differential encoding/decoding setup introduced by Kiran et al, Oggier et al and Jing et al 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 used in the Jing-Hassibi protocol for cooperative diversity, the conditions that need to be satisfied by the relay matrices and the codebook are identified. A class of previously known rate one, full diversity, four-group encodable and four-group decodable Differential Space-Time Codes (DSTCs) is proposed for use as Distributed DSTCs (DDSTCs) in the proposed set up. To the best of our knowledge, this is the first known low decoding complexity DDSTC scheme for cooperative wireless networks.Comment: 5 pages, no figures. To appear in Proceedings of IEEE ISIT 2007, Nice, Franc

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

Algebraic Distributed Space-Time Codes with Low ML Decoding Complexity

"Extended Clifford algebras" are introduced as a means to obtain low ML decoding complexity space-time block codes. Using left regular matrix representations of two specific classes of extended Clifford algebras, two systematic algebraic constructions of full diversity Distributed Space-Time Codes (DSTCs) are provided for any power of two number of relays. The left regular matrix representation has been shown to naturally result in space-time codes meeting the additional constraints required for DSTCs. The DSTCs so constructed have the salient feature of reduced Maximum Likelihood (ML) decoding complexity. In particular, the ML decoding of these codes can be performed by applying the lattice decoder algorithm on a lattice of four times lesser dimension than what is required in general. Moreover these codes have a uniform distribution of power among the relays and in time, thus leading to a low Peak to Average Power Ratio at the relays.Comment: 5 pages, no figures. To appear in Proceedings of IEEE ISIT 2007, Nice, Franc

High Rate Single-Symbol Decodable Precoded DSTBCs for Cooperative Networks

Distributed Orthogonal Space-Time Block Codes (DOSTBCs) achieving full diversity order and single-symbol ML decodability have been introduced recently for cooperative networks and an upper-bound on the maximal rate of such codes along with code constructions has been presented. In this report, we introduce a new class of Distributed STBCs called Semi-orthogonal Precoded Distributed Single-Symbol Decodable STBCs (S-PDSSDC) wherein, the source performs co-ordinate interleaving of information symbols appropriately before transmitting it to all the relays. It is shown that DOSTBCs are a special case of S-PDSSDCs. A special class of S-PDSSDCs having diagonal covariance matrix at the destination is studied and an upper bound on the maximal rate of such codes is derived. The bounds obtained are approximately twice larger than that of the DOSTBCs. A systematic construction of S-PDSSDCs is presented when the number of relays $K \geq 4$. The constructed codes are shown to achieve the upper-bound on the rate when $K$ is of the form 0 modulo 4 or 3 modulo 4. For the rest of the values of $K$, the constructed codes are shown to have rates higher than that of DOSTBCs. It is also shown that S-PDSSDCs cannot be constructed with any form of linear processing at the relays when the source doesn't perform co-ordinate interleaving of the information symbols.Comment: A technical report of DRDO-IISc Programme on Advanced Research in Mathematical Engineerin

Distributed space-time block codes for two-hop wireless relay networks

Recently, the idea of space-time coding has been applied to wireless relay networks wherein a set of geographically separated relay nodes cooperate to process the received signal from the source and forward them to the destination such that the signal received at the destination appears like a Space-Time Block Code (STBC). Such STBCs (referred to as Distributed Space-Time Block Codes (DSTBCs)) when appropriately designed are known to offer spatial diversity. It is known that different classes of DSTBCs can be designed primarily depending on (i) whether the Amplify and Forward (AF) protocol or the Decode and Forward (DF) protocol is employed at the relays and (ii) whether the relay nodes are synchronized or not. In this paper, we present a survey on the problems and results associated with the design of DSTBCs for the following classes of two-hop wireless relay networks: (i) synchronous relay networks with AF protocols, (ii) asynchronous relay networks with AF protocols (iii) synchronous relay networks with DF protocols and (iv) asynchronous relay Fig. 1. Co-located MIMO channel model networks with DF protocols

Single-Symbol ML Decodable Distributed STBCs for Partially-Coherent Cooperative Networks

Space-time block codes (STBCs) that are single-symbol decodable (SSD) in a co-located multiple antenna setting need not be SSD in a distributed cooperative communication setting. A relay network with N relays and a single source-destination pair is called a partially-coherent relay channel (PCRC) if the destination has perfect channel state information (CSI) of all the channels and the relays have only the phase information of the source-to-relay channels. In this paper, first, a new set of necessary and sufficient conditions for a STBC to be SSD for co-located multiple antenna communication is obtained. Then, this is extended to a set of necessary and sufficient conditions for a distributed STBC (DSTBC) to be SSD for a PCRC, by identifying the additional conditions. Using this, several SSD DSTBCs for PCRC are identified among the known classes of STBCs. It is proved that even if a SSD STBC for a co-located MIMO channel does not satisfy the additional conditions for the code to be SSD for a PCRC, single-symbol decoding of it in a PCRC gives full-diversity and only coding gain is lost. It is shown that when a DSTBC is SSD for a PCRC, then arbitrary coordinate interleaving of the in-phase and quadrature-phase components of the variables does not disturb its SSD property for PCRC. Finally, it is shown that the possibility of {\em channel phase compensation} operation at the relay nodes using partial CSI at the relays increases the possible rate of SSD DSTBCs from $\frac{2}{N}$ when the relays do not have CSI to 1/2, which is independent of N