G. Susinder Rajan

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.

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 DST-BCs 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.

A Non-orthogonal Distributed Space-Time Coded Protocol Part I: Signal Model and Design Criteria

In this- two-part series of papers, a generalized non-orthogonal amplify and forward (GNAF) protocol which generalizes several known cooperative diversity protocols is proposed. Transmission in the GNAF protocol comprises of two phases - the broadcast phase and the cooperation phase. In the broadcast phase, the source broadcasts its information to the relays as well as the destination. In the cooperation phase, the source and the relays together transmit a space-time code in a distributed fashion. The GNAF protocol relaxes the constraints imposed by the protocol of Jing and Hassibi on the code structure. In part-I of this paper, a code design criteria is obtained and it is shown that the GNAF protocol is delay efficient and coding gain efficient as well. Moreover the GNAF protocol enables the use of sphere decoders at the destination with a non-exponential maximum likelihood (ML) decoding complexity. In part-II, several low decoding complexity code constructions are studied and a lower bound on the diversity-multiplexing gain tradeoff of the GNAF protocol is obtained

Distributed Space-Time Codes for Cooperative Networks with Partial CSI

Design criteria and full-diversity distributed space time codes (DSTCs) for the two phase transmission based cooperative diversity protocol of Jing-Hassibi and the generalized nonorthogonal amplify and forward (GNAF) protocol are reported, when the relay nodes are assumed to have knowledge of the phase component of the source to relay channel gains. It is shown that this under this partial channel state information (CSI), several well known space time codes for the colocated MIMO (multiple input multiple output) channel become amenable for use as DSTCs. In particular, the well known complex orthogonal designs, generalized coordinate interleaved orthogonal designs (GCIODs) and unitary weight single symbol decodable (UW-SSD) codes are shown to satisfy the required design constraints for DSTCs. Exploiting the relaxed code design constraints, DSTCs was proposed obtained from Clifford algebras which have low ML decoding complexity.

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.

A Non-orthogonal Distributed Space-Time Coded Protocol Part II: Code Construction and DM-G Tradeoff

This is the second part of a two-part series of papers. In this paper, for the generalized non-orthogonal amplify and forward (GNAF) protocol presented in part-I, a construction of a new family of distributed space-time codes based on co-ordinate interleaved orthogonal designs (CIOD) which result in reduced maximum likelihood (ML) decoding complexity at the destination is proposed. Further, it is established that the recently proposed Toeplitz space-time codes as well as space-time block codes (STBCs) from cyclic division algebras can be used in GNAF protocol. Finally, a lower bound on the optimal diversity-multiplexing gain (DM-G) tradeoff for the GNAF protocol is established and it is shown that this bound approaches the transmit diversity bound asymptotically as the number of relays and the number of channels uses increases

Four Group Decodable Differential Scaled Unitary Linear Space-Time Codes

Differential Unitary Space-Time Block codes (STBCs) offer a means to communicate on the Multiple Input Multiple Output (MIMO) channel without the need for channel knowledge at both the transmitter and the receiver. Recently Yuen-Guan-Tjhung have proposed Single-Symbol-Decodable Differential Space-Time Modulation based on Quasi-Orthogonal Designs (QODs) by replacing the original unitary criterion by a scaled unitary criterion. These codes were also shown to perform better than differential unitary STBCs from Orthogonal Designs (ODs). However the rate (as measured in complex symbols per channel use) of the codes of Yuen-Guan-Tjhung decay as the number of transmit antennas increase. In this paper, a new class of differential scaled unitary STBCs for all even number of transmit antennas is proposed. These codes have a rate of 1 complex symbols per channel use, achieve full diversity and moreover they are four-group decodable, i.e., the set of real symbols can be partitioned into four groups and decoding can be done for the symbols in each group separately. Explicit construction of multidimensional signal sets that yield full diversity for this new class of codes is also given.

Low complexity distributed STBCs with unitary relay matrices for any number of relays

Jing and Hassibi introduced a distributed space time block coding scheme for symbol synchronous, coherent, amplify and forward relay networks with half duplex constrained relay nodes. In this two phase transmission scheme, the source transmits a vector of complex symbols to the relays during the first phase and each relay applies a pre-assigned unitary transformation to the received vector or its conjugate before transmitting it to the destination during the second phase. The destination then perceives a certain structured distributed space time block code (DSTBC) whose maximum likelihood (ML) decoding complexity in general, is very high. In this paper, explicit constructions of minimum delay, full diversity, four group ML decodable DSTBCs with unitary relay matrices are provided for even number of relay nodes. Prior constructions of DSTBCs with the same features were either limited to power of two number of relay nodes or had non-unitary relay matrices which leads to large peak to average power ratio of the relays transmitted signals. For the case of odd number of relays, constructions of minimum delay, full diversity, two group ML decodable DSTBCs are given.

A Non-Orthogonal Cooperative Multiple Access (NCMA) Protocol and Low ML Decoding Complexity Codes

A half-duplex constrained non-orthogonal cooperative multiple access (NCMA) protocol suitable for transmission of information from N users to a single destination in a wireless fading channel is proposed. Transmission in this protocol comprises of a broadcast phase and a cooperation phase. In the broadcast phase, each user takes turn broadcasting its data to all other users and the destination in an orthogonal fashion in time. In the cooperation phase, each user transmits a linear function of what it received from all other users as well as its own data. In contrast to the orthogonal extension of cooperative relay protocols to the cooperative multiple access channels wherein at any point of time, only one user is considered as a source and all the other users behave as relays and do not transmit their own data, the NCMA protocol relaxes the orthogonality built into the protocols and hence allows for a more spectrally efficient usage of resources. Code design criteria for achieving full diversity of N in the NCMA protocol is derived using pair wise error probability (PEP) analysis and it is shown that this can be achieved with a minimum total time duration of 2N - 1 channel uses. Explicit construction of full diversity codes is then provided for arbitrary number of users. Since the maximum likelihood decoding complexity grows exponentially with the number of users, the notion of g-group decodable codes is introduced for the setup and a set of necessary and sufficient conditions is also obtained.