Algebraic distributed differential space-time codes with low decoding complexity

Abstract

Abstract-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.

Leveraging coherent distributed space-time codes for noncoherent communication in relay networks via training

“…However, in [2], the destination was assumed to have perfect knowledge of all the channel fading gains from the source Manuscript to the relays and those from the relays to the destination. To overcome the need for channel knowledge, distributed differential space time coding was studied in [3], [4], [5], [6], which is essentially an extension of differential unitary space time coding for point to point MIMO systems to the relay network case. But distributed differential space time block code (DDSTBC) design is difficult compared to coherent DSTBC design because of the extra stringent conditions (we refer readers to [4], [6] for exact conditions) that need to be met by the codes.…”

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

“…Moreover, the use of non-unitary relay matrices forces the destination to perform additional processing to whiten the noise seen by it during ML decoding. To solve this problem, extended Clifford algebras were used in [8], [9] to construct full diversity, four group ML decodable DSTBCs with unitary relay matrices. But, the constructions in [8], [9] were limited to power of two number of relays.…”

“…To solve this problem, extended Clifford algebras were used in [8], [9] to construct full diversity, four group ML decodable DSTBCs with unitary relay matrices. But, the constructions in [8], [9] were limited to power of two number of relays. Though these constructions can be used for arbitrary number of relays by column dropping, this solution entails a significant increase in delay and ML decoding complexity.…”

“…Such DSTBC constructions are available in the literature only for power of two number of relay nodes [8], [9]. By dropping one column, a nonminimal delay, full diversity, four group ML decodable DSTBC with unitary relay matrices is obtained for odd number of relays.…”

Non-Differential DSTBCs for Partially-Coherent Cooperative Communication

“…Differential techniques have been reported in the literature for partially-coherent and non-coherent set ups [6], [7], [9], [10], but the authors are not aware of codes using nondifferential coding techniques. In this paper, we propose a non-differential coding strategy for partially-coherent set up, using cyclic unitary matrix groups (a set of diagonal unitary matrices forming a cyclic group) at the source and a set of diagonal unitary matrices at the relays.…”