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

Abstract

Abstract-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 sourceto-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.

High-rate, single-symbol decodable distributed STBCs for partially-coherent cooperative networks

“…It is noted that the representation in [1] is different from the column vector representation used in this paper. An important consequence is that the Hurwitz-Radon family of matrices satisfy the conditionŝ (18) and hence j T j = I ∀j, which we will use in our proof. Viewing G c as a T 2 × N distributed STBC with T 1 = p and T 2 = 2p, the T 2 × 2T 1 relay matrices A j of G c have the structure…”

“…In Section III, we recapitulate the necessary and sufficient conditions derived in [18] for a DSTBC to be SSD in a PCRC is obtained. In Section IV, we prove that the rate-halving codes from real orthogonal designs are SSD for PCRC.…”

“…This property enables construction of codes that are SSD and have higher rate than 2 N but offer full diversity only for signal constellations satisfying certain conditions. A unified treatment of the results of [18] and of this paper is available as [20].…”

“…In this paper, we use the conditions developed in [18] and show the following results regarding the high rate codes.…”

“…For arbitrary number of relays, recently in [17], distributed orthogonal STBCs (DOSTBCs) have been studied and it is shown that if the destination has the complete channel state information (CSI) of all the source-to-relay channels and the relay-to-destination channels, then the maximum possible rate is upper bounded by 2 N complex symbols per channel use for N relays. Towards improving the rate of transmission and achieving simultaneously both full-diversity as well as SSD at the destination, in our earlier work [18], we study relay channels with the assumption that the relays have the phase information of the source-torelay channels and the destination has the CSI of all the channels. We derived a set of necessary and sufficient conditions for a DSTBC to be SSD in PCRC.…”