High-Rate, Single-Symbol ML Decodable Precoded DSTBCs for Cooperative Networks

Distributed orthogonal space-time block codes (DOSTBCs) achieving full-diversity order and single-symbol maximum-likelihood (ML) decodability have been introduced recently by Yi and Kim for cooperative networks, and an upper bound on the maximal rate of such codes along with code constructions has been presented. In this paper, a new class of single-symbol ML decodable precoded distributed space-time block codes (SSD-PDSTBCs) called semiorthogonal SSD-PDSTBCs (semi-SSD-PDSTBCs) is introduced wherein, the source performs linear precoding of information symbols appropriately before transmitting it to all the relays. It is shown that DOSTBCs are a special case of semi-SSD-PDSTBCs. A special class of semi-SSD-PDSTBCs 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 semi-SSD-PDSTBCs is presented when the number of relays
K
ges 4. The constructed codes are shown to achieve the upper bound on the rate when
K
is of the form
0
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 shown that semi-SSD-PDSTBCs cannot be constructed with any form of linear processing at the relays when the source does not perform linear precoding of the information symbols.