On the distributed space-time signal design for a large number of relay terminals

We study the asymptotic behavior of a cooperative scheme operating in amplify-and-forward (AF) mode when the number of relay terminals tends to infinity. An optimal code design rule is derived through the investigation of a pairwise error probability (PEP) expression. The design rule is based on an Euclidean-distance-type metric including some scaling terms due to different path loss and shadowing effects associated with underlying relay links. Since the design criterion is channel-dependent, it does not allow a practical code design. However, we further demonstrate that "classical" Euclidean distance can be used as a sub-optimal solution for realizing cooperative diversity advantages which we further verify through our simulation study. Our simulation results also indicate that distributed space-time codes based on Euclidean distance yield good results even for a small number of relays.