Diversity order for the amplify-and-forward multiple-relay channel with randomized distributed space-time coding

Cooperative transmission is a convenient means of generating spatial diversity without the need of collocating multiple antennas in a single terminal. In this paper, the asymptotic diversity properties of a cooperative transmission system are investigated. The analysis is carried out for an amplify-and-forward multi-relay protocol implementing a distributed randomized space-time block code. According to this approach, each relay multiplies the received signal by its specific spreading matrix, which is selected as having random independent and identically distributed entries. It is shown that the asymptotic diversity order of this system can vary from 2 to the total number of relays plus one. Furthermore, the achieved diversity order critically depends on the quotient between the number of rows and columns of the spreading matrices, which need to be sufficiently tall in order to guarantee full diversity of the system.