Decode and forward relays: Full diversity with randomized distributed space-time coding

This paper analyzes a cooperative communications system where a set of decode and forward relays provides support to a point to point communication. Each relay linearly transforms the K received symbols, if correctly decoded, into N new ones to be sent to the destination. The coding matrices are randomly generated, making the system simple to design, scalable and robust to synchronism errors. It is shown that such a random code, together with the optimal maximum-likelihood receiver, achieves full diversity for any value of the ratio alpha = K/N. This is not true for the linear minimum mean square error receiver, which loses diversity when alpha increases beyond a given threshold. To avoid dealing with the randomness of the code, the analysis is carried out in the asymptotic domain, i.e. for K and N growing without bound but with ratio converging to a finite quantity alpha. Random matrix theory results are used to derive this asymptotic approximation.