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

  • Authors:
  • David Gregoratti;Xavier Mestre

  • Affiliations:
  • Centre Tecnològic de Telecomunicacions de Catalunya, Parc Mediterrani de la Tecnologia, Castelldefels, Barcelona, Spain;Centre Tecnològic de Telecomunicacions de Catalunya, Parc Mediterrani de la Tecnologia, Castelldefels, Barcelona, Spain

  • Venue:
  • ISIT'09 Proceedings of the 2009 IEEE international conference on Symposium on Information Theory - Volume 1
  • Year:
  • 2009

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Abstract

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 α = K/N. This is not true for the linear minimum mean square error receiver, which loses diversity when α 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 α. Random matrix theory results are used to derive this asymptotic approximation.