### Abstract

We study the design of distributed space-time codes for cooperative communication. We assume that each node is equipped with a single antenna; however, to obtain diversity and coding gains, the cooperating nodes act as elements of a multiantenna system. With few exceptions, most of the literature on the subject proposes coding rules in which each node emulates a predetermined antenna of a multiantenna system. Since the nodes need to know their specific antenna index, either internode communication or a central control unit is required. Our design objective is to obtain diversity and coding gains while eliminating the need for code or antenna allocation. We achieve our objective by introducing novel randomized strategies that decentralize the transmission of a space time code from a set of distributed relays. Our simple idea is to let each node transmit an independent random linear combination of the codewords that would have been transmitted by all the elements of a multiantenna system. In addition to introducing this new class of designs, we fully characterize the diversity order of the corresponding symbol error probability and also analyze how the performance is linked to different choices of the statistics of the random coefficients. We show that the proposed scheme achieves full diversity (N) if N < L, where N is the number of transmitters and L is the number of antennas assumed in the underlying space-time code structure. The diversity order L is achieved if N > L. Interestingly, in certain cases (e.g., N=L=2), we show that the achieved diversity order is fractional (d*=1.5)!

Original language | English (US) |
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Pages (from-to) | 5003-5017 |

Number of pages | 15 |

Journal | IEEE Transactions on Signal Processing |

Volume | 55 |

Issue number | 10 |

DOIs | |

State | Published - Oct 1 2007 |

### Keywords

- Cooperative transmission
- Distributed networks
- Diversity
- Space-time coding

### ASJC Scopus subject areas

- Signal Processing
- Electrical and Electronic Engineering

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## Cite this

*IEEE Transactions on Signal Processing*,

*55*(10), 5003-5017. https://doi.org/10.1109/TSP.2007.896061