On the diversity order of a general cooperative relaying communication system

Cooperative communication technology exploiting distributed spatial diversity is a promising solution for the future high data-rate cellular and ad-hoc wireless communications. To characterize the performance of a cooperative network, the cooperative diversity is commonly used. In this paper, we revisit the concept of diversity and look into the essence of cooperative diversity. We analyze the diversity performance of a general cooperative relaying system with multiple branches. Moreover, each branch consists of one or more hops. Unlike in other analyses, the assumptions that each node being only equipped with a single antenna and that all channel characteristics belonging to the same family are NOT required in our study. Using the decode-and-forward (DF) relaying protocol as an illustration, we provide analytical results on the diversity gain and the coding gain. The results also encompass most of the existing results as special cases. We further show the relationship between the diversity order of a branch and those of the constituent links; and the relationship between the diversity order of the network and those of the constituent branches. In particular, we show that for the uncoded DF protocol, the full diversity order can be achieved by using simple hard-decision detection at the destination. The requirement is to set appropriate signal-to-noise-ratio (SNR) thresholds for the multi-hop branches. To improve the bandwidth efficiency, we also randomly select one branch, among those branches satisfying the SNR-threshold requirement, for the transmission. We show that such a scheme accomplishes the full diversity order and produces a good error performance.