On the performance of amplify-and-forward cooperative systems with fixed gain relays

Multi-hop, multi-branch, and multi-branch multi- hop wireless transmission systems with nonregenerative fixed gain relays employing amplify-and-forward relaying are considered. Simple closed-form expressions for the outage and bit error probabilities of these systems are derived. It is shown that while a multi-hop transmission system does not offer diversity gain, it can perform better than a single hop system if its average individual link SNRs satisfy a certain condition. In addition, the analysis clearly shows the diversity gains achieved by multi- branch and multi-branch multi-hop systems. A design criterion is also presented which guarantees better outage and bit error performances for a multi-branch multi-hop system compared to a multi-branch system with the same number of branches.