Amplify-and-forward cooperative systems with fixed gain relays

Multi-hop and multi-branch wireless transmission systems with nonregenerative fixed gain relays employing amplify-and-forward relaying are studied. Simple closed-form expressions for the outage and bit error probabilities of these systems are derived. The analysis is valid for an arbitrary number of hops, arbitrary number of branches and any fading channel model whose signal power probability density function has nonzero value at the origin. 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 systems for any fading channel model.