Ergodic Capacity of Multi-Hop Wireless Relaying Systems in Rayleigh Fading

The ergodic capacity in Rayleigh fading of multi- hop wireless transmission systems employing either amplify-and-forward relaying or decode-and-forward relaying is studied, assuming channel state information is only known at the receiving terminals. Two upper bounds based on Jensen´s inequality and the harmonic-geometric means inequality as well as an infinite series representation for the ergodic capacity of an amplify-and- forward multi-hop transmission system are derived. Numerical results indicate the upper bound obtained based on Jensen´s inequality is tight. This upper bound is tighter than the upper bound based on harmonic and geometric means for larger numbers of hops and especially for systems in non-identical fading. Numerical results are provided to show the high accuracy of the infinite series approach. In addition, the ergodic capacity of a decode-and-forward multi-hop transmission system is obtained. It is shown that multi-hop transmission systems employing a decode-and-forward relaying scheme achieve higher ergodic capacities than multi-hop transmission systems with amplify-and- forward relaying schemes.