On the ergodic capacity of multi-hop wireless relaying systems

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 are provided to examine the tightness of the upper bounds as well as 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.