Performance analysis of two-hop relayed transmissions over Rayleigh fading channels

Closed form expressions for the statistics of the harmonic mean of two independent exponential variates are presented. These statistical results are then applied to study the performance of wireless communication systems with non-regenerative relays over flat Rayleigh fading channels. It is shown that these results can either be exact or tight lower bounds on the performance of these systems depending on the choice of the relay gain. More specifically, outage probability formulas for noise limited systems are obtained. Furthermore, outage capacity and bit error rate (BER) expressions for binary differential phase shift keying are derived. Finally, comparisons between regenerative and non-regenerative systems are presented. Numerical results show that the former systems clearly outperform the latter ones for low average signal-to-noise-ratio (SNR). They also show that the two systems have similar performance at high average SNR.