Harmonic mean and end-to-end performance of transmission systems with relays

Closed-form expressions for the statistics of the harmonic mean of two independent and identically distributed gamma variates are presented. The probability density function of the harmonic mean of two F variates is also derived. These statistical results are then applied to study the performance of wireless communication systems with nonregenerative relays over flat Nakagami fading channels. More specifically, outage probability formulas for noise-limited systems as well as systems affected by interference are obtained. Furthermore, general expressions for average bit-error rates are also derived. Finally, comparisons between regenerative and nonregenerative systems are presented. Numerical results show that the former systems clearly outperform the latter ones for low average signal-to-noise ratios (SNRs). They also show that the two systems have similar performance at high average SNRs.