Upper bound for the performance metrics of amplify-and-forward cooperative networks based on harmonic mean approximation

In many studies of amplify-and-forward cooperative networks, a harmonic mean approximation has been used for the instantaneous signal-to-noise ratio of each dual hop relaying branch. This approximation overestimates the signal-to-noise ratio and results in a lower bound for the performance metrics, such as outage probability and average error probability. In this paper, a framework is introduced to obtain a tight upper bound for these performance metrics, as a function of harmonic mean approximation. It is shown that this upper bound is the tightest possible one among all harmonic mean related approximations. This bound is derived by modifying the same analysis used in the previous studies to compute the lower bound, without increasing the order of computational complexity. Numerical results and simulations show that the proposed upper bound for the performance metrics well follows the exact values.