On the exact capacity of dual-hop af relaying with adaptive channel inversion

A new exact closed-form expression is derived for the capacity of dual-hop amplify-and-forward (AF) relaying systems with adaptive channel inversion operating over Nakagami-m fading channels. Truncated channel inversion, at a certain cutoff signal-to-noise ratio (SNR), is assumed to avoid capacity loss resulting in the case of non-truncated channel inversion. The cutoff SNR is selected so as to maximize the system capacity. The results represent the first exact solutions for dual-hop AF systems under adaptive transmission. The capacity of the systems under study is derived in terms of modified Bessel functions of the second kind, commonly available in mathematical software. The accuracies of the analytical results are verified by Monte Carlo simulations.