Tight Bounds for Ergodic Capacity of Dual-Hop Fixed-Gain Relay Networks under Rayleigh Fading

Abstract

Since a closed-form expression for the exact ergodic capacity of dual-hop fixed-gain relay networks is not mathematically tractable, thus we will present tight closed-form bounds for the ergodic capacity in Rayleigh fading channels. First we express the exact ergodic capacity in terms of a Lommel function and a single integral and then we apply integral inequalities to present one upper bound and two lower bounds on the ergodic capacity. We also show that our closed-form bounds match perfectly with Monte-Carlo simulations, particularly for moderate and high average signal-to-noise ratio (SNR) of the first hop.