Tight Bounds for Ergodic Capacity of Cooperative Relaying over Rayleigh Fading Channels

In this letter, a closed-form expression for the exact ergodic capacity of decode-and-forward (DF) systems is derived. Since the closed-form expression includes exponential integral functions and is not mathematically tractable, we simplify the expression by using Taylor series to obtain the lower and upper bounds of the ergodic capacity. However, the bounds may be loose in low signal-to-noise ratio (SNR). Integral inequalities are applied to get tighter bounds. The simulation results also show that our closed-form bounds match perfectly with the exact ergodic capacity in moderate and high SNR.

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