On the Ergodic Capacity of Wireless Relaying Systems over Rayleigh Fading Channels

The ergodic capacities in Rayleigh fading of various wireless relaying systems with an arbitrary number of half-duplex relays are analyzed, assuming channel state information is only known at the receivers. Closed-form analytical expressions for calculation of the ergodic capacities of these systems are derived. It is shown that systems with nonregenerative fixed gain relays achieve higher ergodic capacities than the corresponding systems with nonregenerative variable gain relays. A modified fixed gain relay, which incorporates the power constraint at the relays, is proposed. It is shown that systems with modified fixed gain relays slightly outperform the corresponding systems with nonregenerative variable gain relays and fixed gain relays at small signal-to-noise ratios, but attain almost the same ergodic capacities as systems with nonregenerative variable gain relays as the signal-to-noise ratio increases. In addition, the ergodic capacity of a hybrid system with both regenerative and nonregenerative relays is studied. Systems with regenerative relays employing decode-and-forward relaying offer higher ergodic capacities than the corresponding systems with any classes of nonregenerative relays or hybrid relays.