The achievable rates of three decode-and-forward half-duplex (DFHD) and two decode-and-forward full-duplex (DFFD) protocols are studied under a peak power constraint (PPC) and an average power constraint (APC). Two of the DFHD and one of the DFFD protocols are known. One new, much simpler, DFHD protocol, and one new DFFD protocol are proposed. The fairness in comparing the protocols in terms of energy cost is formulated, and the protocols are compared to each other in a power-fair regime. The two previously proposed DFHD protocols, one of which is superior to the other under the PPC, are found to have almost the same performances when compared power-fairly. The proposed protocols are built upon the water filling principle and power optimization such that, although inferior to their predecessors in a PPC regime, they can slightly surpass them under the APC. The protocols considered here take advantage of the previously proposed opportunistic relaying (ORe) concept. The original ORe is not directly applicable to the rateless schemes. However, it is shown that the ORe, after a novel modification, is compatible with, and implementable in the rateless protocols. The ORe brings about practical benefits and economical use of network resources in relaying systems.

Exact statistics of the local signal-to-noise ratios (SNRs) of the best relay in decode-and-forward (DF) opportunistic relaying (ORe) are derived. It is observed that although the different links are assumed to suffer independent fadings, the best-relay local SNRs are dependent. Both joint and marginal statistics are determined for the general case of nonidentical SNR distributions, and a source-relay-symmetric (S-R-sym.), relaydestination-symmetric (R-D-sym.) case. Both general fading and Rayleigh fading cases are considered. Using the statistics derived, exact, closed-form expressions for the outage probability and ergodic capacity of DF ORe are calculated in the S-R-sym., R-D-sym., Rayleigh fading case. The exact results for the outage probability show almost linearly increasing diversity order with the number of relays. The exact results for the ergodic capacity show a multiplexing gain almost equaling one half and a power gain increasing with the number of relays that exhibits diminishing returns.

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