Maximum likelihood detection upper bound for detect-and-forward relaying over AWGN channels

The maximum likelihood (ML) detection rule for the detect-and-forward relaying in Additive White Gaussian Noise (AWGN) channels which takes into account the detecting errors at the relay is formulated. In order to focus the study on relaying, channel coding is eliminated. Based on the derived ML detection rule, the upper bound on the probability of error at the destination's receiver is analyzed. The source-relay-destination channel is assumed to be equivalent to an AWGN channel with an equivalent signal-to-noise ratio (SNR) γ
_eq
. For the first time, the γ
_eq
is analyzed and its exact analytical expression is derived.