Outage probability of cooperative diversity systems with opportunistic relaying based on decode-and-forward

Opportunistic relaying with cooperative diversity has been introduced in [1] as a simple alternative protocol to the distributed space-time coded protocol while achieving the same diversity-multiplexing tradeoff performance as a point-to-point multiple-input multiple-output scheme. In this paper, we derive the upper and lower bounds for the cumulative distribution function of the signal-to-noise ratio per hop, and then provide their probability density function and moment generating function.We also derive approximate but tight closed-form expressions for the lower and upper bounds of the outage probability of opportunistic relaying based on decode-and-forward transmission under the assumption of unbalanced/balanced hops and independent, identically distributed Rayleigh fading channels.