Lifetime Analysis of a Two-Hop Amplify-and-Forward Opportunistic Wireless Relay Network

An expression is derived for the probability mass function (PMF) of the relay transmit power in a variable gain amplify-and-forward (VG-AF) opportunistic wireless relay network (OWRN). The PMF is used to calculate the average relay transmit power. An expression is also obtained for evaluating the transition probabilities between energy states in a Markov chain model of the OWRN. This model is used to compute the average OWRN lifetime for a small number of relays, allowable transmit power levels, and low initial relay energy levels. Unfortunately, the computational complexity of this approach becomes prohibitive as the number of relays, transmit power levels, and initial energy levels increase. A low-complexity method, based on an existing expression and the average relay transmit power, is used to estimate the average network lifetime. The method is shown to yield very accurate results for practical initial relay energy levels.