  In this paper, we study two-way relay networks (TWRNs) in which two source
nodes exchange their information via a relay node indirectly in Rayleigh fading
channels. Both Amplify-and-Forward (AF) and Decode-and-Forward (DF) techniques
have been analyzed in the TWRN employing a Markov chain model through which the
network operation is described and investigated in depth. Automatic
Repeat-reQuest (ARQ) retransmission has been applied to guarantee the
successful packet delivery. The bit energy consumption and goodput expressions
have been derived as functions of transmission rate in a given AF or DF TWRN.
Numerical results are used to identify the optimal transmission rates where the
bit energy consumption is minimized or the goodput is maximized. The network
performances are compared in terms of energy and transmission efficiency in AF
and DF modes.
