A Closed-Form Expression of Optimal Time for Two-Way Relay Using DF MABC Protocol

In this paper, we propose the optimal time allocation for two-way relay using decode-and-forward (DF) multiple access broadcast (MABC) protocol. We analytically determine the optimal transmit time durations for the first and the second time slots, which maximize the achievable sum rate under a sum time constraint for a given squared magnitude of the channel coefficients and transmit power values. Numerical results show that the achievable sum rate of the optimal time allocation is greater than or equal to that of the equal time allocation.