The single relay selection (SRS) scheme in two-way relay cooperative systems has been focus of attention. This is because it offers higher spectral efficiency (SE) compared to multi-relay scheme and one-way relay cooperative systems. The SRS problem for two-way relays is not much studied in compare to one-way relay networks, and only few researches have been carried out. In all proposed problems in SRS scheme, researchers have ignored collisions in SRS scheme, and only considered an ideal system. In this paper, we investigate SE of the SRS based on distributed method which has not adequately addressed for two-way relay. Moreover, we investigate the effects of collision on SE, by considering an amplifier and forward network in a two-way cooperative system. Our numerical and simulation results show that in a small two-way relay system, the time selection period is the main factor in the system performance. However, in a large system, the probability of collision is the main consideration in designing a two-way relay system with high spectral efficiency.