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The authors study the performance of wireless bidirectional relay-assisted networks in the presence of imperfect channel state information, where two end-source terminals S1 and S2 communicate with the assistance of M relay terminals Rj's. The max'min relay selection criterion is used to select the best relay that maximises the minimum signal-to-noise ratio of the links S1 → Rj → S2 and S2 → Rj → S1 over all relay terminals. The authors investigate the impact of imperfect channel estimation on the outage probability Pout of the system by means of the correlation coefficient pSi of the estimated channel gains and their actual values. Furthermore, the authors show that in a bidirectional relay-assisted network neither of the links S1 → Rj → S2 and S2 → Rj → S1 dominates the performance of the system. Instead, the performance is determined by the average performance of the two links, based on that the authors then discuss the power allocation in such networks. The authors demonstrate that in order to minimise Pout of the entire system, increasing the transmission power of the link with better estimation cannot compensate for the effect of the worse link and therefore the optimum power allocation with the least complexity is to transmit at each source terminals S1 and S2 with equal powers. Numerical results are also presented to corroborate the analytical expressions.