In this paper, the performance of the soft-decision-and-forward (SDF) protocol in the cooperative communication network with one source, one relay, and one destination, where each node has two transmit and receive antennas, is analyzed in terms of the bit error rate (BER) obtained from the pairwise error probability (PEP). Using the moment generating function and Q-function approximation, the PEP of SDF protocol is calculated and we confirm that the SDF with two antennas achieves the full diversity order. For the slow-varying Rayleigh fading channel, the optimal power allocation ratio can be determined so as to minimize the average PEP (or BER). Due to the difficulty of deriving the optimal value analytically, an alternative strategy of maximizing the product signal-to-noise ratio (SNR) of direct and relay links, which we call the suboptimal power allocation, is considered. Through a numerical analysis, we show that the performance gap between the suboptimal and optimal power allocation strategies is negligible in the high SNR region.