Cooperative diversity is an emerging technique that enables single-antenna terminals to share their resources (bandwidth and power) and achieve transmit diversity in a distributed fashion. In this work, an adaptive decode-and-forward(DF) cooperative diversity system based on quadrature signaling is proposed. Then a tight closed-form approximate bit error rate(BER) expression is derived in terms of the average received inter-user and uplink channel signal-to-noise ratios (SNRs) and power allocation factor. The derived BER performance is validated by simulations, which makes it possible to optimize the power allocation between the local and relay signals numerically under the channel scenarios of interest. Simulations show that equal power allocation strategy outperforms noncooperative system and the full diversity order of two is achieved at high inter-user channel SNRs, moreover, it is optimum in ideal cooperation scenario. In general scenarios, optimum power allocation strategy can be exploited to achieve additional performance benefits.