In this paper, we consider the application scenario where multiple Base Stations (BSs) cooperate to transmit signals to a mobile terminal in the same frequency and any of the cooperative BSs is allowed to enter into sleeping mode to save energy. The mobile terminal employs the Joint Maximum Likelihood Sequence Estimation (JMLSE) based Joint Signal Detection (JSD) to simultaneously detect multiple co-channel signals and judge whether a cooperative BS is active or not. The detection error probability of JSD is analyzed in this paper. For the case of BS sleeping, the error probability is computed based on a tentative modulation scheme which incorporates the M constellation points of conventional M-QAM and the additional constellation point 0. For the case of BS cooperation, the error probability bounds are derived based on a genie-aided receiver, and a new Tighter Lower Bound (TLB) is derived by replacing the genie with a less generous one. Simulation results have verified that the computed error probability can provide a rapid and accurate estimation of the Symbol Error Rate (SER) performance.