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An exact expression for the bit error probability of a maximum-likelihood receiver used to detect two bandlimited binary phase-shift keying signals in a synchronous additive white Gaussian noise channel in the presence of carrier phase recovery errors is derived. The users employ pulse-shaping filters whose impulse responses satisfy Nyquist's first criterion for zero intersymbol interference. The receiver's error probability is compared with that of the perfect phase recovery case for various values of signal-to-interference ratio (SIR) to show its sensitivity to carrier phase errors. It is shown that the receiver is more robust to carrier phase mismatch at large values of SIR than at small values of SIR.