The exact error rate has been derived for the noncoherent, optical matched-filter CDMA receiver, which decides for the data of a single user by comparing a photoelectron count to a threshold. The results differ from those of previous work in that they adhere fully to the semiclassical model of light and do not depend on limit theorems for large user groups or strong received optical fields. The analysis is valid for arbitrary quantum efficiencies, binary signature sequences, random gain distributions, and dark currents, and it is broad in application. Single-user demodulation based on a conditionally compound-Poisson observation has been considered, focusing on the special case of prime codes, equal energies, and utility-gain photodetectors in order to compare the optimal threshold and minimum error rate to those obtained using the approximations discussed. It has been found that the approximation of perfect optical-to-electrical conversion yields poor estimates of the error rate and optimal threshold at moderate incident optical intensities and dark currents. Further, the combined approximation of perfect optical-to-electrical conversion and Gaussian-distributed MAI yields an underestimate of the optimal threshold and an error rate that is neither an upper nor a lower bound. It has also been shown that when prime sequences are employed, the chip-synchronous approximation leads to an overestimate of the error rate.