In-band crosstalk can pose important limitations in an all-optical wavelength-division-multiplexed (WDM) network. Recent studies have demonstrated that differential phase shift keying (DPSK), can tolerate higher in-band crosstalk-noise levels compared to amplitude shift keying (ASK). In this paper, the performance of a DPSK receiver, limited by in-band crosstalk noise, is studied theoretically. The model takes into account both the in-band crosstalk noise as well as the amplified-spontaneous-emission (ASE) noise of the optical amplifiers. The model is based on the evaluation of the moment-generating function (MGF) of the decision variable through which, the error probability (EP) can be calculated by applying the saddle point approximation. This provides a rigorous model for the evaluation of the EP of a DPSK receiver in the presence of ASE and in-band crosstalk noises. In the absence of the ASE noise, a closed-form formula for the EP is also given that is useful for estimating the error floor set by the in-band crosstalk noise.