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The performance evaluation of optical differential quadrature phase-shift keying (DQPSK) systems through numerical simulation using a Gaussian approach (GA) for the equivalent differential phase (EDP) statistics is analyzed. It is shown that the GA describes quite accurately the probability density function (PDF) of EDP for a large range of DQPSK receiver (RX) imperfections. A semi-analytical simulation method (SASM) for bit error probability (BEP) evaluation based on the GA for the EDP is derived, proving to be quite accurate in presence of RX imperfections. The SASM takes into account the signal-noise beat variance dependence on signal waveform distortion and arbitrary optical and electrical filtering frequency responses. Closed-form expressions for the mean and standard deviation of EDP are derived which allows evaluating the DQPSK system performance in a quite time-efficient manner. Discrepancies not exceeding 0.1 dB on the optical SNR penalty estimated by the SASM for a BEP of 10-4 when compared with Monte Carlo simulation are observed for the majority of the acceptable RX imperfections. Only the time-misalignment of the signals at the balanced detector input leads to higher discrepancies but not exceeding 0.3 dB even for considerable time-misalignment.