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The bit-error-rate (BER) estimation of communication systems can be very time consuming when dealing with complex communication systems and complex modulation schemes such as orthogonal frequency-division multiplexing (OFDM). The signals of such modulation schemes have crest factors (also known as peak-to-average power ratios) that strongly depend on the transmitted symbol. This paper describes a quasi-analytical method to compute the BER, which takes the probability density function (pdf) of the crest factor into account. For each crest factor, the BER is computed using either a Monte Carlo estimate or a quasi-analytical method, which uses the Best Linear Approximation (BLA) model to determine the signal-to-distortion ratio. This BLA model determines a best linear model (in least-squares sense) of the nonlinear system, together with additive noise sources that comprise not only additive noise but also stochastic nonlinear distortions. This best linear model also includes the compression characteristics introduced by the nonlinear system. The proposed quasi-analytical BER method is demonstrated on measurements of an asymmetric digital subscriber line (ADSL) modem driver and on system-level simulations of an OFDM wireless local area network (WLAN) system. The results show that the technique achieves similar accuracies with almost two orders of magnitude fewer simulations than without taking the pdf of the crest factor into account.