The paper presents an optimum receiver for digitally modulated signals in additive class-A impulsive noise for flat fading channels. The receiver is based on maximum likelihood (ML) approach. Two algorithms are presented to estimate the unknown fading channel. The convergence properties of the estimation algorithms are investigated and compared. The performance of the receiver is evaluated by simulation. The performance is measured by the bit error probability. Computer simulations are illustrated to validate the theoretical developments. It is shown that the performance of the developed receiver is sensitive to the impulsive index of the noise. Decreasing the value of the impulsive index degrades the performance of the receiver and reduces the receiver resistivity against frequency and time offset.