In communication systems, the channel noise is usually assumed to be white and Gaussian distributed. Therefore, an optimum receiver structure designed for the additive white Gaussian noise (AWGN) channel is employed in applications. However, in wireless communication systems, noise is often caused by strong interferences. Moreover, there are other effects such as phase offset that degrade the performance of the receiver. Designing the optimum receiver for different channel models is difficult and not reasonable because channel model and channel statistics are not known at the receiver. In this paper, we propose a neural network-based approach to demodulate the transmitted signal over unknown channels. Naturally, the collection of the training data, design and training of the neural network, and finally reconfiguration of the system according to the designed neural network are implemented on software-defined digital signal processing facilities. In particular, we show that the proposed receiver is capable of jointly canceling the strong interferences and phase offset. Simulation results in various signal environments are presented to illustrate the performance of the proposed system. It is shown that the proposed approach has the same performance as the correlation demodulator structure for AWGN channels, while it has a clear advantage for unknown channel models. Moreover, it is shown that the neural network-based receiver may be used for channel estimation and equalization over Rayleigh channels. Numerical results indicate that the performance of the proposed receiver is very close to the Rayleigh theoretical bound.