The rapid changes and developments in cellular and wireless networks aim to provide more reliable communications with high data rate transmission. So far, one solution which is being considered for improving the reliability and eciency of mobile communications is cooperative communications. Implementing di fferent relay scenarios leads to the improvement of the security, ecient, and fast transmission with a good quality of service. The work of this thesis is on the piecewise-and-forward (PF) relay network. This relay protocol is implemented for decreasing the complexity of signal detection at the receiver. Our focus is to investigate the performance of PF relay networks based on the statistical variations which are caused by the fading environment. We considered a relay network with one source and one destination while multiple parallel relays aid the transmission process. At the destination the maximum likelihood (ML) method is implemented for detecting the received signals. Therefore, the probability density function (PDF) of received signals should be used at the ML detector. We analytically investigate the PDF of the received signals, when the transmitted signals are faced with Rayleigh fading. For verifying the theoretical calculations, we use Monte-Carlo simulations in MATLAB to evaluate the results. Afterwards, the bit error rate (BER) has been considered for investigating the performance of the PF relay network over a Rayleigh fading channel. Furthermore, the BER performance of the PF relay network is compared with three well known relay networks, amplify-and-forward (AF), decode-and forward (DF), and estimate-and-forward (EF) relay networks.