In a wireless network, users can relay information to exploit cooperative diversity, thereby increasing reliability and reducing power consumption. This thesis focuses on noncoherent communication theory for cooperative diversity. This thesis develops a general framework for maximum likelihood (ML) demod- ulation for cooperative diversity with a decode-and-forward protocol at the relays. A piecewise-linear (PL) demodulator is developed as an accurate approximation of nonlinear ML detectors. This PL detector leads to an involved yet closed-form ap- proximation for the error probability of ML detectors. Numerical results show that the approximation is very tight. Analysis based on the Bhattacharyya upper bound suggests cooperative diversity with decoding relays does not achieve full diversity order. This conclusion is supported by the high SNR approximation of error prob- ability obtained from the PL approximation. This thesis also presents some results about the application of convolutional codes in cooperative diversity. Given the same spectral e ciency, simulation results suggest that cooperative diversity can perform better than non-cooperative single-hop in the block fading channel given both schemes use ML detectors designed for the i.i.d. fading channel.