This work proposes an Expectation-Maximization (EM) based joint channel estimation and data detection algorithm and a time sharing hopped cooperative communication for the downlink of a communication network. The algorithm was applied to the downlink of a single hop relaying network. The relaying technique is a variant of the decode and forward technique. However, it is a time sharing single hop cooperative communication technique applied to a multi-carrier code division multiple access used in cellular networks. The proposed EM algorithm is compared with the minimum mean square estimation (MMSE) method using simulation. In addition, the proposed relaying technique is compared with cooperative communication on the considered cellular network for frequency-selective fading channels. Simulation results illustrate that our proposed EM algorithm performs better than the MMSE algorithm and that our proposed relaying technique is better than the normal case and the cooperative diversity case.