This paper is concerned with channel estimation and data detection for a cellular multi-carrier code division multiple access network using single-hop relaying in the presence of frequency selective fading channels. The proposed expectationmaximization (EM) algorithm was used to jointly estimate both the coefficients of the channel between a relay and a base station and the data. EM algorithm is particularly suited to multi-carrier code division multiple access systems because they have multi-carrier signal format. The considered network uses single-hop relaying technique to provide a higher quality transmission to the users with low quality channels. The base station (managing mechanism) gives them an opportunity to send their messages via the users with high quality channels in a time sharing mode. The performance of the proposed EM algorithm, with and without hopping and with cooperative communication technique, was analyzed by a computer simulation, and the results are presented. Copyright (c) 2011 John Wiley & Sons, Ltd.