Abstract: An FDM-CPM multi-user detector (30) jointly detects the received symbols for all users by determining from the received multi-user signal an a-posteriori probability mass function (pmf) of a time-sequence of states and transmitted symbols of all users, by iterative message passing corresponding to a specific factorisation of the pmf. The factorisation involves a combined variable representing possible transmitted symbols and CPM states of each user for each symbol time interval, so as to make the iterative process convergent. Non exponential complexity is enabled by disregarding multiple access interference (MAI) from at least some of the other users. Applications can include hubs for satellite communication ground stations.