In a synchronous, serial, data-transmission system using orthogonal groups of signal elements, the received signal elements of a group are detected simultaneously in an iterative process, a separate detection process being used for each received group of elements. At transmission rates of up to 9600 bits-per-second over voice frequency channels, a particularly cost-effective detection process operates by solving the appropriate set of simultaneous equations. Many different iterative techniques may be used to solve these equations, and the first objective of the research project is to determine which of the available techniques achieves the best compromise between the rate of convergence to the required solution and the equipment complexity involved.