The aim of this work is to study data transmission over a microwave digital mobile radio channel at 900 MHz, where the channel is subjected to multipath fading. Besides the fading, the other impairments assumed here are additive noise, co-channel interference and adjacent channel interference. Two modulation techniques are investigated in this work, namely Quadrature-Amplitude-Modulation (QAM) and Quadrature-Phase-Shift- Keying (QPSK). The channel is characterised digitally, assuming multipath Rayleigh fading in the presence of noise. The detection process studied here are near-maximum likelihood schemes: non-linear equalisation methods are also considered in detail. The thesis is also concerned with carrier synchronisation and channel estimation under conditions of Rayleigh fading. Since the carrier syncn,honisation is a most important requirement in mobile radio, a Digital Phase Locked Loop (DPLL) technique has been designed and investigated in the form of a feedback digital synchronisation system. Two types of channel estimation technique, namely feedforward and feedback estimators, are also investigated in this work. The feedback estimator is modified by the addition of a digital control system, in order to reduce its delay, and to cope with rapidly fading signals. Successful carrier synchronisation is demonstrated by the use of space diversity. The study was completed using models of the component parts of the system, and by the use of extensive computer simulations to analyse the system under various operating conditions.