The combination of frequency diverse array (FDA) radar technology with the multiple input multiple output (MIMO) radar architecture and waveform diversity techniques potentially promises a high integration gain with respect to conventional phased array (PA) radars. In this paper, we propose an approach to the design of the transmitter and the receiver of a coherent FDA (C-FDA) radar, that enables it to perform the demodulation with spectral overlapping, due to the small frequency offset. To this purpose, we derive the generalized space-time-range signal model and we prove that the proposed C-FDA radar has a higher coherent array gain than a PA radar, and at the same time, it effectively resolves the secondary range-ambiguous (SRA) problem of FDA-MIMO radar, allowing for mainlobe interference suppression and range-ambiguous clutter suppression. Numerical analysis results prove the effectiveness of the proposed C-FDA radar in terms on anti-interference and anti-clutter capabilities over conventional radars.