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The paper deals with the problem of radar detection of a target echo embedded in log-normal clutter and white Gaussian noise. Relevant features of this article, with respect to previous papers on the same subject, refer to the coherent model assumed for the clutter and the processing chain. In more detail, the in-phase and quadrature components of clutter have been modelled to give a log-normal amplitude distribution and a near uniform distribution of the phase. Any shape of the correlation among consecutive clutter samples is also allowed in the model. At the same time, the processing chain is also coherent, i.e. it operates on the two components of the signals. Two architectures have been considered for the processor. The first, used in current practice, is formed of a linear transversal filter (for the clutter attenuation and the target echo enhancement) cascaded with a quadratic envelope detector and a comparison with a suitable threshold. The second processor considered differs from the previous one in the filter for clutter cancellation. A nonlinear homomorphic filter has been conceived to obtain a better suppression of clutter. The detection performance of the two processing chains have been evaluated, by means of computer simulation, in a number of operational cases of intrest. The paper gives a first contribution to the problem of finding better models of disturbance and of deriving more efficient processing chains.