A train of radar pulses from one resolution cell can be processed coherently to reject echoes from external clutter and detect targets moving radially with respect to the clutter. Optimum methods of signal processing are defined for systems in which the interpulse spacings are multiply staggered to avoid target blind speeds. Likelihood ratio tests are developed for systems in which the target Doppler frequency is known a priori and for systems employing a bank of filters to cover the target Doppler band. To implement such tests, the N pulses in the train are added with complex weights and the amplitude of the sum compared with a detection threshold. The set of weights which maximizes the average signal-to-clutter ratio is also computed for a single-filter system with unknown target Doppler frequency. When the clutter autocorrelation function is exponential, the clutter covariance matrix can be inverted analytically. This latter result is useful for comparing different interpulse-spacing codes for a particular system application.