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Coprime arrays and coprime time samplers have been receiving attractive attention recently due to their advantages of large apertures and achievable degrees of freedom with low cost. In this paper, different from traditional airborne radar with uniform transmitting pulses, the considered radar is configured with a coprime array in receiver and transmits the pulses with coprime repetition intervals. Because this sampling structure violates the conditions of the conventional clutter rank estimation rules, we first propose a novel method to estimate the clutter rank based on effective aperture-bandwidth product. Then, two space-time adaptive processing (STAP) algorithms, namely, the sample matrix inverseand principal components-STAP, are proposed by using the reconstructed virtual space-time snapshots. Additionally, a thoroughly theoretical convergence analysis of the proposed algorithms is conducted. Exclusive simulation results are provided to demonstrate the effectiveness of the proposed STAP algorithms.