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In this study, the authors consider the problem of direction of arrival (DOA) estimation in compressive sensing multiple-input and multiple-output (CS-MIMO) radars with co-prime receive arrays. A sparse aperture completion scheme is proposed to fill the ‘holes’ that in the difference co-array, achieving the full virtual receive aperture. Structured measurement matrices are devised in order that the output data of match filters can be seen as space–time compressed signal of a virtual uniform linear array. By employing the space–time recovery scheme, the sparse target scene can be accurately recovered while the amount of samples is further reduced. Numerical results demonstrate that the proposed scheme can achieve accurate DOA estimation with space–time compressed data and outperform the CS-based difference co-array methods.