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In this paper, we consider the problem of joint direction-of-arrival and order estimation in array processing with compressed sensing. In particular, we show how to solve these problems jointly using a subspace approach based on the notion of angles between subspaces. In the process, we also discuss the conditions on the measurement matrix and demonstrate how to implement the estimator algorithm efficiently when using compressed sensing. Our simulation results show that it is indeed possible to solve these problems and that good performance can be obtained, although the use of compressed sensing does have an impact on the performance of the estimator.