  Sparse support recovery arises in many applications in communications and
signal processing. Existing methods tackle sparse support recovery problems for
a given measurement matrix, and cannot flexibly exploit the properties of
sparsity patterns for improving performance. In this letter, we propose a
data-driven approach to jointly design the measurement matrix and support
recovery method for complex sparse signals, using auto-encoder in deep
learning. The proposed architecture includes two components, an auto-encoder
and a hard thresholding module. The proposed auto-encoder successfully handles
complex signals using standard auto-encoder for real numbers. The proposed
approach can effectively exploit properties of sparsity patterns, and is
especially useful when these underlying properties do not have analytic models.
In addition, the proposed approach can achieve sparse support recovery with low
computational complexity. Experiments are conducted on an application ex-ample,
device activity detection in grant-free massive access for massive machine type
communications (mMTC). Numerical results show that the proposed approach
achieves significantly better performance with much less computation time than
classic methods, in the presence of extra structures in sparsity patterns.
