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

Joint Design of Measurement Matrix and Sparse Support Recovery Method via Deep Auto-encoder