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In this paper, we investigate jointly sparse signal recovery and jointlysparse support recovery in Multiple Measurement Vector (MMV) models for complexsignals, which arise in many applications in communications and signalprocessing. Recent key applications include channel estimation and deviceactivity detection in MIMO-based grant-free random access which is proposed tosupport massive machine-type communications (mMTC) for Internet of Things(IoT). Utilizing techniques in compressive sensing, optimization and deeplearning, we propose two model-driven approaches, based on the standardauto-encoder structure for real numbers. One is to jointly design the commonmeasurement matrix and jointly sparse signal recovery method, and the otheraims to jointly design the common measurement matrix and jointly sparse supportrecovery method. The proposed model-driven approaches can effectively utilizefeatures of sparsity patterns in designing common measurement matrices andadjusting model-driven decoders, and can greatly benefit from the underlyingstate-of-the-art recovery methods with theoretical guarantee. Hence, theobtained common measurement matrices and recovery methods can significantlyoutperform the underlying advanced recovery methods. We conduct extensivenumerical results on channel estimation and device activity detection inMIMO-based grant-free random access. The numerical results show that theproposed approaches provide pilot sequences and channel estimation or deviceactivity detection methods which can achieve higher estimation or detectionaccuracy with shorter computation time than existing ones. Furthermore, thenumerical results explain how such gains are achieved via the proposedapproaches.

Jointly Sparse Signal Recovery and Support Recovery via Deep Learning with Applications in MIMO-based Grant-Free Random Access