  In this paper, we investigate jointly sparse signal recovery and jointly
sparse support recovery in Multiple Measurement Vector (MMV) models for complex
signals, which arise in many applications in communications and signal
processing. Recent key applications include channel estimation and device
activity detection in MIMO-based grant-free random access which is proposed to
support massive machine-type communications (mMTC) for Internet of Things
(IoT). Utilizing techniques in compressive sensing, optimization and deep
learning, we propose two model-driven approaches, based on the standard
auto-encoder structure for real numbers. One is to jointly design the common
measurement matrix and jointly sparse signal recovery method, and the other
aims to jointly design the common measurement matrix and jointly sparse support
recovery method. The proposed model-driven approaches can effectively utilize
features of sparsity patterns in designing common measurement matrices and
adjusting model-driven decoders, and can greatly benefit from the underlying
state-of-the-art recovery methods with theoretical guarantee. Hence, the
obtained common measurement matrices and recovery methods can significantly
outperform the underlying advanced recovery methods. We conduct extensive
numerical results on channel estimation and device activity detection in
MIMO-based grant-free random access. The numerical results show that the
proposed approaches provide pilot sequences and channel estimation or device
activity detection methods which can achieve higher estimation or detection
accuracy with shorter computation time than existing ones. Furthermore, the
numerical results explain how such gains are achieved via the proposed
approaches.
