Joint active user detection and channel estimation for massive machine-type communications: a difference-of-convex optimization perspective

Sparsity-based joint active user detection and channel estimation (JADCE) algorithms are crucial in grant-free massive machine-type communication (mMTC) systems. The conventional compressed sensing algorithms are tailored for noncoherent communication systems, where the correlation between any two measurements is as minimal as possible. However, existing sparsity-based JADCE approaches may not achieve optimal performance in strongly coherent systems, especially with a small number of pilot subcarriers. To tackle this challenge, we formulate JADCE as a joint sparse signal recovery problem, leveraging the block-type row-sparse structure of millimeter-wave (mmWave) channels in massive multiple-input multiple-output orthogonal frequency division multiplexing (MIMO-OFDM) systems. Then, we propose an efficient difference-of-convex function algorithm (DCA) based JADCE algorithm with multiple measurement vector (MMV) frameworks, promoting the row-sparsity of the channel matrix. To mitigate the computational complexity further, we introduce a fast DCA-based JADCE algorithm via a proximal operator, which allows a low-complexity alternating direction multiplier method (ADMM) to resolve the optimization problem directly. Finally, simulation results demonstrate that the two proposed difference-of-convex (DC) algorithms achieve effective active user detection and accurate channel estimation compared with state-of-the-art compressed sensing based JADCE techniques.