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

Abstract

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.

1. Introduction

Millimeter-wave (mmWave) massive multiple-input multiple-output (massive MIMO) systems are remarkable for their gigabit-per-second high-speed data transmission rates and are considered a critical technology that can advance the sixth generation (6G) wireless communication networks. To mitigate severe propagation loss, numerous antenna elements are required by the base station (BS) for beamforming. However, the conventional antennas are associated with considerable hardware costs and power consumption owing to the large number of radio frequency (RF) chains required (Chukhno et al., 2024). To address this problem, a massive multipanel MIMO system integrates the antenna elements into a uniform antenna array with a partially connected hybrid structure, thus demonstrating advantages such as spatial diversity, flexible array deployment, and reduced hardware cost and power consumption. As a result, the massive multipanel MIMO systems have emerged as ideal array configurations for mmWave communications.

In addition, massive machine-type communication (mMTC) is an attractive application scenario for the 6G wireless communication networks for supporting various Internet of Things (IoT) applications. Compared to traditional communication schemes, mMTC is characterized by large-scale user connections, short packet transfers, low power consumption, and sporadic communication (i.e., only a fraction of users are active at any given coherent time interval). In view of avoiding the high signal overhead and high delay of traditional grant-based random access solutions, the grant-free random access protocol is popularly considered a candidate technology for the 6G wireless networks (Gao et al., 2024). Using this protocol, active users can transmit data signals by delivering preallocated pilot sequences without authorization from the BS. On this basis, it is paramount to perform joint active user detection and channel estimation (JADCE), which detects active users for ensuring efficient utilization of spectrum resources and obtains accurate channel state information (CSI) for improving communication quality and reliability (Liu KH et al., 2023).

Due to the sparseness of the user activity patterns, the JADCE problem can be expressed as a joint sparse signal recovery problem, which can be resolved by various compressed sensing algorithms (Liu KH et al., 2019, 2022, 2023; Gan et al., 2021; Wan et al., 2022; Zhu et al., 2023). Based on the grant-free nonorthogonal multi-access systems, this paper proposes a difference-of-convex optimization approach to tackle the JADCE problem in strongly coherent systems, offering a robust and efficient solution for next-generation wireless networks.