Activity detection plays an important role in grantfree random access, a promising approach for handling a large number of users in use cases like massive machine type communication (mMTC). Existing activity detection algorithms cover various scenarios but overlook wideband distributed antenna systems, a practical configuration for next-generation wireless networks. When following conventional activity detection methods, sparse Bayesian learning (SBL) could be an option in this case. However, SBL-based methods for wideband systems lack the consistency of maximum likelihood estimation (MLE), resulting in unsatisfactory detection performance. This paper proposes a novel distributed activity detection framework for wideband cell-free multiple-input and multiple-output (MIMO). Specifically, we provide a novel uplink channel model for activity detection in wideband cell-free MIMO, accounting for asynchronous reception. Additionally, we present possible SBLbased methods, identifying their limitations, which motivates the development of a new approach for activity detection. Next, we propose a covariance-matching distributed activity detection framework that matches the sample covariance matrix to the estimated covariance matrix. Simulation results demonstrate the effectiveness of the proposed distributed algorithm.

Massive multiple-input-multiple-output (MIMO) and millimeter wave have been adopted as the enabling technologies for the 5G and beyond 5G (B5G) systems. A challenging problem introduced by the use of large antenna size and wide bandwidth is beam squint, i.e., spatial-wideband effect. Beam squint can significantly degrade the channel estimation performance for conventional channel estimators. Research effort on channel estimation under beam squint conditions has been very limited. For the few available work that attempts to address this problem, they require either all subcarriers or multiple symbols used as pilot for channel estimation, so large overhead becomes inevitable. Therefore, in this paper, we propose an efficient channel estimation method that only requires a small number of subcarriers. The channel estimation problem is formulated as a nonlinear least squares optimization problem. Initial parameter estimation is critical, which will affect the efficiency and convergence of the proposed algorithm. Using a densely-spaced antenna structure and consecutive subcarriers assignment approach, we can effectively avoid the aliasing effect and reduce the ambiguity during the initialization phase. A subcarrier assignment criterion is proposed to achieve the optimal performance. Closed-form expressions of the Cramér-Rao lower bound (CRLB) and the achievable rate are derived to evaluate the performance. Both simulation results and theoretical analysis show that even with a small number of subcarriers, the estimation error closely approaches the CRLB, and its effect is negligible compared with the noise when evaluating the signal-to-noise ratio with a simple linear detector. Furthermore, the number of pilot subcarriers has little impact on the achievable rate.