Eigenvalue-Based Active User Enumeration for Grant-Free Access Under Carrier Frequency Offsets

This letter investigates a grant-free non-orthogonal multiple access (GF-NOMA) system in the presence of carrier frequency offsets. We propose two schemes for enumerating active users in such a GF-NOMA system, which is equivalent to estimating the sparsity level. Both schemes utilize a short common pilot and the eigenvalues of the sample covariance matrix of the received signal. The two schemes differ in their treatment of noise variance: one exploits known variance information, while the other is designed to function without this knowledge. Simulation results demonstrate the effectiveness of the proposed schemes in terms of the normalized root-mean-squared error.