Sparse Activity Detection in Intelligent Reflecting Surface Assisted Wireless Networks

The sparse activity detection in intelligent reflecting surface (IRS) assisted wireless networks is investigated in this paper. With generalized approximate message passing (GAMP) algorithm, we first obtain the minimum mean square error (MMSE) estimates of the equivalent effective channel coefficients from the base station (BS) to the users, and convert the received pilot signals into additive Gaussian noise corrupted versions of the equivalent effective channel coefficients. Subsequently, multiple decisions on the activity of each user are made using the likelihood ratio test based on the Gaussian noise corrupted equivalent effective channel coefficients. At last, final decisions on the activity of all users are made with the optimal fusion rule, taking into account the previous decisions on the activity of each user and the corresponding reliabilities. Numerical results show that the average error probability of the sparse activity detection method proposed in this paper diminishes as the SNR, number of pilots, number of antennas at the BS or number of elements at the IRS increases.