Joint Activity Detection and Channel Estimation for Intelligent Reflecting Surface Assisted Wireless IoT Networks

Intelligent reflecting surfaces (IRSs) provide the ability to tune the wireless environments by introducing passive scattering elements between the base station (BS) or access points (APs) and users, and it is a promising technology for next generation wireless networks. In this paper, we consider joint activity detection and channel estimation in both centralized and distributed IRS assisted IoT networks. We determine the explicit distribution for the equivalent channel coefficients from the BS or APs to the users. It is shown that this distribution can be equivalently represented with a Gaussian scale mixture (GSM) model. With generalized approximate message passing (GAMP) algorithm, the received pilot signals at the BS or APs are decoupled into scalar Gaussian noise corrupted versions of the effective channel coefficients. Subsequently, minimum mean square error (MMSE) estimate of the effective channel coefficients and threshold detection rules are acquired. Finally, the optimal fusion rule is used to obtain the activity detection results of each user. As an additional low-complexity approach, we approximate the equivalent channel coefficients with a Gaussian approximation (GA) model. We derive the theoretical mean square error for the MMSE estimate of the effective channel coefficients using the GA model and the state evolution equations of the GAMP algorithm, under the assumption that the direct links from the BS to the users can be neglected due to unfavorable propagation conditions. Numerical results show that the Gaussian approximation for the distribution of the equivalent channel coefficients is accurate even for moderate number of elements at the IRS. And the theoretical mean square error for the MMSE estimate of the effective channel coefficients under the assumption that direct link is negligible is shown to overlap with the corresponding numerical simulations.