IRS-Assisted IoT Activity Detection Under Asynchronous Transmission and Heterogeneous Powers: Detectors and Performance Analysis

This paper introduces a unified framework for activity detection in IRS-assisted IoT networks that simultaneously addresses three critical practical challenges: asynchronous transmissions, heterogeneous power levels used by devices to report their local observations, and signal blockage in dynamic environments. The system leverages an intelligent reflecting surface (IRS) to enhance detection reliability, with optional incorporation of a direct line-of-sight (LoS) path. Departing from conventional approaches that handle these challenges in isolation, we formulate a comprehensive detection problem as a binary hypothesis test and develop a structured hierarchy of four detectors: an optimal detector alongside three computationally efficient detectors designed for practical scenarios with different levels of prior knowledge about noise variance, channel state information, and device transmit powers. This hierarchical approach systematically bridges the gap between theoretical optimality and implementation practicality. For each detector, we derive closed-form expressions for both detection and false alarm probabilities, establishing theoretical performance benchmarks and revealing fundamental scaling laws. Extensive simulations validate our analytical results and extract actionable design guidelines by systematically evaluating the impact of key system parameters including the number of antennas, samples, users, and IRS elements on detection performance, providing valuable insights for 6G IoT system designers. The proposed framework effectively bridges theoretical optimality with implementation practicality, providing a scalable solution for IRS-assisted IoT networks in emerging 6G systems.