Hybrid Generalized Approximate Message Passing for Active User Detection and Channel Estimation with Correlated Group-Heterogeneous Activity

The random access procedure is a bottleneck to the development of wireless networks supporting the use cases of massive machine-type communication and ultra reliable and low-latency communication. Such networks are densely and massively popupated and must meet stringent latency and reliability requirements. Due to these characteristics, grant-free random access is envisioned to alleviate the control overhead generated by the classical random access procedure. However, active user detection and channel estimation algorithms are required. Existing algorithms assume that the activity of each device is homogeneous and independent, which is not the case in many applications (e.g., due to sensors observing a common phenomenon). In order to address this problem, we introduce a new flexible model taking into account a group-heterogeneous activity, using the framework of copula theory. It is then leveraged by a hybrid generalized approximate message passing algorithm to solve the active user detection and channel estimation problem. Our numerical results show that the user detection and channel estimation are both improved with this new algorithm w.r.t. state-of-the-art Bayesian algorithms, with gains up to 10 times fewer detection errors and 10 dB less channel estimation error.