RISs-Enabled Separation of Multi-User Collided Signals in IQ Domain Based on Two-Stage Online Optimization

Reconfigurable intelligent surfaces (RISs) can serve multiple users by fully exploiting the channel diversity of users. Motivated by existing parallel decoding schemes in the in-phase and quadrature (IQ) domain, we investigate uplink parallel reception of multi-user transmissions assisted by multiple RISs. RISs adjust their phase shift to help separate the multi-user collided signals in the IQ domain, and then the signals from different users can be considered as collaboratively building up a higher-order meta-constellation. Eliminating the entanglement in the meta-constellation, different user signals can be demodulated simultaneously. To guarantee the effective separation and demodulation of multiple data streams in collided signals, we minimize the error probability under maximum likelihood detection. Besides, catering to the highly dynamic communication channel at reduced signaling overhead, we propose a design which requires channel state information (CSI) at two time scales. The base station selects the served users based on statistical CSI during each frame, while the transmit power of users and the phase vector of RISs are adaptive to the instantaneous CSI. This results in a challenging mixed-integer two-stage stochastic problem. Thus, a two-stage online algorithm is proposed, in which the short-term subproblems are transformed to convex optimization problems, while the long-term master problem can be transformed to an integer programming with an objective function exhibiting the structure of a convex function and affine constraints. Simulation results show that with the aid of RISs, the detection error probability drops by four orders of magnitude compared to the case without RIS.