Cooperative Reflection and Synchronization Design for Distributed Multiple-RIS Communications

To reap the promised gain achieved by distributed reconfigurable intelligent surfaces (RISs)-enhanced communications in a wireless network, timing synchronization among these metasurfaces is an essential prerequisite in practice. This paper proposes a unified framework for the joint estimation of the unknown timing offsets and the RIS channel parameters, as well as the design of cooperative reflection and synchronization algorithm for the distributed multiple-RIS communication. Considering that RIS is usually a passive device with limited capability of signal processing, the individual timing offset and channel gains of each hop of the RIS links cannot be directly estimated. To make the estimation tractable, we propose to estimate the cascaded channels and timing offsets jointly by deriving a maximum likelihood estimator. Furthermore, we theoretically characterize the Cramér-Rao lower bound (CRLB) to evaluate the accuracy of this estimator. By using the proposed estimator and the derived CRLBs, an efficient resynchronization algorithm is devised jointly at the RISs and the destination to compensate the multiple timing offsets. Based on the majorization-minimization framework, the proposed algorithm admits semi-closed and closed form solutions for the RIS reflection matrices and the timing offset equalizer, respectively. Simulation results verify that our theoretical analysis well matches the numerical tests and validate the effectiveness of the proposed resynchronization algorithm.