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Double-reconfigurable intelligent surface (RIS) is a promising technique,achieving a substantial gain improvement compared to single-RIS techniques.However, in double-RIS-aided systems, accurate channel estimation is morechallenging than in single-RIS-aided systems. This work solves the problem ofdouble-RIS-based channel estimation based on active RIS architectures with onlyone radio frequency (RF) chain. Since the slow time-varying channels, i.e., theBS-RIS 1, BS-RIS 2, and RIS 1-RIS 2 channels, can be obtained with active RISarchitectures, a novel multi-user two-timescale channel estimation protocol isproposed to minimize the pilot overhead. First, we propose an uplink trainingscheme for slow time-varying channel estimation, which can effectively addressthe double-reflection channel estimation problem. With channels' sparisty, alow-complexity Singular Value Decomposition Multiple Measurement Vector-BasedCompressive Sensing (SVD-MMV-CS) framework with the line-of-sight (LoS)-aidedoff-grid MMV expectation maximization-based generalized approximate messagepassing (M-EM-GAMP) algorithm is proposed for channel parameter recovery. Forfast time-varying channel estimation, based on the estimated large-timescalechannels, a measurements-augmentation-estimate (MAE) framework is developed todecrease the pilot overhead.Additionally, a comprehensive analysis of pilotoverhead and computing complexity is conducted. Finally, the simulation resultsdemonstrate the effectiveness of our proposed multi-user two-timescaleestimation strategy and the low-complexity Bayesian CS framework.

Active 3D Double-RIS-Aided Multi-User Communications: Two-Timescale-Based Separate Channel Estimation via Bayesian Learning