In this letter, we study efficient channel estimation and passive beamforming designs for a double-intelligent reflecting surface (IRS) aided single-user communication system, where a user communicates with an access point (AP) via the cascaded user-IRS 1-IRS 2-AP double-reflection link. First, a general channel estimation scheme is proposed for the system under any arbitrary inter-IRS channel, where all coefficients of the cascaded channel are estimated. Next, for the typical scenario with a line-of-sight (LoS)-dominant inter-IRS channel, we propose another customized scheme to estimate two signature vectors of the rank-one cascaded channel with significantly less channel training time than the first scheme. For the two proposed channel estimation schemes, we further optimize their corresponding cooperative passive beamforming for data transmission to maximize the achievable rate with the training overhead and channel estimation error taken into account. Numerical results show that deploying two cooperative IRSs with the proposed channel estimation and passive beamforming designs achieves significant rate enhancement as compared to the conventional case of single IRS deployment.
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