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Intelligent reflecting surfaces (IRSs) can improve the wireless link between the transmitter and receiver by configuring the propagation environments of the system. In order to achieve intelligence of the configuration, the channel state information is required. In this paper, we study the downlink channel estimation problem in an IRS-aided frequency division duplexing (FDD) multiple-input multiple-output (MIMO) system. We propose a two-phase training scheme such that the direct channel (non-IRS channel) and the cascaded channel (IRS-aided channel) can be tracked by two Kalman filters separately. The pilots transmitted by the base station (BS) and the reflective coefficients at the IRS are then jointly optimized to improve the channel estimation accuracy. Since the formulated problem is non-convex, the optimal solution is not straightforward. A lower bound of the objective function is derived to serve as the baseline for evaluating the performance of a certain pilot and reflective coefficients design. In two special cases, namely the direct channel dominant scenario and the cascaded channel dominant scenario, we find that the optimal pilots and the optimal reflective coefficient matrix can be approximated by some columns of the discrete Fourier transform (DFT) matrices as the number of antennas at the BS and the number of reflective elements at the IRS get larger. We further propose a codebook-based low-complexity design for a general scenario which can significantly reduce the control overhead of the IRS and cut the computational burden. Numerical results are provided to verify the efficiency of the proposed channel estimation method. [ABSTRACT FROM AUTHOR]

Unlike the time-division duplexing systems, the downlink (DL) and uplink (UL) channels are not reciprocal in the case of frequency-division duplexing (FDD). However, some long-term parameters, e.g., the time delays and angles of arrival of the channel paths, enjoy reciprocity. In this paper, by efficiently exploiting the aforementioned limited reciprocity, we address the DL channel state information (CSI) feedback in a practical wideband massive multiple-input multiple-output system operating in the FDD mode. With orthogonal frequency-division multiplexing waveform and assuming frequency-selective fading channels, we propose a scalable framework for the DL pilots design, DL CSI acquisition, and the corresponding CSI feedback in the UL. In particular, the base station (BS) can transmit the FFT-based pilots with carefully selected phase shifts. Then, the user can rely on the so-called time-domain aggregate channel to derive the feedback of reduced dimensionality according to either its own knowledge about the statistics of the DL channels or the instruction from the serving BS. We demonstrate that each user can just feed back one scalar number per DL channel path for the BS to recover the DL CSIs. Comprehensive numerical results further corroborate our designs. [ABSTRACT FROM PUBLISHER]