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This paper proposes a closed-loop sparse channel estimation (CE) scheme for wideband millimeter-wave hybrid full-dimensional multiple-input multiple-output and time division duplexing based systems, which exploits the channel sparsity in both angle and delay domains. At the downlink CE stage, random transmit precoding matrix is designed at base station (BS) for channel sounding, and receive combining matrices at user devices (UDs) are designed whereby the hybrid array is visualized as a low-dimensional digital array for facilitating the multi-dimensional unitary ESPRIT (MDU-ESPRIT) algorithm to estimate respective angle-of-arrivals (AoAs). At the uplink CE stage, the estimated downlink AoAs, namely, uplink angle-ofdepartures (AoDs), are exploited to design multi-beam transmit precoding matrices at UDs to enable BS to estimate the uplink AoAs, i.e., the downlink AoDs, and delays of different UDs, whereby the MDU-ESPRIT algorithm is used based on the designed receive combining matrix at BS. Furthermore, a maximum likelihood approach is proposed to pair the channel parameters acquired at the two stages, and the path gains are then obtained using least squares estimator. According to spectrum estimation theory, our solution can acquire the super-resolution estimations of the AoAs/AoDs and delays of sparse multipath components with low training overhead. Simulation results verify the better CE performance and lower computational complexity of our solution over state-of-the-art approaches.

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