Recent applications of the Full Duplex (FD) technology focus on enabling simultaneous control communication and data transmission to reduce the control information exchange overhead, which impacts end-to-end latency and spectral efficiency. In this paper, we present a simultaneous direction estimation and data transmission scheme for millimeter Wave (mmWave) massive Multiple-Input Multiple-Output (MIMO) systems, enabled by a recent FD MIMO technology with reduced hardware complexity Self-Interference (SI) cancellation. We apply the proposed framework in the mmWave analog beam management problem, considering a base station equipped with a large transmit antenna array realizing downlink analog beamforming and few digitally controlled receive antenna elements used for uplink Direction-of-Arrival (DoA) estimation. A joint optimization framework for designing the DoA-assisted analog beamformer and the analog as well as digital SI cancellation is presented with the objective to maximize the achievable downlink rate. Our simulation results showcase that the proposed scheme outperforms its conventional half-duplex counterpart, yielding reduced DoA estimation error and superior downlink data rate.
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