<p>Full duplex (FD) is an auspicious wireless technology that holds the potential to double data rates through simultaneous transmission and reception. This paper proposes two innovative designs of hybrid beamforming (HYBF) for a multicell massive multiple-input-multiple-output (mMIMO) millimeter wave (mmWave) FD system. Initially, we introduce a novel centralized HYBF (C-HYBF) scheme, which employs the minorization-maximization (MM) method. However, while centralized beamforming designs offer superior performance, they suffer from high computational complexity, substantial communication overhead, and demand expensive computational resources. To surmount these challenges, we present a framework that facilitates per-link parallel and distributed HYBF (P$\&$D-HYBF) in the mmWave frequency band. This cooperative approach enables each base station (BS) to independently solve its local, low-complexity sub-problems in parallel, resulting in a substantial reduction in communication overhead and computational complexity. Simulation results demonstrate that P$\&$D-HYBF achieves comparable performance to C-HYBF, and with only a few radio-frequency (RF) chains, both designs surpass the capabilities of fully digital half duplex (HD) systems.</p>
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