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Millimeter wave (mmWave) communication is a promising New Radio in Unlicensed (NR-U) technology to meet with the ever-increasing data rate and connectivity requirements in future wireless networks. However, the development of NR-U networks should consider the coexistence with the incumbent Wireless Gigabit (WiGig) networks. In this paper, we introduce a novel multiple-input multiple-output non-orthogonal multiple access (MIMO-NOMA) based mmWave NR-U and WiGig coexistence network for uplink transmission. Our aim for the proposed coexistence network is to maximize the spectral efficiency while ensuring the strict NR-U delay requirement and the WiGig transmission performance in real time environments. A joint user grouping, hybrid beam coordination and power control strategy is proposed, which is formulated as a Lyapunov optimization based mixed-integer nonlinear programming (MINLP) with unit-modulus and nonconvex coupling constraints. Hence, we introduce a penalty dual decomposition (PDD) framework, which first transfers the formulated MINLP into a tractable augmented Lagrangian (AL) problem. Thereafter, we integrate both convex-concave procedure (CCCP) and inexact block coordinate update (BCU) methods to approximately decompose the AL problem into multiple nested convex subproblems, which can be iteratively solved under the PDD framework. Numerical results illustrate the performance improvement ability of the proposed strategy, as well as demonstrate the effectiveness to guarantee the NR-U traffic delay and WiGig network performance.

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