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We provide a fresh perspective on the problem of characterizing the DoFregion of the $K$-user MISO BC with arbitrary levels of partial CSIT. In aprevious achievability proof, Piovano and Clerckx characterized all facesdescribing a polyhedral outer bound region, and then with the aid ofmathematical induction, prescribed a scheme based on rate-splitting withflexible assignment of common DoF and power levels to achieve each such face.We propose an alternative approach in which we deal directly with the regionachievable through rate-splitting and employ a Fourier-Motzkin procedure toeliminate all auxiliary variables, hence reducing the achievable region to theknown outer bound. A key insight emerging from our proof is that tuning onlyone power variable, as well as assigning the common DoF, is sufficient toachieve the entire DoF region, as opposed to $K$ power variables previouslyemployed.

DoF Region of the MISO BC with Partial CSIT: Proof by Inductive Fourier-Motzkin Elimination