th of data traffic and recent advancement on ML fuel the data-driven communication system design. In particular, collected data can help innovative designs on modulation, coding, scheduling, architecture, resource management, and even end-to-end [217]. ML is one of the most powerful tools and can effectively explore massive data and make accurate predictions and plannings. For example, future communication design may not start from problem formulation and then be solved with traditional convex (or non-convex) optimization. Rather, the model design can learn from data and reach something we have yet seen. Another big challenge that data-driven approach can address is the network scalability, which is of critical importance in massive IoT era. Appendix A Proof of Theorem 5.1 To prove the Theorem, we first consider the KKT conditions of P3. Specifically, with some simple algebraic manipulation, (5.11) can be rewritten as (A.1) Similarly, (5.13) and 5.15 can be rewritten as (A.2) (A.3) respectively, For notational simplicity, we let X = I h and denote a , X E as the KKT multiplier. Then the Lagrange dual function L can be expressed as L(Wk, V,Ai,k,Bk, D Z,K) = Tr() (A.4) where and K are the terms irrelevant of Wk. Taking the partial derivative of the dual function regarding Wk, we have 5G and Beyond Wireless Communication Networks, First Edition. Haijian Sun, Rose Qingyang Hu, and Yi Qian. © 2024 John Wiley & Sons Ltd. Published 2024 by John Wiley & Sons Ltd. Appendix A Proof of Theorem 5.1 nanA0 (A.5) In addition, the dual problem needs to satisfy the completeness slackness (A.6a) (A.6b) Right multiplying Wk with (A.5), and substituting (A.6b), we can get Wk (A.7) Since all the KKT multipliers are positive numbers or positive semidefinite matrix, 0. Thus it is non- singular. Left multiplying a non-singular matrix with Wk does not change the rank of Wk. Therefore, we have Rank(Wk) Rank - min (A.8) Next, we show the rank of is less than or equal to 2. By summing (A.6a) in terms of index i, then left-multiplying [MO] a