Due to the explosively increasing number of mobile users and the new types of data demands in the fifth generation (5G) mobile wireless network, research in wireless networks has shifted toward the development of the sixth-generation (6G) wireless network. Although the research for software-defined network (SDN) architectures in 5G mainly focuses on the dynamic programming for the internet backbone, these software programming techniques can be also applied at the network edge to support the exponentially increasing demands from mobile users under constrained wireless resources. In order to study the interference problem resulted by massive mobile users, the scaling law is a powerful tool to show how fast the levels of network imperfections can be tolerated as the number of mobile users increases. In this paper, we investigate the scaling behavior of software-defined architectures over 6G wireless networks. We consider the wireless channel in three scenarios: single-input-single-output (SISO), multiple-input-single-output (MISO), and multiple-input-multiple-output (MIMO), where we derive the corresponding scaling law for each scenario, respectively. Our derived scaling law shows how the network performance scales with the number of mobile users in a wireless network. Then, we propose a software-defined network slicing scheme to select the optimal mobile users and derive their optimal resource allocations, according to our derived scaling law, under SISO, MISO, and MIMO wireless channel, respectively. Finally, we validate and evaluate the derived scaling behavior of the software-defined architecture over 6G wireless networks through numerical analyses.
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