Virtual multiple-input multiple-output (V-MIMO) technology promises significant performance enhancements to cellular systems in terms of spectral efficiency (SE) and energy efficiency (EE). How these two conflicting metrics scale up in large cellular V-MIMO networks is unclear. This paper studies the EE-SE trade-off of the uplink of a multi-user cellular V-MIMO system with decode-and-forward type protocols. We first express the trade-off in an implicit function and further derive closed-form formulas of the trade-off in low and high SE regimes. Unlike conventional MIMO systems, the EE-SE trade-off of the V-MIMO system is shown to be susceptible to many factors including protocol design (e.g., resource allocation) and scenario characteristics (e.g., user density). Focusing on the medium and high SE regimes, we propose a heuristic resource allocation algorithm to optimize the EE-SE trade-off. The fundamental performance limits of the optimized V-MIMO system are subsequently investigated and compared with conventional MIMO systems in different scenarios. Numerical results reveal a surprisingly chaotic behavior of V-MIMO systems when the user density scales up. Our analysis indicates that low frequency reuse factor, adaptive resource allocation, and user density control are critical to harness the full benefits of cellular V-MIMO systems.
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