Relaxed Gradient Projection for PCI Assignment in 5G Network

The optimization of Physical Cell Identity (PCI) assignment is a critical challenge in 5 G network deployment, as improper assignments can lead to severe network issues, including collisions, confusions, and mod- 3 interference. This paper proposes a novel Relaxed Gradient Projection (RGP) method that integrates discrete and continuous optimization techniques to effectively minimize these issues. Unlike conventional discrete approaches such as graph coloring, heuristic methods, and binary quadratic programming (BQP) approaches, RGP reformulates the PCI assignment problem into a continuous optimization problem over the Cartesian product of probability simplexes. A gradient projection algorithm then computes near-optimal assignments, which are subsequently rounded to discrete PCI assignments. Extensive numerical evaluations on real-world 5 G network data demonstrate that RGP significantly reduces mod- 3 interference while maintaining superior performance in minimizing collisions and confusions. Moreover, RGP scales efficiently to large networks, offering a practical and computationally efficient solution for PCI optimization.