Pilot Assignment With Approximation Ratio in Cell-Free Massive MIMO Systems

This paper proposes a novel pilot assignment scheme for cell-free massive Multi-Input Multi-Output (MIMO) systems to alleviate the contamination problem caused by pilot sharing. The proposed scheme comprises simplifying and rounding operations, where the simplifying operation transforms the complex pilot assignment into an intuitive optimization problem. Similar to other schemes, the proposed simplifying operation transforms the pilot assignment into a max <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">p</i>-cut problem belonging to NP-hard using graph theory. However, due to the persistent challenges of the NP-hard problem, this paper further reduced the max <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">p</i>-cut to a tractable convex problem by adopting the semidefinite relaxation technique. Subsequently, the rounding process, including two rounding techniques, is designed to convert the optimal solution of the convex problem into a practical pilot assignment. The first stage rounding proposes a stochastic optimization technique that provides a reliable and efficient assignment, while the second stage uses a low-complexity reassignment to ensure the utilization of all planned pilots. We demonstrate that the proposed rounding process has a favorable approximation ratio while ensuring the usage constraint. Experimental results indicate advancements in the proposed scheme.