Pilot Length Minimization via AP-UE Clustering in Cell-Free Systems

The benefits of cell-free multiple-input multiple-output (CF MIMO) systems over traditional cellular systems, viz., a dramatic improvement of spectral efficiency (SE) and uniform quality of service, crucially depend on the quality of the estimated channels at the access points (APs). However, in a CF MIMO system, where a large number of user-equipments (UEs) are served by distributed APs, ensuring pilot contamination-free channel estimates across all the APs requires inordinately high pilot length, which substantially reduces the time available for data transmission. This paper proposes a novel pilot design and allocation algorithm that ensures no pilot contamination among any pair of UEs that are proximal to a common AP, and this is guaranteed at all APs. Further, our algorithm procures the pilot allocation with a minimum number of orthogonal pilots being reused across the UEs. Specifically, we recast the problem as a graph-vertex coloring problem and solve it via a low-complexity algorithm known to be optimal for all bipartite graphs. Unlike existing solutions, our algorithm does not require additional signaling overhead, e.g., signal-to-interference plus noise ratio exchanges, for pilot assignment. Numerical results illustrate the superiority of the proposed technique over existing methods from the literature.