Graph‐colouring based pilot assignment to mitigate downlink pilot contamination for cell‐free massive MIMO systems

In cell-free massive multiple-input-multiple-output (CF-MMIMO) systems, a massive number of access points, mastered by central processing units are distributed in a coverage area to serve much smaller number of user equipments (UEs) simultaneously over the same time/frequency resources. In opposition to the centralized MMIMO, CF-MMIMO particularity is that its channel hardening degree is not sufficiently accentuated, thus, it will be judicious to include downlink (DL) pilots in order for the DL channel to be estimated. This paper considers the DL pilot assignment for the CF-MMIMO systems by defining a metric, involving the inter-user interference. This metric gives insights into DL pilot contamination. A threshold is then defined to optimize the number of DL pilots, which maximizes the minimum per-user DL throughput. This approach gives a conflict graph, where each UE is regarded as a vertex of the graph. This is a combinatorial optimization problem that can be approximated using graph-colouring algorithms. The simulation results reveal that the proposed method outperforms interestingly, in terms of per-user DL throughput, the existing methods such as statistical channel state information, the orthogonal, and the random pilot assignment in the DL training.