Joint Max-Min Power Control and Clustering in Cell-Free Wireless Networks: Design and Analysis

Cell-free wireless networks have attracted significant interest for their ability to eliminate cell-edge effects and deliver uniformly high service quality through macro-diversity. In this paper, we develop an algorithm to jointly optimize uplink transmit powers and dynamic user-centric access point (AP) clusters in a centralized cell-free network. This approach aims to efficiently mitigate inter-user interference and achieve higher max-min signal-to-interference-plus-noise ratio (SINR) targets for users. To this end, we re-purpose an iterative power control algorithm based on non-linear Perron-Frobenius theory and prove its convergence for the maximum ratio combiner (MRC) receiver under various AP subset selection schemes. We further provide analytical results by framing the joint optimization as a conditional eigenvalue problem with power and AP association constraints, and leveraging Perron-Frobenius theory on a centrally constructed matrix. The numerical results highlight that optimizing each user's serving AP cluster is essential to achieving higher max-min SINR targets with the simple MRC receiver.