Joint Antenna Positioning and Pilot Power Allocation for Uplink Fluid Antenna-Aided Cell-Free Massive MIMO Systems

This paper investigates joint fluid antenna (FA) position optimization and pilot power allocation for uplink cell-free massive MIMO networks supporting ultra-reliable low-latency communication (URLLC) traffic under pilot contamination. By continuously adjusting FA elements within a prescribed aperture, we adapt the spatial correlation structure to the varying propagation environment. We formulate a joint problem to minimize the average normalized mean-squared error (NMSE) subject to QoS constraints governed by finite blocklength and Markov-modulated Poisson process queueing analyses. To ensure tractability, we establish an analytical quadratic relationship between the NMSE and the effective signal-to-interference-plus-noise ratio through eigenstructure alignment factors. This mapping translates complex latency requirements into explicit NMSE thresholds, maintaining a median absolute approximation error below 0.03 dB and less than 10% relative error for over 90% of practical-regime samples. Given the nonconvex nature of the formulation, we propose an alternating optimization framework. Antenna positions are iteratively updated via successive convex approximation using analytical gradients and closed-form Euclidean projections. Pilot powers are allocated through a block coordinate descent scheme that employs safeguarded Newton steps to guarantee monotonic convergence. Furthermore, we introduce an auto-calibrated regularization variant to navigate the Pareto frontier between estimation accuracy and energy consumption. Numerical results show the proposed positioning yields up to 22% NMSE improvement over fixed uniform arrays while operating 7-8x faster than particle swarm optimization. The power allocation achieves within 0.5% of the global optimum at over two orders of magnitude lower computational cost, providing up to 39% pilot energy reduction with negligible estimation penalty.