Power allocation for cell-free MIMO integrated sensing and communication

In this paper, we investigate integrated sensing and communication (ISAC) in a cell-free (CF) multiple-input multiple-output (MIMO) network with single-antenna access points (APs), where each AP functions either as a transmitter for both sensing and communication or as a receiver for target-reflected signals. We derive closed-form Cramer-Rao lower bounds (CRLBs) for location and velocity estimation under arbitrary power allocation ratios, assuming the radar cross-section (RCS) is deterministic and unknown over the observation interval. A power allocation optimization problem is formulated to maximize the communication signal-to-interference-plus-noise ratio (SINR), subject to CRLB-based sensing constraints and per-transmitter power limits. To solve the resulting nonlinear and non-convex problem, we propose a penalty function and projection-based modified conjugate gradient algorithm with inexact line search (PP-MCG-ILS), and an alternative method based on a modified steepest descent approach (PP-MSD-ILS). Additionally, for power minimization in pure sensing scenarios, we introduce a penalty function-based normalized conjugate gradient algorithm (P-NCG-ILS). We analyze the convergence behavior and qualitatively compare the computational complexity of the proposed algorithms. Simulation results confirm the accuracy of the derived CRLBs and demonstrate the effectiveness of the proposed power allocation strategies in enhancing both sensing and overall ISAC performance.