Discrete-Time CRLB-based Power Allocation for CF MIMO-ISAC with Joint Localization and Velocity Sensing

In this paper, we investigate integrated sensing and communication (ISAC) in a cell-free (CF) multiple-input multiple-output (MIMO) network, where each access point functions either as an ISAC transmitter or as a sensing receiver. We devote into the ISAC sensing metric using the discrete-time signal-based Cramer-Rao lower bounds (CRLBs) for joint location and velocity estimation under arbitrary power allocation ratios under the deterministic radar cross section assumption (RCS). Then, we consider the power allocation optimization problem for the CF MIMO-ISAC as the maximization of 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). We show that the proposed algorithms are scalable and can be extended to a broad class of optimization problems involving nonlinear inequality constraints and affine equality constraints. In addition, we extend the PP-MCG-ILS algorithm to the pure sensing scenario, where a penalty function-based normalized conjugate gradient algorithm (P-NCG-ILS) is developed for sensing power minimization. Finally, 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.