Optimal Power Allocation for Localization in Multi-Band Systems

This study examines the localization performance of frequency-dependent, reflective targets within multi-band sensing systems. We derive the Cramer-Rao bound (CRB) for target direction and distance, and use their weighted combination in an error metric known as squared position error bound (SPEB) for our analysis purposes, assuming a multi-antenna system. Furthermore, we solve the optimal power allocation problem across multiple carrier frequencies for minimizing the total sum SPEB, under total power constraints. We model the target reflectivity as a frequency-dependent variable and divide it into two cases: 1) binary targets (reflecting at a single frequency) and 2) general targets (arbitrary reflectivity at each carrier frequency). Simulation results reveal that for both cases, the uniform power distribution is suboptimal; instead, optimal power allocation is a weighted fraction of total available power with weights dependent on the number of antennas available at each carrier frequency. Furthermore, for binary targets with frequencies having equal aperture, error performance improves quadratically with the ratio of higher to lower carrier frequencies.