Phase synchronization errors are practically inevitable, so in this paper the quantitative tool to asses the effect of antenna placement for localization performance with phased synchronization errors is provided. The lower bound of mean-square error (MSE) is set by the hybrid Cramer-Rao bound (HCRB) for the joint estimation of the target location and phase synchronization errors at the receivers. It is shown that HCRB follow up to a lower limit, determined by the synchronization error variance and the number of transmit and receive sensors. For uniform antenna distributing, symmetrical placement is optimal, and all forms give exactly the same performance. The localization performance of nonuniform arrays when the antennas are spread out as much as possible is a little better than symmetrical placement at high SNR. Simulation results verify the correctness of conclusions.
