  In this study, the hybrid Cramer-Rao bound (CRB) is developed for target
localization, to establish the sensitivity of the estimation mean-square error
(MSE) to the level of phase synchronization mismatch in coherent Multiple-Input
Multiple-Output (MIMO) radar systems with widely distributed antennas. The
lower bound on the MSE is derived for the joint estimation of the vector of
unknown parameters, consisting of the target location and the mismatch of the
allegedly known system parameters, i.e., phase offsets at the radars.
Synchronization errors are modeled as being random and Gaussian. A closed-form
expression for the hybrid CRB is derived for the case of orthogonal
waveforms.The bound on the target localization MSE is expressed as the sum of
two terms - the first represents the CRB with no phase mismatch, and the second
captures the mismatch effect. The latter is shown to depend on the phase error
variance, the number of mismatched transmitting and receiving sensors and the
system geometry. For a given phase synchronization error variance, this
expression offers the means to analyze the achievable localization accuracy.
Alternatively, for a predetermined localization MSE target value, the derived
expression may be used to determine the necessary phase synchronization level
in the distributed system.
