In this paper, a channel state information (CSI)-free, fake path injection (FPI) scheme is proposed for location-privacy preservation. By leveraging the geometrical feasibility of the fake paths, under mild conditions, it can be proved that the illegitimate device cannot distinguish between a fake and true path, thus degrading the illegitimate devices' ability to localize. Two closed-form, lower bounds on the illegitimate devices' estimation error are derived via the analysis of the Fisher information of the location-relevant channel parameters, thus characterizing the enhanced location privacy. A transmit precoder is proposed, which efficiently injects the virtual fake paths. The intended device receives the two parameters of the precoder design over a secure channel in order to enable localization. The impact of leaking the precoder structure and the associated localization leakage are analyzed. Theoretical analyses are verified via simulation. Numerical results show that a 20dB degradation of the illegitimate devices' localization accuracy can be achieved and validate the efficacy of the proposed FPI versus using unstructured Gaussian noise or a CSI-dependent beamforming strategy.