Fake path injection is an emerging paradigm for inducing privacy over wireless networks. In this paper, fake paths are injected by the transmitter into a SIMO multipath communication channel to preserve her physical location from an eavesdropper. A novel statistical privacy metric is defined as the ratio between the largest (resp. smallest) eigenvalues of Bob's (resp. Eve's) Cramér-Rao lower bound on the SIMO multipath channel parameters to assess the privacy enhancements. Leveraging the spectral properties of generalized Vandermonde matrices, bounds on the privacy margin of the proposed scheme are derived. Specifically, it is shown that the privacy margin increases quadratically in the inverse of the separation between the true and the fake paths under Eve's perspective. Numerical simulations further showcase the approach's benefit.