  Passive synthetic aperture radar (SAR) uses existing signals of opportunity
such as communication and broadcasting signals. In our prior work, we have
developed a low-rank matrix recovery (LRMR) method that can reconstruct scenes
with extended and densely distributed point targets, overcoming shortcomings of
conventional methods. The approach is based on correlating two sets of bistatic
measurements, which results in a linear mapping of the tensor product of the
scene reflectivity with itself. Recognizing this tensor product as a rank-one
positive semi-definite (PSD) operator, we pose passive SAR image reconstruction
as a LRMR problem with convex relaxation. In this paper, we present a
performance analysis of the convex LRMR-based passive SAR image reconstruction
method. We use the restricted isometry property (RIP) and show that exact
reconstruction is guaranteed under the condition that the pixel spacing or
resolution satisfies a certain lower bound. We show that for sufficiently large
center frequencies, our method provides superior resolution than that of
Fourier based methods, making it a super-resolution technique. Additionally, we
show that phaseless imaging is a special case of our passive SAR imaging
method. We present extensive numerical simulation to validate our analysis.
