arXiv:2611.06805v1 Announce Type: new Abstract: Integrated sensing and communication (ISAC) transmit designs typically optimize the transmit covariance under proper signaling, leaving the potential sensing benefits of pseudo-covariance unexplored. This paper investigates the conditions under which transmit pseudo-covariance can influence the angle Cramer-Rao bound (CRB) of a deterministic target in the presence of clutter. For a prescribed transmit covariance and a single clutter patch, we establish that CRB sensitivity occurs if and only if the clutter is illuminated, exhibits nonzero non-circularity, and overlaps the angle-informative component of the target response. This characterization demonstrates that angular separation alone does not determine whether transmit impropriety can improve sensing performance. We derive a closed-form optimal incident-field pseudo-variance that minimizes the angle CRB over the set of feasible transmit pseudo-covariances. Under fully non-circular clutter scattering, the optimal design eliminates the clutter-induced CRB penalty. Numerical results for a 32-antenna ISAC system show CRB reductions of up to 99% relative to proper sensing under complete overlap and 30% under partial overlap, as well as up to approximately 7 dB lower clutter-induced CRB penalty across target-clutter separations. These findings identify transmit pseudo-covariance as a conditional sensing design resource whose effectiveness depends on clutter statistics and projected target-clutter geometry.