  The existing research on physical layer security commonly assumes the number
of eavesdropper antennas to be known. Although this assumption allows one to
easily compute the achievable secrecy rate, it can hardly be realized in
practice. In this paper, we provide an innovative approach to study secure
communication systems without knowing the number of eavesdropper antennas by
introducing the concept of spatial constraint into physical layer security.
Specifically, the eavesdropper is assumed to have a limited spatial region to
place (possibly an infinite number of) antennas. From a practical point of
view, knowing the spatial constraint of the eavesdropper is much easier than
knowing the number of eavesdropper antennas. We derive the achievable secrecy
rates of the spatially-constrained system with and without friendly jamming. We
show that a non-zero secrecy rate is achievable with the help of a friendly
jammer, even if the eavesdropper places an infinite number of antennas in its
spatial region. Furthermore, we find that the achievable secrecy rate does not
monotonically increase with the jamming power, and hence, we obtain the
closed-form solution of the optimal jamming power that maximizes the secrecy
rate.
