  Millimeter-wave (mmWave) using conventional phased array (CPA) enables highly
directional and fixed angular beamforming (FAB), therefore enhancing physical
layer security (PLS) in the angular domain. However, as the eavesdropper is
located in the direction pointed by the mainlobe of the information-carrying
beam, information leakage is inevitable and FAB cannot guarantee PLS
performance. To address this threat, we propose a novel fixed region
beamforming (FRB) by employing a frequency diverse subarray (FDSA) architecture
to enhance the PLS performance for mmWave directional communications. In
particular, we carefully introduce multiple frequency offset increments (FOIs)
across subarrays to achieve a sophisticated beampattern synthesis that ensures
a confined information transmission only within the desired angle-range region
(DARR) in close vicinity of the target user. More specifically, we formulate
the secrecy rate maximization problem with FRB over possible subarray FOIs, and
consider two cases of interests, i.e., without/with the location information of
eavesdropping, both turn out to be NP-hard. For the unknown eavesdropping
location case, we propose a seeker optimization algorithm to minimize the
maximum sidelobe peak of the beampattern outside the DARR. As for the known
eavesdropping location case, a block coordinate descend linear approximation
algorithm is proposed to minimize the sidelobe level in the eavesdropping
region. By using the proposed FRB, the mainlobes of all subarrays are
constructively superimposed in the DARR while the sidelobes are destructively
overlayed outside the DARR. Therefore, FRB takes prominent effect on confining
information transmission within the DARR. Numerical simulations demonstrate
that the proposed FDSA-based FRB can provide superior PLS performance over the
CPA-based FAB.
