  Cognitive radio networks (CRNs) and millimeter wave (mmWave) communications
are two major technologies to enhance the spectrum efficiency (SE). Considering
that the SE improvement in the CRNs is limited due to the interference
temperature imposed on the primary user (PU), and the severe path loss and high
directivity in mmWave communications make it vulnerable to blockage events, we
introduce an intelligent reflecting surface (IRS) into mmWave CRNs. Due to the
estimation mismatch and the passivity of Eavesdroppers (Eves), perfect channel
state information (CSI) of wiretap links is challenging to obtain, which
promotes our research on robust secure beamforming (BF) design in the
IRS-assisted mmWave CRNs. This paper considers the collaborate scenario of
Eves, which allows us to investigate the BF design in the harsh eavesdropping
environment. Specifically, by using a uniform linear array (ULA) at the
cognitive base station (CBS) and a uniform planar array (UPA) at the IRS, and
supposing that imperfect CSIs of angle-of-departures for wiretap links are
known, we formulate a constrained problem to maximize the worst-case achievable
secrecy rate (ASR) of the secondary user (SU) by jointly designing the transmit
BF at the CBS and reflect BF at the IRS. To solve the non-convex problem with
coupled variables, an efficient alternating optimization algorithm is proposed.
Finally, simulation results indicate that the ASR performance of our proposed
algorithm has a small gap with that of the optimal solution with perfect CSI
compared with the other benchmarks.
