  In this paper, we propose beamformed energy detection (BFED) spectrum sensing
schemes for a single secondary user (SU) or a cognitive radio to detect a
primary user (PU) transmission in the presence of an interferer. In the
millimeter wave (mmWave) band, due to high attenuation, there are fewer
multipaths, and the channel is sparse, giving rise to fewer directions of
arrivals (DoAs). Sensing in only these paths instead of blind energy detection
can reap significant benefits. An analog beamforming weight vector is designed
such that the beamforming gain in the true DoAs of the PU signal is maximized
while minimizing interference from the interferer. To demonstrate the bound on
the system performance, the proposed sensing scheme is designed under the
knowledge of full channel state information (CSI) at the SU for the PU-SU and
Interferer-SU channels. However, as the CSI may not be available at the SU,
another BFED sensing scheme is proposed, which only utilizes the estimate the
DoAs. To model the estimates of DoAs, perturbations are added to the true DoAs.
The distribution of the test statistic for BFED with full CSI schemes is
derived under the null hypothesis so that the threshold of the Neyman-Pearson
detector can be found analytically. The performance of both schemes is also
compared with the traditional energy detector for multi-antenna systems.
