Security estimation model with directional antennas

In a hostile environment the adversarypsilas antenna can detect a transmitter when the signal to noise ratio at the adversary antenna is large enough. A directional antenna concentrates transmit power into certain direction and forms a directional beam pointing to the receiver, so it can decrease the radiation region in which nodes could receive the electromagnetic signals with high quality. This paper explores the benefit of security in wireless transmission through directional antennas. We define a probability of detection model to know the level of a transmitter being detected by another node at arbitrary location. We employ the average probability of detection to estimate the overall security benefit level of directional transmission over omni transmission. Our analysis shows that the average probability of detection of directional antenna is much smaller than that of omni antenna with the same EIRP.We also studied the influence of d and thetas to the probability of detection in both directional antenna and omni antenna.