On the Narrow Beam Communication System Acquisition Problem

It is desired to establish a communication link between two separated transmit-receive terminals, each having narrow beamwidths and specified uncertainty as to relative angular locations. To achieve the communication link the narrow beams must point directly at each other. The purpose of this paper is to determine the search or acquisition time required by the two terminals to achieve the desired state of knowledge whereby the transmit-receive beams of both terminals are pointed in the required directions, signals are mutually recognized and the communication link is thereby established. The acquisition time is a random variable and can thus be described in terms of an expected value and standard deviation. Markov chain concepts are employed to derive equations for the expected acquisition time in terms of system parameters such as relative angular uncertainty, beamwidth, probability of detection of a signal in noise, false alarm probability, etc. Single as well as multiple receive beam systems are considered. Curves relating the expected acquisition time to probability of detection and pointing probability are presented.