Using a Vector of Observations to Identify the Number of Frequency-Hopping Transmitters

We present a time-distributed analytical framework for identifying the most likely number of frequency-hopping transmitters in an environment, considering both a perfect detection scenario as well as a scenario in which misdetection occurs. A maximum likelihood (ML) estimation formulation is adopted and a set of analytical equations are developed for the two measurement scenarios of (1) a single integrated measurement over the observation time window, and (2) an observation vector consisting of measurements at successive time instants. Simulation results confirm the correctness of the analytical formulation. We show that this approach can lead with high probability to a correct decision regarding the number of interferers, and explore the tradeoffs involved in different misdetection probabilities and in the two different measurement scenarios.