Expected Probability of Radiometric Detection by Channelized Radiometer

Low probability of detection (LPD) communication techniques are often used in tactical environments, and the introduction of commercial-grade cognitive radios has made them relevant in civilian environments. In highly mobile networks, updating the probability of detection often enough to ensure accurate predictions can be computationally expensive. This paper derives the expected probability of radiometric detection by a multi-channel radiometer and presents a flexible framework for approximating that probability which allows the user to balance accuracy and time complexity. This approximation provides a MiniMax solution under the condition that the probability of detection is never underestimated. An example is given which has relative error less than 10
⁻⁵
and runs more than 50 times faster than numerical integration and 10 times faster than solutions derived from Q function approximations.