Recursive Ideal Observer Detection of Known M-ary Signals in Multiplicative and Additive Gaussian Noise

This paper presents the derivation of the recursive algorithms necessary for real-time digital detection of -ary known signals that are subject to independent multiplicative and additive Gaussian noises. The motivating application is minimum probability of error detection of digital data-link messages aboard civil aircraft in the earth reflection multipath environment. For each known signal, the detector contains one Kalman filter and one probability computer. The filters estimate the multipath disturbance. The estimates and the received signal drive the probability computers. Outputs of all the computers are compared in amplitude to give the signal decision. The practicality and usefulness of the detector are extensively discussed.