Error probabilities in optical PPM receivers with Gaussian mixture densities

A Gaussian mixture density arises when a discrete variable (e.g., a photodetector count variable) is added to a continuous Gaussian variable (e.g., thermal noise). Making use of some properties of photomultiplier Gaussian mixture distributions, some approximate error probability formulas can be derived. These appear as averages of M-ary orthogonal Gaussian error probabilities. The use of a pure Gaussian assumption is considered, and when properly defined, appears as an accurate upper bound to performance.