An optimum detector for coherent M-ary signaling in the presence of impulsive noise

Digital communication systems operating in the ELF/VLF range are strongly affected by atmospheric noise which has an impulsive component on a white Gaussian background. We derive an optimum detector for coherent M-ary signaling in the presence of such noise. In the special case of coherent binary signaling, the performance of a suboptimum linear detector is analyzed.