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This paper considers the problem of optimally detecting digital waveforms in the presence of additive white Gaussian noise. A technique for representing the transmitted signals and the additive noise which leads to a geometric interpretation of the detection problem is presented on a tutorial level. Subsequently, this technique is used to derive the optimum detector for each of three basic data transmission systems: m-level Phase Shift Keyed, m-level Amplitude Shift Keyed and m-level Frequency Shift Keyed. Corresponding probability of error curves are derived, compared and discussed with reasonable detail.
Date of Publication: December 1962