Abstract :
The problem of optimum and suboptimum detection of normal signals in additive normal noise backgrounds is examined by the methods of statistical decision theory. Some general results for optimum receiver structure, error probabilities, and average risk are obtained for the case of colored noise backgrounds. A detailed study of threshold reception in white-noise backgrounds is included, along with calculations of Bayes risk, bias terms, and minimum detectable signals for broad-band RC-noise signals and narrow-band, i.e., high-Q, LRC-noise signal processes. Optimum detector structures for signal processes with rational intensity spectra are also determined for the white noise case, and particular attention is paid to optimum receiver design in terms of physically realizable elements. Suboptimum receiver structure and performance are considered briefly, as well as a number of limiting cases of more special interest. General methods of attack are illustrated, with details given in Appendixes I-V. Application of the results to a variety of communication problems is indicated.
