The detectability of fading radiotelegraph signals in noise

An ideal receiver for binary synchronous telegraphy is postulated; this receiver is defined as one that interprets each element of a received signal with the minimum probability of error. The relations between error liability and signal/noise ratio are determined for steady signals and for Rayleigh-fading signals in white Gaussian noise, using up to four diversity branches. The noisy-signal performance of a practical receiver can be described in terms of the amount by which it falls short of the ideal, and it is proposed that this measure of imperfection, expressed as an energy ratio, be known as the `demodulation factor¿. The analysis leads to a mathematical specification for the ideal diversity receiver, and this provides a starting-point for the design of practical receivers. The outputs of diversity branches are combined, weighted according to signal energy, instead of the largest output being selected. Very deep fading proves to be of little importance. It is found that the use of a 7-unit error-detecting code in place of an unprotected 5-unit code is roughly equivalent to doubling the number of diversity branches. Cross-correlation between the mark and space signals in two-tone or frequency-shift systems is found to be insignificant under the conditions ordinarily encountered in long-distance radiotelegraphy. Although it is primarily concerned with high-frequency radiotelegraphy, the study may prove useful in other fields, including that of microwave pulse communication.