#### Abstract

Most of the work which has been done with binary communication systems up until now has assumed operation in a symmetric mode. This work is concerned with the problem of evaluating various combinations of modulation and detection in both symmetric and non-symmetric modes of operation. The most frequently used criterion for describing performance in a binary system is total probability of error, A discussion of this and other criteria such as realizable rate and minimum energy per bit factors is given. A new criterion called information efficiency is defined which is based on realizable information rate on a per symbol basis. The primary advantage of this criterion is that it gives a truer indication of performance than probability of error in the case of unsymmetric operation. Several types of conventional binary systems are analyzed and compared under the conditions that additive gaussian white noise is the only perturbing influence. Systems considered include amplitude shift keying or a carrier on-off type of modulation with linear envelope detection and with synchronous detection, phase shift keying of a phase reversal type of modulation with both synchronous and phase comparison detection schemes, Performance curves showing information efficiency and probability of error as functions of signal-to-noise ratio are given. A similar type of analysis is given for a group of matched filter systems which includes both coherent and non-coherent matched filter detection of amplitude and frequency shift keyed signals in the face of gaussiam white noise and the coherent matched filter detection of phase shift keyed signals,, Also included are some results concerning the use of differentially coherent detection of phase shift keyed signals. The response of various systems to variations in decision thresholds is examined and it is shown that phase shift keyed systems are superior in this respect. The optimum detection of amplitude shift keyed signals requires a variable threshold level for different conditions at the detector input, fee case of fixed threshold systems is examined and it is shown that a fixed threshold limits the maximum attainable performance of the system and that there is a distinct trade-off between this maximum possible performance at high signal-to-noise ratios, and good performance (i.e., near optimum) at low signal-to-noise ratios. The problem of Rayleigh fading is discussed and indications of fading on the performance of the various systems is given. Finally, all of the systems discussed are compared on the same basis by using a time bandwidth product which allows the signal-to-noise ratios bn which the conventional system analysis is based to be converted to an energy per symbol to noise spectral density ratio, which is the basis for matched filter analysis.

#### Date of this Version

5-1-1962