On the Performance of Digital Modulation Systems That Expand Bandwidth

Various m-ary digital modulation schemes [such as coherent phaseshift keying ( C P S K ) , differentially coherent phase-shift keying ( D C P S K ) , frequency-shift keying (FSK), and others] are currently under investigation for use in satellite, terrestrial, and other radio communication systems.1,2,3 In such systems, the transmission channel is noisy, and bandlimited, and one is interested in finding an optimum form of modulation for the transmission of information from one point to another. By optimum form of modulation, we mean that we would like to transmit (with a given error rate) as much information as possible in a given band of frequencies and for a given amount of (channel) signal power. The complexity of the equipment required for particular kinds of modulation, or other considerations in the system, may rule out these optimum transmission schemes in favor of simple and suboptimum 1033 1034 THE BELL SYSTEM TECHNICAL JOURNAL, JULY-AUGUST 1970 schemes of modulation and demodulation. In order to compare the performance of these simpler practical modulation systems with that of the optimal systems, it is first essential to investigate the performance of these optimal systems. In this paper we shall assume that the noise in the channel available for communication is gaussian and has a uniform power spectral density over all useful frequency bands. [In terrestrial systems, in the frequency bands above 10 GHz, close spacings of the repeaters are almost always mandatory for reliable communication (during fading conditions produced by rain).2 If low noise receivers are used in the system, it is possible that the total interference power (due to co-channel and adjacent channel interferers) received by the system may be very much larger than the (thermal) noise power in the system.3 In this case, note that the total noise corrupting the channel may not be assumed gaussian in all modulation systems (especially if the number of interferers is small).