Ideal Binary Pulse Transmission by AM and FM

In binary pulse transmission by carrier amplitude or frequency modulation it is ordinarily desirable, both for efficient bandwidth utilization and for improved performance under adverse noise conditions, to use bandpass channels of the minimum practicable bandwidth, as determined by considerations of intersymbol interference and filter design. It is shown that intersymbol interference can be avoided in binary pulse transmission by FM without the need for a wider channel band than in double-sideband AM, for equal pulse transmission rates. Explicit general expressions are derived for the appropriate shaping of the bandpass channel and for the shapes of received pulses, for cases in which rectangular binary pulses are transmitted by FM, without premodulation or postdetection pulse shaping by low-pass filters. Illustrative comparisons are made of binary pulse transmission by AM and FM for two special cases of general interest in communication theory and pulse-system design. The more general case of partial pulse shaping by premodulation and postdetection low-pass filters is also considered. The performance of FM and AM systems in the presence of noise depends on the division of channel shaping between transmitting and receiving filters. The optimum division with FM and AM is determined for random noise, and comparisons are made of signal-to-noise ratios for optimized FM and AM systems. It is shown that there is a single universal relation between error probability and signal-to-noise ratio, applying to an infinite universe of optimized baseband systems and optimized AM systems with ideal synchronous detection, and that this relation is the same as for baseband transmission over an idealized flat channel of minimum bandwidth. The analysis indicates that, with binary FM and appropriate postdetection low-pass filters, it is possible in principle to realize an improvement in signal-to-noise ratio over bipolar double-sideband AM with synchronous detection (phase reversal), for equal channel bandwidths, average signal power and pulse transmission rates, although this may not be feasible with practicable filters.