Error Probabilities for Certain Spread Channels

John N. Pierce

ene 1964 · Air Force Cambridge Research Laboratories, Office of Aerospace Research, United States Air Force

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On an overspread channel, the total average energy in a received signal is divided among a large number of independently fading components, and the distribution of energy among these components can be only partially controlled by the signal design. It is shown, by numerical results for a specific class of modulating waveforms and scattering functions, that this unavoidable energy division can be almost as efficient as the controlled division of energy achieved by frequency diversity on an under-spread channel. It is also shown that M-ary transmission alphabets are effective in combating extremely severe channel overspreading. Asymptotic results, derived for long rectangular modulating pulses, permit determination of a lower bound on channel capacity that depends only on certain marginal properties of the scattering function.