Abstract
The statistical properties of a random variable E that denotes either the time-averaged power in a received band of noise or the total energy in a received transient waveform are studied for situations where the variablity in E is due to uncertainty in the detailed structure of the multipath transmission channel. The transmission channel impulse response function is modeled by a nonstationary Gaussian random process—a model that predicts the Rayleigh probability density for received amplitudes of transmitted pure tones. General expressions are derived for the mean and variance of E. These expressions are reduced to the practically important case of impulse response functions that are δ-correlated in time. Approximate expressions and bounds are derived for the relative variance of E. Special cases of the results are shown to be in essential agreement with results previously obtained in studies of the responses of rooms to bands of noise.
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