Synchronous communications in a lossy medium using transient waves

The problem of detecting an electromagnetic signal with the initial time variation of a rectangular pulse is presented. The medium between the transmitter and the receiver is assumed to introduce ohmic losses. The implication of additive thermal noise on the error probability and the detectable propagation velocity is investigated. The results are shown for a synchronous binary communications model in which the receiver has knowledge of the starting time of each observation interval. A correlator receiver is assumed for optimal signal detection in the mean-square-error sense. It is shown that the observable propagation velocity of the signal is a function of the receiver characteristics and the parameters of the signal used. Formulas relating the pulse width, signal-to-noise ratio, propagation distance, error probability, and the observed propagation velocity are derived. Plots for specific examples are presented