Errors in Detection of RF Pulses Embedded in Time Crosstalk, Frequency Crosstalk, and Noise

Consider many P C M messages occupying adjacent frequency bands in the same transmission medium, as, for example, in the proposed long distance waveguide communication system.1 At some point the messages must be separated and read; these operations are performed by the receivers. Each receiver will be considered to consist of a filter and an envelope detector that takes periodic instantaneous samples and decides if the level of the signal is above or below a threshold. Suppose that at a certain sampling time there is no pulse to be detected. Nevertheless, the received signal will be composed of the summation of three types of interference: time crosstalk or intersymbol interference, frequency crosstalk, and noise.* Time crosstalk is measured by the envelope of the message at the sampling time in the absence of other messages and noise; it is due to the trailing and leading edges of the other pulses that make the message. It is known that if the sampling is instantaneous the time crosstalk can be reduced to zero by proper choice of filters and input signal,2 but in a * T h r o u g h o u t this paper we understand " n o i s e " to be thermal noise. 921