JOINT OPTIMIZATION OF TRANSMITTER AND RECEIVER IN SINGLE PULSE TRANSMISSION.

A time domain approach is presented to the joint optimization of transmitted waveform and linear receiving filter for single pulse transmission. It is shown that for additive Gaussian noise, integral equations can be found for the optimal sending pulse shape and the corresponding matched filter. For any physically realizable channel, realizable solutions for these equations exist. In general, the integral equations cannot be solved analytically, but it appears that it is easy to find numerical approximations. These calculations are carried out for the case of a channel consisting of a coaxial cable. It appears that the rectangular waveform is suboptimum for this kind of channel.