Abstract
This paper initiates a new investigation of optimum transmission waveforms in the presence of per-path pulse wave shape distortion - a physical mechanism unique to impulsive signals. First, the transient electromagnetic analysis is carried out to derive, for the first time, closed-form expressions for the impulse responses of several canonical channels that are suitable for communication engineers. Second, numerical calculation using the inverse Fourier transform of the frequency-domain expressions is compared with the derived closed-form expressions, to verify the validity of these derived impulse responses. Third, propagation mechanisms responsible for multipath and per-path pulse shape distortion can be clearly identified using the closed-form impulse responses. Finally, using these closed-form expressions as a departure point, optimum transmission waveforms determined by a Fredholm integration equation are investigated, for different physical mechanisms, including one path or no multipath (wedge), two paths (rectangular building) and more than two paths (two half plane waveguide).
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