Canonical representation of the radar range equation in the time domain

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Abstract
The classical radar range equation, in its various forms, is the most widely-used analytical tool employed by radar systems designers to determine the relationships among various radar system parameters. Implicit in the usual expressions of this equation is a narrow-band assumption, which permits the simple real-valued multiplication of frequency-dependent terms. The lack of a recognized canonical representation of the radar equation in a wide-band or time-domain form has hindered the development of an understanding of impulse and other wide-band radars. Presented here is a wide-band radar range equation which has been rigorously derived and exercised. A comparison is made to the narrow-band equation and it is shown that, in the narrow-band situation, the two are equivalent. Several examples demonstrating the utility of the time-domain equation are presented. A discussion provides guidance on when the wide-band or time-domain forms are necessary or when the narrow-band form or some compromise are adequate.

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