The Development of Fast Algorithm for Continuous-Time Subsectional Polynomial E-Pulse Synthesis

Abstract

This paper discusses the development in the E-pulse technique, also known as the method of extinction pulse, which is an aspect-independent approach to ultra-wideband radar target discrimination in which each target can be characterized by the set of its natural resonances. It is shown that subsectional polynomial E-pulse can be constructed without composing a linear problem and further solution of the underlying matrix equation set. The key concept of the proposed algorithm consists of several steps, where the first one is building a skeleton E-pulse of an especial waveform, the second step is its extension, and the final step is the series of integration. The polynomial structure of the pulse allows above listed steps to be performed over the coefficients of basic functions rather than the functions themselves. As a result, the proposed solution could perform up to a thousand times faster than one based on direct matrix solution. It also provides the coefficients of the polynomial E-pulse sections without solving a linear problem associated with ill-conditioned sparse matrix in its left-hand side. The E-pulse signals synthesized by means of the fast algorithm are proven to be exactly the same as one synthesized by the direct approach. The numerical example given in the paper exposures the main features of the E-pulse technique. The discrimination scheme where two aircraft scaled model targets are involved is simulated.It was shown that the E-pulse discrimination number provides the effective tool for measuring the energy of the late-time part of the convolution as a measure of the difference of two pole sets belonging to the responses under comparison.