Comparative analysis on pulse compression with classical orthogonal polynomials for optimized time-bandwidth product

Abstract

The theme of this paper is to analyze and compare the pulse compression with classical orthogonal polynomials (Chebyshev, Laguerre, Legendre and Hermite polynomials) of different orders. Pulse compression is used in radar systems to improve the range resolution by increasing the time-bandwidth product of the transmitted pulse. It is done by modulating the instantaneous angle of the transmitted pulse. Three types of angle modulations are considered in this paper. Initially, the angle is varied in proportional to the original polynomials. Secondly, the angle is proportional to integral of the polynomial and thirdly, the angle is proportional to derivative the polynomial. The main purpose of this analysis is to obtain and use the best of all these polynomials in pulse compression. This is done by comparing the quantitative parameter of pulse compression - time-bandwidth product. Optimization to maximize the time-bandwidth product is also considered in the analysis.