Modified Price Nonlinear Frequency Modulated Waveform for Improved Performance

A modified Price formula nonlinear frequency curves for pulse compression with ultra-low sidelobe level (SLL) and efficient use of the frequency spectrum is proposed. Although the frequency curve of the original Price formula is known to give a relatively low remaining SLL, this level is not suitable for applications such as meteorological radar, which needs to detect tiny targets in a dense and widespread cluttered environment. This paper introduces new parameters for obtaining an ultra-low SLL. After a parameter study, hybrid optimization based on the genetic algorithm and the Nelder-Mead search was used for finding the optimal solution. In this method, even without amplitude windowing, an SLL lower than <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"><tex-math notation="LaTeX">$-100$</tex-math></inline-formula> dB could be achieved with time-bandwidth product of 200. In addition, another design with a one-sided occupied spectrum (<inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"><tex-math notation="LaTeX">$ f_{-90\text{dB}}$</tex-math></inline-formula>) of only 32.85 MHz and a Doppler tolerance of <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"><tex-math notation="LaTeX">$-0.24$</tex-math></inline-formula> dB was made.