ANALYSIS OF GAUSSIAN PULSE, MONOPULSE, DOUBLET AND PARAMETRIC SIGNAL IN UWB SYSTEMS BASED ON THE FOKKER-PLANCK EQUATION

Abstract

This study presents a comprehensive analysis of pulse waveforms for ultra-wideband systems using the Fokker-Planck equation as a rigorous mathematical framework. The research examines four signal types: Gaussian pulses, monopulses (first derivative of Gaussian), doublets (second derivative), and parametric signals representing transitional states between Gaussian and monopulse forms. Closed-form analytical expressions are derived for the RC-integrator response, signal-to-interference-plus-noise ratio (SINR), and bit error rate (BER) under optimal threshold detection. Key findings demonstrate that monopulses achieve superior SINR performance and lower BER compared to Gaussian pulses due to spectral properties, particularly the zero direct-current spectral component. This characteristic is critical in multi-user systems, as it prevents signal direct-current offset accumulation at receivers. The parametric signal formulation enables smooth transitions between pulse shapes, facilitating adaptive optimization based on propagation conditions. Doublets exhibit high spectral concentration at elevated frequencies but demonstrate reduced detection performance due to energy distribution. The results provide both theoretical advancement to impulse signal detection theory and practical applications for designing high-sensitivity ultra-wideband receivers. The developed framework supports optimization of RC-filter parameters and development of adaptive signal processing algorithms for next-generation ultra-wideband systems.