Mathematical Model for Gaussian-Like Pulse Design for a UWB System Based on the Generalized Bessel Polynomials

Ultra-wideband (UWB) communication is a wireless transmission technology that allows for high data rates and bandwidths. Interference occurs with coexisting wireless systems when data is transmitted over the multipath channel. Hence, the emission power limitations must comply with the Federal Communication Commission (FCC) spectral mask regulation. The optimal pulse design is critical to meet the FCC requirements. This article presents a mathematical model to design Gaussian-like pulses for a UWB system using generalized Bessel polynomials (GBPs). Polynomials in communication circuit fields can form an appropriate transfer function for signal approximation. Our proposed mathematical model, which presents a characteristic of GBP compared to a simple Gaussian pulse, is closed-form. The simulation used MATLAB software to adjust GBP parameters and the derivative of the proposed pulse to obtain a suitable fit for the FCC spectral mask. The results show the proposed pulse that can meet the FCC spectral mask at the optimal points at 75.3 dB with frequency 1.61 GHz, 41.3 dB with 3.1 to 10.6 GHz, and 51.3 dB with 10.6 GHz. This verifies that a mathematical model can be applied to approximate the Gaussian-like pulse for a UWB application.