Maximization of the power “UWB” signal by random method while respecting official constraints

In this paper, we try to maximize the power of ultra-wideband signal “UWB” sent to the target without breaching the restriction limits of the Federal Communications Commission “FCC”. The signal is a series of monocycle Gaussian pulses, characterized by the frequency center “FC”, Pulse Repetition Interval “PRI”. And the amplitude “A”. Maximizing the signal power under the FCC constraints: get a PSD (Power Spectral Density) as close to the barrier −41.3 dB as possible in the frequency domain. The method of random variables can be used to determine the optimal characteristics of the signal. We will also impose 0,025 as a maximum ratio between the center frequency and the PRI to avoid overlap between pulses. This signal is used to be sent to the human body in order to detect heart beats. To see the waveform near the heart : Firstly, we modeled the human body as the consisting of four semi-infinite layers. These layers are characterized by their dielectric relative constant, thickness and electrical conductivity. Then, we use the Finite Difference Time Domain (FDTD) to model the UWB propagation channel. This method was an efficient tool to predict the distribution of electromagnetic field along the propagation channel.