Gaussianpulsesfor60GHz.doc

Direct pulse The ideal pulse The ideal pulse can be derived from the Fourier transform of the frequency MASK. The ideal PSD is Gaussian series gj(t) is the Gaussian pulse (j=0) or its jth derivatives (j1) which can be described as各级导数 (1) where the amplitude A is used to normalize the pulse amplitude, and α is pulse shaping factor. Φgg(f) is the power density spectrum of g(t), and it can be given by (2) where G(f) is the Fourier Transform (FT) of g(t). The FTs of Gaussian pulse series are shown as (3) Then we can get the PSD of the Gaussian pulse series with expression (2) and (3), (4) Fig 1. α=36ps, k=15, i.e. 15th derivative of Gaussian pulse Fig 2. α=36ps, PSD of derivative of Gaussian pulse Fig 3. α=45ps, Gaussian derivative pulse series. Fig 4. α=45ps, PSD of derivative of Gaussian pulse. Fig 3 and Fig 4 show that there is little difference in derivatives of Gaussian pulse in terms of shapes of their PSD and bandwidth. Hann window pulse , where fs is the modulation frequency that primarily impacts the bandwidth of the transmitted signal, fs=1/ Tp. Rectangular Triangular The center frequency of Hann window, Rectangular and Triangular pulse is 0 GHz. These direct pulses can not meet the 60GHz spectrum requirements. Orthogonal modified Hermite pulse Hermite polynomials can be modified to become orthogonal as (5) Where n=0,1,2,…and -∞t∞. Here are some examples: Fig 5 Orthogonal modified Hermite pulses with different n Fig 6 the PSD of Orthogonal modified Hermite pulses with different n Pulses for 60GHz with Frequency shift Gaussian pulse series A set of Gaussian monocycles approximately meeting the spectrum requirement was the original proposal for UWB communication systems and has been widely adopted in the investigation of UWB applications. However, the pulse waveforms for 60GHz systems are required for the 7GHz range available at 60GH