Orthogonal hermite functions based orthogonal pulse shaping method

Ultra-Wideband (UWB) communication has attracted more attentions due to its advantages in short range applications. As one of the key techniques in UWB systems, many pulse shaping methods have been proposed. The semi-definite programming (SDP) based pulse shaping method can obtain the pulse with highest power efficiency by far. However, an accurate timing of 40 ps is required, and such requirement cannot be implemented precisely using modern hardware. Furthermore, the power efficiency of the second orthogonal pulse will be lower than the first pulse. To solve such problems, the linear combination of orthogonal Hermite functions is used in the SDP method and a modification method is then proposed to eliminate the direct current (DC) component. Simulation results show that orthogonal pulses without DC component can be obtained and the power efficiency of the obtained pulses are more than 80%. Moreover, the obtained orthogonal pulses will have shorter pulse duration due to the energy concentration property of orthogonal spaces.