Optimizing orthogonal pulse waveforms for ultra-wideband communications

Ultra-wideband (UWB) systems use narrow pulses to transfer information; however, its performance is considerably affected by the power efficiency of the pulse waveform. In order to fully utilize frequency bands as divided by the FCC mask, waveform power utilization efficiency must be maximized. Therefore semi-definite programming (SDP) was used to design a set of orthogonal waveform of ultra-wideband pulses. The pulse waveforms designed here have short time duration that satisfies the FCC mask in frequency domain and have high power utilization efficiency. Moreover, the orthogonality among, pulses is good, which is the result of a small cross-correlation coefficient for zero time-shift when they are radiated. By transforming the 2-norm in the objective function to 1-norm, the power utilization efficiency of orthogonal pulse waveforms can be further increased to enhance the signal-to-noise ratio for the receiver.