Research on a realization method of the optimized efficient spectrum signals using Legendre series

In this paper, the mathematical functional model of the optimized baseband symbol signals is established in accordance with the criterion for minimized out-of-band energy radiation. The functional is limited with the restrictions on conditions of boundary, single baseband symbol signal energy and constant envelope. With the introduction of Legendre series, the baseband symbol signals with optimized efficient spectrum are obtained by determining the minimum of the functional. The properties of spectrum and PAPR (peak-to-average power ratio) of the obtained signals are analysed and compared with MSK signals. A scheme for quadrature modulation and coherent demodulation is presented, and the simulation of quadrature modulation and coherent demodulation is achieved by using MATLAB, the simulation results demonstrate that the method is available.