A Realization Method of the Optimized Efficient Spectrum Signals Using Fourier Series

Improving the utilization of signal bandwidth is one of the most important research topics in the field of communications. The mathematical functional model of the optimized baseband symbol signals is established according to 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. By using the Fourier series and determining the minimum of the functional, the baseband symbol signals with optimized efficient spectrum are obtained. The properties of spectrum and PAPR (peak-to-average power ratio) of the obtained signals are analyzed and compared with MSK signals. A scheme for quadrature modulation and coherent demodulation is presented and its feasibility is proven by computer simulations.