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Aiming at the digital quadrature modulation system, a mathematical Pan-function model of the optimized baseband symbol signals with a symbol length of 4T was established in accordance with the minimum out-band energy radiation criterion. The intersymbol interference (ISI), symbol-correlated characteristics, and attenuation factor were introduced to establish the mathematical Pan-function model. The Pan-function was added to the constraints of boundary conditions, energy of a single baseband symbol signal, and constant-envelope conditions. Baseband symbol signals with the optimum efficient spectrum were obtained by introducing Fourier series and minimizing the Pan-function. The characteristics of the spectrum and peak-to-average power ratio (PAPR) of the obtained signals were analyzed and compared with the minimum shift keying (MSK) and quadrature phase-shift keying (QPSK) signals. The obtained signals have the characteristics of a higher spectral roll-off rate, less out-band radiation, and quasi-constant envelope. We simulated the performance of the obtained signals, and the simulation results demonstrate that the method is feasible

A Pan-Function Model for the Utilization of Bandwidth Improvement and PAPR Reduction