This paper deals with the synthesis of dual-use signal to simultaneously achieve detection and communication for a dual-function radar communication (DFRC) system. A new position index and phase (PIP) modulation is proposed for information embedding, where position index modulation is realized by selecting the information embedding subpulses (InSp) positions. Moreover, differential phase modulation is utilized to distinguish InSp from other available subpulses. As for radar detectability, peak sidelobes level (PSL) of signal auto-correlation function is minimized. Meanwhile, constant-envelope and phases constraints are forced to ensure compatibility with the current hardware technique and modulation demand, respectively. To tackle the resulting nonconvex and NP-hard optimization problem, a spectral majorization-minimization (SM) dual-use baseband signal design method is proposed. In each iteration, the original problem is approximated by a tractable problem with a closed-form solution. Finally, simulation and semi-physical experimental results demonstrate the designed dual-use signal is capable of realizing high data rate communication and ensuring acceptable radar performance.