Joint radar-communication (JRC) has emerged as a prominent topic of interest in recent years. In JRC systems, the main beam of the antenna array is typically utilized for radar purposes, while the sidelobes can be repurposed for communication tasks. In this paper, we propose a novel approach using a synthesized phased array transmitter capable of accommodating low-order modulation input and delivering high-order modulation output for JRC applications. This transmitter offers high data rates for communication users employing low-order modulation input signals, such as binary phase-shift keying (BPSK). The synthesis principles are carefully elucidated, and simulation array patterns are presented using a 16-element linear array to demonstrate the effectiveness of the proposed high-order modulation scheme.