This brief presents a new Continuous Phase Modulation (CPM) module for multi- <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$h$ </tex-math></inline-formula> transmission based on modular arithmetic processing. It is well known that CPM systems are sensitive to changes in the modulation index, which is implied when fixed-point format is used in the hardware implementation. In this scenario, modular arithmetic allows a more accurate signal processing regarding SQNR performance. This proposal has been shown to improve performance compared to other state-of-the-art methods, even when the modulation indices do not have an exact representation in a given fixed-point format. Due to its highly reconfigurable architecture, this hardware block is suitable for Software Defined Radio (SDR) platforms. A complete digital architecture is also provided. Implementation results show that the new proposal have clear advantages in terms of hardware resources and operating frequency against other CPM transmitters in open-literature.