Abstract: Since the classical generation methods such as the inversion method and rejection method are very complicated in hardware implementation, we develop an improved method for reproducing Gaussian noises in real-time. The proposed method modified the Sum-of-Sinusoids (SoS) method based on the central limit theory by introducing the Hadamard matrix transformation. On this basis, the theoretical amplitude distribution of output random variables is derived, and by utilizing the field programmable gate array (FPGA) hardware, the effect of the width of fixed-point data and the depth of look-up tables on the distribution and periodicity of output variables was analyzed. Numerical simulation results show that the amplitude distribution of the new method obtains better precision than that of the traditional SoS method. In addition, the accuracy of the tail distribution and the repetition period are both improved significantly, which also shows the proposed method can meet the requirements of channel noise emulation in reality.