Gaussian Random Number Generator, Research And Design

Gaussian random numbers are widely used in financial modeling, simulation of economic systems, molecular dynamics simulation, and communication systems. Take communication systems for example, the most frequently used noise is white Gaussian noise. Through modeling white Gaussian noise by Gaussian random numbers offer a suitable way to research and simulate the communication channel.Numerical methods for Gaussian random number generation have a long history in mathematics and communication based on software. These have been far less attention focused on efficient hardware implementation of Gaussian noise generators. Due to recent advances in field-programmable technology, hardware-based simulations are getting increasing attention due to their huge performance advantages over traditional software-based methods.Most of Recent available hardware Gaussian random number generators base on the transformation from uniform random numbers generated from the LFSRs or simple advanced LFSRs. In the early 1981, LFSRs are blamed as the terrible uniform random number generators. But many people pay more attention to the simple structure in hardware implementation of LFSRs to their drawbacks.Instead of LFSRs, this paper applies cellular automata to produce uniform random numbers which not only has simple hardware structure, but also better ability to generate quality uniform random numbers when in the condition of equal period with LFSRs.Two efficient designs for generating Gaussian random numbers are proposed and optimized for hardware implementation on Field Programmable Gate Arrays in this paper. One is based on the cellular automata, then transfer the uniform random numbers generated by cellular automata into Gaussian random numbers trough Box-Muller algorithms and central limit theorem. The Matlab simulation indicates that the mean is 0.00421.and the variance is 1.00046, which is more suitable than the Gaussian random numbers produced by 64-order LFSR whose mean is 0.06392, and variance is 1.1756. What is more, this method can produce Gaussian random numbers with 7.8σwhich is very close to the Theoretical value 8.2σ.Refer to less hardware resources, this paper also implement Gaussian random generator based on 32-order programmable cellular automata. And its mean is 0.02456 and its variance is 1.08941.Another is based on Wallace algorithm, cellular automata in this proposed method is used only to mix the initial Gaussian random numbers pool to minimize the correlation between output samples. Matlab, Modelsim and ISE 9.1i simulation results show that this method is the best one with mean -0.00181, variance 1.0007 and lest hardware resources targeted on Xilinx Virtex-2 XC2V4000-6 FPGA. Then throughχ~2 test and A-D test to test the quality of Gaussian random numbers based on Wallace method. p value of these two tests are all over 0.05, indicating the samples are with Gaussian distribution.