Matlab Simulation And Fpga Implementation Of The Chen-mobius Digital Communication System

In the 1990s, Professor Chen Nanxian, academician of Chinese Academy of Science, applied the Mobius inversion formula in infinite series form to solve a series important inverse problems in applied physics; and created the wonderful methods of applying,extending the Mobius transform in Number theory (i.e. The Chen-Mobius transform) to solve various inverse problems in physics. His works were highly evaluated by the top scientific magazine NATURE in 1990.Professor Su Wuxun, Zhang Weibin etc., applied the methods of Mobius transform to the calculations of the inverse transforms of the Fourier series of eight common used waveforms (including rectangular pulse, even and odd symmetrical square wave and triangle wave, sawtooth wave, half-wave cosine and full-wave cosin waveforms), and derived the expanded formula of the sine, cosine and general periodic functions on these waveforms. They also derived the very important functions which are orthogonal with the corresponding common-used waveforms respectively and can be used to calculate the expanded coefficients and in information modulation-demodulation. Then they applied the methods of Mobius transform in the coherent modulation-demodulation system and put forward a new communication system, named the Chen-Mobius communication system. In the new system, the orthogonal functions replace the trigonometric functions in the coherent modulation-demodulation of traditional communication system. These two orthogonal functions set as the modulation-demodulation function set greatly improved the transmission performances of our communication system and enhance the secrecy. Also these two orthogonal function set are easy to produce.Chen-Mobius digital communication system was validated by software simulation and hardware realization. First, The single-channel,four-channel and eight-channel digital communication systems by Chen-Mobius transform were simulated and analyzed by MATLAB software. The error rates were computed according to different ratios of average signal power to average noise power (S/N )and based these results, the figure of the error rates to S/N were given; Secondly, on the QuartusⅡsoftware platform, Chen-Mobius digital communication system was built and simulated by the methods of VHDL language input and schematic design, including design synthesis,pin assignments,simulation analysis and timing analysis etc; Thirdly, based on QuartusⅡsoftware simulation, Chen-Mobius digital communication system was realized on the Altera's Stratix GX FPGA development board; At last, based the results of software simulation and hardware realization, the application of the system was simply analyzed.The figues of error rates to S/N was derived by software simulation in the Chen-Mobius communication system, and so the better performance of anti-jamming was validated. The system was realized on FPGA, and so it was validated that the system is realizable. From both the aspects, Chen-Mobius communication system is just a new point of departure, but it indicates bright application foreground.