Mathware and Software for Analyzing the Bit Error Rate Performance of a Digital Modem with Noise Signals at K-Users

In most cases, the analysis of the autocorrelation systems bit error rate (BER) performance is often performed with random variables Gaussian approximation. While the use of Gaussian approximation simplifies analytical studies, it also results in a loss of the theoretical estimate accuracy. Our objective is to analyze the potential BER performance of a multichannel digital multiple access modem with noise signals of the white Gaussian noise type when operating over a channel with constant parameters in which an additive Gaussian noise acts. The BER performance analysis of a signal system is performed by applying the functional transformation of random components in the demodulator with the characteristic function apparatus use. This method relies on defining the overall density of the distribution by determining the distribution of one of the random variable’s terms. All terms have the same composition and represent the sum of mutually independent random variables. Having found the distribution of one of the terms, we can use its characteristic function to determine the characteristic of the total value distribution function. By applying the inverse Fourier transform, we acquire desired distribution density. The digital multichannel modem BER performance analysis determines the theoretical estimate of the system potential BER performance, which is necessary for the comparative analysis of systems with broadband signals. The study has shown that the application of this technique results in the acquisition of analytical expressions for calculating the potential BER performance of the modem, which is additionally confirmed by the results of simulation modeling.