Mathematical Modeling of Signal Processing Using Discrete Wavelet Transform and Non-Positional Modular Code

Currently, the orthogonal frequency multiplexing (OFDM) method is the basis for the construction of most wireless communication systems. This is due to the fact that, due to the orthogonality of the carriers, OFDM systems have a high information transfer rate. The achievement of high speed was due to the use of a number of technical solutions. Firstly, the developers proposed to reduce the length of cyclic prefixes. Secondly, they began to increase the QAM constellation. Thirdly, due to the reduction of the correcting abilities of the codes, the coding speed was increased. Fourth, they began to use spatial coding (MIMO) methods. At the same time, signal processing based on forward and inverse fast Fourier transforms (FFT) was not modified. The paper considers a mathematical model of signal processing using discrete wavelet transform (DWT) and non-positional arithmetic code. The implementation of this model will lead to an increase in the transmission rate in OFDM systems. Firstly, DWT allows you to perform digital signal processing in less time compared to FFT. Secondly, the use of modular residue class codes (MCRS) provides a parallel organization of modular operations, which include addition, subtraction and multiplication. Therefore, mathematical modeling of the signal processing process using discrete wavelet transform and non-positional arithmetic code is an urgent task.