Development of a Mathematical Model for Performing the Haar Wavelet Transform in Parallel Modular Codes

The basis of most wireless transmission systems is Orthogonal Frequency Multiplexing (OFDM) based technology using Fast Fourier Transform (FFT). Owing to its merits, OFDM technology has found application in satellite Internet systems (SIS) built both on the basis of geostationary and low-orbit spacecraft (SC). Thus, OFDM signals with 52 traffic channels are currently used. One way to increase the data rate in OFDM is to use Haar wavelet transforms (WTs) instead of FFTs. This orthogonal signal transformation improves the spectral efficiency of OFDM. It is possible to provide a higher execution speed of the Haar WP by switching to parallel computing. This allows you to do modular codes of residue classes (MCRC). Using these codes, you can perform modular operations in parallel. For MCRC codes, these are addition, subtraction, and multiplication operations. And the article proposes a mathematical model of the modified Haar WP in the OFDM. An example of the implementation of the Haar WP on the transmitting and receiving sides of the OFDM system is presented. Implementation of the developed MCCI model based on FPGA made it possible to increase the speed of orthogonal signal conversion by a factor of 1.96 compared to the Haar WP implemented in GF(p).