Finite Radon Transform as Subcarriers Mapping Technique for OFDM System

—Radon Transform (RT) becomes a mathematical basis for solving computerized tomography, and finds application in medical imaging and image processing. Finite groups represent digital images; the Finite Radon Transform (FRAT) is then applied. To overcome the periodization effect of a finite transform, Do and Vetterli [1] introduce a novel ordering of the FRAT coefficients. This paper introduced a detailed mathematical analysis of the optimal ordering of FRAT coefficients that introduces new normal vectors that are clearly identified with examples producing the FRAT transform. Lately FRAT is used with OFDM systems as an M-Ary mapping technique, thus, the signal constellation of some of the different orders of FRAT is presented as well as generating the OFDM symbols from the output of FRAT. This procedure leads to extra investigation on the performance of FRAT-based OFDM systems in comparison with the QAM mapping techniques.