J. Today’s Ideas - Tomorrow’s Technol.

OFDM: A Mathematical Review

Praveen Kumar Malik and M P Tripathi

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Cyclic prefix, Inter symbol interference, Multi carrier modulated systems.

PUBLISHED DATE December 2017
PUBLISHER The Author(s) 2017. This article is published with open access at www.chitkara.edu.in/publications

Mathematical review of the Orthogonal Frequency Division Multiplexing is demonstrated in terms of Inter symbol interference, Multi carrier modulated system and cyclic prefix. Modeling of the mathematical equation of the Orthogonal Frequency Division Multiplexing, Inverse fast Fourier transform and fast Fourier transform is explained with the suitable example using MATLAB. Bit error rate performance of OFDM is also presented with the help of statistical computation


Orthogonal frequency division multiplexing (OFDM) is a broadband key technology which is employed in “4G wireless communication system”. It is also used in “Long term evolution” (LTE) 4G cellular standard and Worldwide interoperability for microwave access (Wi max) also. These are now day’s dominants standards and both are based on OFDM. LTE –A long term evolution advanced which is latest communication standard in broad band is also based on OFDM.

LTE is a wireless communication standard which can support a large bandwidth. In general GSM has a bandwidth of about 200KHz but OFDM can have bandwidth of about 100MHz. Naturally data rate in OFDM will be higher which is used in 3G and 4G to enable data rate of up to 100MBps or more then 500MBps. Several IEEE Wi-Fi wireless local area networks WLAN (802.11, 802.11G, 802.11N, 802.11AC) standards are used for high data rate which are based on the OFDM.

Page(s) 97–111
URL http://dspace.chitkara.edu.in/jspui/bitstream/123456789/700/1/1-OFDM%20A%20Mathematical%20Review%20-%20Praveen%20Malik.pdf
ISSN Print : 2321-3906, Online : 2321-7146
DOI https://doi.org//10.15415/jotitt.2017.52001

A MATLAB based program is written to compute the above specified methods and following are the results of the program. For simplicity of the data presentation, following terms are assumed. Number of bits per channel is 32 but can be extended upto 128 Number of subcarrier channel is 4 Total number of bits to be transmitted at the transmitter is 128 Size of each OFDM block to add cyclic prefix 16 Channel is AWGN in nature Random samples are taken for the transmission purpose. These samples are in the binary form.

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