# Orthogonal Frequency Division Multiplexing

Thus the Discrete Inverse Fourier Transform is k: A representation of the sample facts in the domain of time. n: This is a representation of the sample facts in the domain of frequency. N: The numerical representation of the sample points. In computing, more specifically communication, the OFDM transmitters and receivers contain IFFT. The main reason as to why the IFFT is preferred in this field is its precision, flexibility and execution speed. The results of the lower and upper wing computation are stored in buffers. The second stage receives input from the first stage. The operations in the second stage are similar to that of the first stage except for the fact that the four lower wing. s use two twiddle factors that are alike. Input for stage three comes from the output in stage two.

N is a numerical representation of FFT while r is recognized as the radix of the algorithm. Every stage had three computations performed within it; twiddle factor multiplication, Sara shuffling and the fabulously known butterfly computation. The Cooley Turkey algorithms are implemented by the use of FFT hardware architecture. These hardware architectures include; Parallel architecture: It is essential for the acceleration of data shuffling, twiddles factor multiplication and butterfly computation in a single stage by taking advantage of several processing elements. Similar hardware is used per stage. Additionally, the cyclic prefix could be applied in single carrier systems to enhance the bulk of multipath multiplication. Often, cyclic prefix is applied in conjunction with modulation to keep sinusoids attributes in multipath channels. Sinusoidal signals make up the eigenfunctions time-invariant and linear systems, implying that if the channel is presumed to be time-invariant and linear, a sinusoid of infinite period would be termed as an eigenfunction.

A cyclic prefix is applied in OFDM to curb multipath by channel approximation simple (Henkel et al, 2002). For instance, consider an OFDM system that has N subcarriers, the message symbol can be denoted as. Random length padding makes it difficult for a potential attacker from identifying the plaintext message real length (Wang et al, 2005). Classical ciphers function by arranging plaintext into particular patterns such as rectangles or squares, failure of the plaintext to ft would imply supplying additional letters to fill out the intended pattern. Useless letters are used for the practice of filling out, which is beneficial as it makes cryptanalysis more difficult. Zero-padding has been suggested as a suitable substitute to CP-(cyclic prefix) orthogonal frequency –division multiplexing (OFDM) to ascertain symbol recovery despite the zero channel locations (Wang et al, 2005).

When an OFDM symbol is zero padded ISI due to adjacent symbol would still be eradicated unlike if cyclic prefix used in OFDM, although it cannot be modeled using circular convolution. OFDM has the capacity to boost wireless local area networks (WLAN) rates up to 54mb/s. A lot of challenges and problems are however experienced with OFDM with one being orthogonality, carrier orthogonality is a restriction that may contribute to improper functioning of OFDM systems if not well taken care of. OFDM may suffer possible loss of efficiency in case of numerical manipulation that may lead to occurrence of an error of computation (Kumar et al, 2009). Synchronization is another problem experienced with OFDM, the receiver has to collect the incoming signal, correctly, in case of processing of wrong samples, and the fast Fourier transform would not correctly recover the received data on the carriers, more embarrassment is experienced when the receiver is turned on.

Peak Average Power Ratio (PAPR) is another challenge when the phase of varying subcarriers sums up to form large peaks resulting to a complication in OFDM systems (Kumarr et al, 2009). “Digital Communications Fundamentals and Applications,” Second Edition, Upper saddle River, N. J. Prentice Hall Inc. ISBN 978-0-13084-788-7 Wang, J et al (2005), “Iterative Padding Subtraction of the PN sequence for the TDS-OFDM over Broadcast Channels. ” IEEE Transactions on Consumer Electronics, 51(4), 1148-115 Mohapatra, B. Sun, Y. An Efficient Method of Image-Sound Conversion Based on IFFT for Vision Aid for the Blind. Lecture Notes on Software Engineering, 54-57. doi:10. lnse.

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