International Journal on Communications Antenna and Propagation (IRECAP), Vol. xx, n. x May 2013 Copyright © 2013 Praise Worthy Prize S.r.l. - All rights reserved Int. Journal on Communications Antenna and Propagation, Vol. x, N. An Evaluation of Coded Wavelet for Multicarrier Modulation with OFDM K. O. O. Anoh, T. Ghazaany, A. S. Hussaini, R. A. Abd-Alhameed, SMR Jones and J. Rodriguez Abstract - Orthogonal frequency division multiplexing (OFDM) is pronounced in wireless communication systems. Methods for improving the performance of the OFDM-based systems are mostly sought. A method of doing this involves error correction coding and another, a better multicarrier modulation kernel. In this work, convolutional error correction coding with interleaving is introduced in wavelet multicarrier modulation OFDM system (wavelet-OFDM) to improve the performance of multicarrier systems as the signal traverses the multipath and noisy transmission channels. This is compared with FFT-based multicarrier modulation (FFT-OFDM). Results show that coded wavelet-OFDM saves more than a half of the transmit power than the uncoded wavelet. Also it will be shown that, the interleaved and non-interleaved coded wavelet-OFDM well outperform interleaved coded and non- interleaved coded FFT-OFDM systems respectively. Copyright © 2013 Praise Worthy Prize S.r.l. - All rights reserved Keywords - Multicarrier Modulation, Wavelet, OFDM, Convolution Coding, Error Correction, Viterbi Decoding, Interleaving. Nomenclature (.) ψ Mother wavelet (.) , a k ψ Daughter wavelet of k th scale and a th shift (.) ϕ Scaling function A L,n Approximate wavelet signal coefficient D m,n Detail wavelet signal Coefficient α Multipath gain d Uncoded input information C Coded output information q memory depth G 1 and G 2 polynomial generators k n G Polynomial generator n m D Interleaved data of n-rows and m-depth S Transmitted signal (.) z AWGN channel (.) p Multipath channel R Spanning set (.) 2 l Square summable space (.) h Scaling filter (.) g Wavelet filter I. Introduction Besides its use in digital video broadcasting (DVB), up to one billion cell phones over the world today use forward error correction (FEC) with, for instance, the Viterbi decoding algorithm [1]. In digital communications however, FEC is required to improve the capacity of a channel and the probability of error by adding some carefully designed redundant bits to the source information in the transmitter before transmission [2]. For instance, convolutional coding with Viterbi decoding improves the performance of communication systems in additive white Gaussian noise (AWGN) channel. Interleaving on the other hand spreads the burst error of coded signal blocks that are in deep fade [3, 4]. Information bits contained within these parts of deep fade may not be recoverable at the receiver, unless with some great effort. Error correction coding is one of the prominent techniques required to minimize this susceptibility of the transmit signal from such channel corruption. In application, coding in digital communications can be convolutional or block coding or both with interleaving. With interleaving, the information bearing bits are spread out in time such that if there is a deep fade or noise burst, not all the information bits are corrupted [5]. Consequently, interleavers scramble the time order of the source bits before they are channel coded. They ensure that the information corruptions centralized in the areas of deep fades are fairly spread over the entire symbol frame. Coding influences the named corruption sources so that the probability of receiving transmitted bits in error can be as low as possible. For instance, by adopting punctured convolutional codes, channels characterized mostly by rainfall can be bearably handled [6] with less effective information bits redundancy. In this study, no puncturing mechanism has been considered. Rain, multipath effect, shadowing of tall buildings, and mobility of objects with respect to another or mobility of the receiver (mobile) with respect to the transmitter cause signal energy to decay along the propagation path. In effect, the signal undergo some severe corruption so that they can be, sometimes, deeply faded. In the meantime, combining OFDM with convolutional coding improves the system performance towards Shannon limit [7]. With OFDM, there is an excess bandwidth cost as much as the cyclic prefix (CP) length and the convolutional coding redundant bits. In a frequency selective channel where OFDM dominates in performance [8], adding CP pre-empts inter-symbol interference (ISI) with the interleaved convolutional coding further spreading the errors of the channel well enough in time so that the transmitted bits be most probably recovered. Over a Rayleigh channel, the Rayleigh law affects the amplitude of each OFDM sub- carrying symbol which are correlated in practice [9].