A Typical model of an OFDM transceiver with inverse and forward transforms that can be substituted as FFT-, DWT- or WPT- OFDM. 

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... r k as indicated in Fig. 1 is written as r k = y k + g k k = 0 , 1 , 2 , ...L − 1 (7) where y k is the transmitted OFDM signal, g k is the noise consisting of AWGN and impulsive noise, and is given by g k = w k + i k (8) where w k is the additive Gaussian process with mean zero and variance σ w 2 and i k can be expressed as to the ’T’ blocks in the WPT-OFDM transceiver in Fig. 3. At each branch, the wavelet packet forms the wavelet basis function which is split into scaling and wavelet coefficients corresponding to the LPF and HPF coefficients respectively [8]. This also means that they have orthonormal bases and perfect reconstruction properties as discussed in the previous section. Examples of the wavelet basis function at level 3 are (3 , 0) , (3 , 1) , (3 , 2) , (3 , 3) , (3 , 4) , (3 , 5) , (3 , 6) , and (3 , 7) . Due to this characteristic, the wavelet packets offer a more complex and flexible operation. The number of nodes depending on the number of levels. At the front end of the receiver, the signals U k is received by the system and processed by the WP forming block. For this purpose, the same command as in the transmitter is invoked. After the WP tree is formed, the WPT reconstruction will output the wavelet basis functions at the last terminals to be further process to the QAM demodulator for the data recovery. IV. I MPULSIVE N OISE E FFECT Impulsive noise effect to the OFDM system has been discussed in many literatures [8], [9], [10]. In this section, we describe the general principles of the impulse noise when it affects an OFDM system. We also mention the recurrence parameter of Poisson distribution which will affect the system performance. Assuming that the receiver having ...

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... I NTRODUCTION Orthogonal Frequency Division Multiplexing (OFDM) is a promising multicarrier wireless system for transmission of high-rate data stream with power efficiency and fading immunity. Conventional OFDM systems use IFFT and FFT algorithms at the transmitter and receiver respectively to multiplex the signals and transmit them simultaneously over a number of subcarriers. The system employs guard intervals or cyclic prefixes (CP) so that the delay spread of the channel becomes longer than the channel impulse response to minimize inter-symbol interference (ISI). However, the CP has the disadvantage of reducing the spectral containment of the channels. Alternative methods are to use wavelet transforms replacing IFFT and FFT [1], [2], [5], [6], [7]. By using these transforms, the spectral containment of the channels is better since they are not using CP [1], [2], [5], [6]. They can be considered as Discrete Wavelet Transform OFDM (DWT-OFDM) or Wavelet Packet Transform OFDM (WPT-OFDM). Both transforms employ Low Pass Filter (LPF) and High Pass Filter(HPF) operating as Quadrature Mirror Filters satisfying perfect reconstruction and orthonormal bases properties. The transforms use filter coefficients as approximate and detail in LPF and HPF respectively. The approximated coefficients is sometimes referred to as scaling coefficients, whereas, the detailed is referred to wavelet coefficients [3]. Sometimes these two filters can be called subband coding since the signals are divided into sub-signals of low and high frequencies respectively. The purpose of this paper is to view the effects of impulse noise on the wavelet-based OFDM particularly using DWT and WPT-OFDM as substitutions for Fourier-based OFDM. A recent work has focussed on the effect of impulse noise when wavelet packet division multiplexing (WPDM) is used [8]. Some discussions are related to the performance comparison between OFDM and Time Division multiplexing (TDM). However, there is no indication of comparative study and performance using DWT and WPT as alternative replacement of FFT. Although the studies in [9] provides strong analysis of impulsive noise and its effect on the performance of OFDM system, the discussion is mainly for the application in the power line communications (PLC). To the best of the Authors’ knowledge, there is no work showing the steps of how to simulate flexible transformed models of DWT- and WPT- OFDM as alternative replacements of FFT-OFDM under the effect of impulse noise. This paper is divided into four main sections: section II will briefly explain conventional FFT- OFDM, section III will describe in detail the models for DWT- OFDM and WPT-OFDM, section IV will provide the impulse noise effects on the OFDM system, and section V will discuss the bit error rate (BER) performance considering two different scenarios of impulse noise effects. II. F OURIER -B ASED OFDM A typical block diagram of an OFDM system is shown in Fig. 1. The inverse and forward blocks can be FFT- based, DWT-based or Wavelet Packet (WP)-based OFDM. The system model for FFT-based OFDM will not be discussed in detail as it is well known in the literature. Thus, we merely present a brief description about it. The data d k first being processed by a constellation mapping. M-ary QAM modulator is used for this work to map the raw binary data to appropriate QAM symbols. These symbols are then input into the IFFT block. This involves taking N parallel streams of QAM symbols (N being the number of sub-carriers used in the transmission of the data) and performing an IFFT operation on this parallel stream. The output in discrete time domain is as ...