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Performance Analysis of a Novel OFDM System Based on Dual – Tree Complex Wavelet Transform (DT-CWT) Mohamed H. M. Nerma1, Nidal S. Kamel2 and Varun Jeoti3 Electrical & Electronic Engineering Department, University Technology PETRONAS, Malayisa 1 E-mail: mohamed_hussien@ieee.org , 2nidalkamel@petronas.com.my , and 3varun_jeoti@petronas.com.my ABSTRACT As demand for higher data rates is continuously rising, there is always a need to develop more efficient wireless communication systems. The work described in this paper is an effort in this direction. We have proposed a novel OFDM system base on DT-CWT. In the proposed scheme, DT-CWT is used in the place of FFT. The proposed scheme offers the best PAPR performance than the conventional OFDM and wavelet packet modulation (WPM) systems at the expense of acceptable computational complexity without using any pruning techniques. The complementary cumulative distribution function (CCDF) of PAPR for the proposed scheme signal achieves about 3 dB improvement in PAPR over the traditional OFDM and WPM signals at 0.1% of CCDF. Also the proposed scheme achieves excellent improvements in BER over conventional OFDM and WPM systems. The need for CP is eliminated in the system design due to the good orthogonality and time frequency localization proprieties of the wavelet. Keywords: OFDM, WPT, CWT, DT-CWT, FFT, MCM, BER, PAPR. 1.1 Wavelet Modulation 1 INTRODUCTION Wavelet Transform (WT) is a relatively new transform compared to the discrete Fourier transform Orthogonal frequency division multiplexing (DFT). WT provides the time-frequency (OFDM) and wavelet packet modulation (WPM) representation of signals, whereas DFT gives only have emerged as an efficient multicarrier modulation the frequency representation. The properties of schemes for wireless, frequency selective, wavelet, such as localization in time and frequency, communication channels. Ease of implementation, orthogonality across scale and translation presents to high spectral efficiency, resilience to impulse noise a new perspective in digital communication. It is and multipath are a few advantages of OFDM and used as a modulation technique in many WPM systems. However, a major drawback in the communication fields including multicarrier signals of these two systems are their large envelope modulation (MCM) and wireless communication [6]. function, which limits the efficiency of the non- The conventional multicarrier systems are DFT linear power amplifiers specific to wireless based systems. In MCM, the broadband channel communications by forcing them to operate at lower splits into larger number of sub-channels. The high average power. This problem is quantified by the data rate bit-streams are divided into parallel sub Peak – to – average power ratio (PAPR) and results streams with lower data rate [7]. from the superposition of a large number of usually However, DFT based MCM systems suffer from statistically independent sub-channels that can the high side lobes due to rectangular shaped DFT constructively sum up to high peaks. Also from the window and also these systems waste precious central limit theorem (CLT) [1], this causes the bandwidth due to the redundant cyclic prefix (CP). OFDM and WPM signals to have complex Gaussian Moreover, the pulse shaping function used to process behavior and the instantaneous power is chi- modulate each subcarrier extends to infinity in the square distributed. Various schemes have been frequency domain this leads to high interference and developed to reduce high PAPR in OFDM [2] [3], lower performance levels. WT based MCM systems, and WPM signals [4] [5]. namely wavelet based OFDM systems (WOFDM) can help to mitigate these problems. Therefore, conventional DFT based orthogonal systems are being replaced by wavelet based transceivers. The UbiCC Journal, Volume 4, Number 3, August 2009 813 wavelet based transceiver uses quadrature mirror filters (QMF) in the synthesis and analysis filter 2 banks (FBs). The wavelet filters posses the advantages of having greater side-lobe attenuation To reduce the PAPR in OFDM and WPM and requires no CP [8]. WPT modulation in wireless systems, several techniques have been proposed, communication has been proposed in [9]. The which basically can be divided in three categories. characteristics of multicarrier modulated signal are First, there are signal distortion techniques, which dependent on the basis functions being used in a reduce the peak amplitudes simply by nonlinearly modulation scheme. Therefore, using WPT as basis distorting the OFDM signal at or around the peaks. functions, the sensitivity to multipath channel Examples of distortion techniques are clipping, peak distortion, inter symbol interference (ISI), inter windowing and peak cancellation. The second carrier interference (ICI), and synchronization can be category is coding techniques that use a special reduced as compared to traditional OFDM and the forward-error correcting code set that excludes system performance of WOFDM with reference to OFDM symbols with a large PAPR. The third ISI, ICI and signal-to-noise ratio (SNR) is shown to technique is based on scrambling each OFDM be far better than the conventional OFDM (DFT- symbol with different scrambling sequences and OFDM) [9], [10]. selecting that sequence that gives the smallest PAPR [13]. 1.2 Peak – to – Average Power Ratio (PAPR) This paper is organized as follows: In section II The PAPR of the baseband transmitted signal we discuss the dual-tree complex wavelet transform is defined as the ratio of the peak power (DT-CWT); in section III we discuss the half-sample ( max | |2 ); i.e., the maximum power of delay condition; in section IV we make a comparisons between traditional OFDM and WPM the transmitted signal over the average power systems; in section V we discuss the OFDM based ( E | |2 ). In digital implementations of on DT-CWT; in section VI we discuss the PAPR in communications transceivers, rather than using the OFDM based on DT-CWT; the BER results are continuous time signal in PAPR computation, presented in section VII; and we conclude this paper we instead work with , the discrete time samples in section VIII by discussion the simulation results. of x(t), provided that an oversampling factor of at least 4 is used. PAPR is then expressed as [11]: 2 THE DUAL – TREE COMPLEX WAVELET TRANSFORM (DT-CWT) max | | 1 E | | Since the early 1990s the WT and WPT have received more and more attention in modern where . denotes ensemble average calculated communications and have been widely used in over the duration of the OFDM or WPM symbols. wireless communication [14]. A number of In both OFDM and WPM systems, the signal modulation schemes based on wavelets have been going into the channel is a sum of random proposed [15 - 23]. In fact, complex wavelet symbols modulating orthogonal basis functions. transform (CWT) is applied perfectly to digital Based on the CLT, it is claimed that is complex image processing. Kingsbury [24 - 28] introduced Gaussian and its envelope follows a Rayleigh and made a concrete description of DT-CWT. The distribution. This implies a large PAPR. A high DT-CWT employs two real discrete WT (DWT); the PAPR of the transmitted signals demands a very upper part of the FB gives the real part of the linear transmission path and limits the practical transform while the lower one gives the imaginary deployment of low-cost non-linear power amplifiers part. This transform uses the pair of the filters ( , forcing them to operate with reduced power the low-pass/high-pass filter pair for the upper efficiency. Driving amplifiers operating close to FB respectively) and ( , the low- saturation with signals of high PAPR results in the pass/high-pass filter pair for the lower FB generation of unwanted spectral energy both in-band respectively) that are used to define the sequence of and out-of-band, which in turn reduces the systems wavelet function and scaling function as performance and gives rise to adjacent channel follows interference (ACI). In this work, the performance of the OFDM √2 ∑ 2 3 based on DT-CWT in PAPR reduction is demonstrated through the CCDF of PAPR, which is √2 ∑ 2 4 a performance metric independent of the transmitter amplifier. Given the reference level PAPR0 > 0, the Where 1 1 0 , the wavelet probability of a PAPR being higher than the function , the scaling function and the reference value is the CCDF and is expressed as follows [12]: high-pass filter for the imaginary part are UbiCC Journal, Volume 4, Number 3, August 2009 814 defined similarly. The two real wavelets associated with each of the two real transform are and . To satisfying the perfect reconstruction (PR) conditions, the filters are designed so that the complex wavelet is approximately analytic. Equivalently, they are designed so that is approximately the Hilbert transform of . 5 The analysis (decomposition or demodulation) and Figure 2: The Inverse dual tree discrete CWT (IDT- the synthesis (reconstruction or modulation) FBs DCWT) Synthesis (modulation) FB. used to implement the DT-CWT and their inverses are illustrated in fig. 1 and fig. 2 respectively. The 7 inverse of DT-CWT is as simple as the forward transform. To invert the transform, the real part and 0.5 8 the imaginary part are each inverted. In practical implementation of the DT-CWT, the 3 THE HALF-SAMPLE DELAY CONDITION delay condition (7) and (8) will be satisfied only approximately; the wavelets and will The two low pass filters should satisfy a very simple property: one of them should be form only an approximate Hilbert pair; and the approximately a half-sample shift of the other [29] complex wavelet will be only approximately analytic. While the FT is based on 0.5 6 complex valued oscillating cosine and sine components form a complete Hilbert transform pairs; Since and are defined only on the i.e., they are 90 out of phase with each other. integers, this statement is somewhat informal. Together they constitute an analytic signal that is However, we can make the statement rigorous using supported on only one-half of the frequency axis FT. In [5] it is shown that, if 0 [24]. . , then . The converse has been proven in [30] [31], making 3.1 Filter Design for the DT-CWT the condition necessary and sufficient. The necessary There are various approaches to the design of and sufficient conditions for biorthogonal case were filters for the DT-CWT, such as linear-phase proven in [32]. biorthogonal method, quarter shift method, and common factor method. These filters are satisfied the following desired properties: 1- Approximately half-sample delay property. 2- PR (orthogonal or biorthogonal). 3- Finite support (finite impulse response (FIR) filters). 4- Vanishing moments/good stop-band. 5- Linear phase filters. It turns out that the implementation of the DT-CWT requires that the first stage of the dual-tree (DT) FB requires a different set of filters from the succeeding stages, and the succeeding stages can be used same sets of filters. See fig. (1). If the same PR filters are used for each stage, then the first several stages of the FB will not be approximately analytic [24]. Figure 1: The dual tree discrete CWT (DT-DCWT) Analysis (demodulation) FB. 4 OFDM AND WPM SYSTEMS We can rewrite the half-sample delay condition in Traditionally, OFDM is implemented using FFT. terms of magnitude and phase function separately as This transform however has the drawback that is shown in (7) and (8) as follows. uses a rectangular window, which creates rather high sidelobes. Moreover, the pulse shaping function used to modulate each subcarrier extends to infinity in the UbiCC Journal, Volume 4, Number 3, August 2009 815 frequency domain (FD) this leads to high receiver side a DT-CWT is used in place of FFT interference and lower performance levels. ISI and block in conventional OFDM system or in place of ICI can be avoided by adding a CP to the head of DWPT block in WPM system. Data to be transmitted OFDM symbol. Adding CP can largely reduce the are typically in the form of a serial data stream. PSK spectrum efficiency. The WPM system has a higher or QAM modulations can be implemented in the spectral efficiency and providing robustness with proposed system the choice depends on various regard to inter-channel interference than the factors like the bit rate and sensitivity to errors. The conventional OFDM system, because of the out-of- transmitter accepts modulated data (in this paper we band energy (low sidelobes). Moreover WPM is able use 16 QAM). This stream is passed through a serial to decompose T-F plane flexibly by arranging FB to parallel (S/P) converter, giving N lower bit rate constructions. In addition, using FFT in the data stream, and then this stream is modulated traditional OFDM gives resolution only in the FD through an IDT-CWT matrix realized by an N-band while using WPT in WPM system gives resolution in synthesis FB. Before the receiver can demodulate the both FD and time domain (TD) [16]. subcarriers, it has to perform the synchronization. WPM system do not required CP, thereby For the proposed system, known data interleaved enhancing the spectrum efficiency. According to the among unknown data are used for channel IEEE broadband wireless standard 802.16.3, estimation. Then, the signal is down sampled by N avoiding CP gives wavelet OFDM an advantage of and demodulated using elements of the DT-CWT roughly 20% in bandwidth (BW) efficiency. matrix realized by an N-band analysis FB. The signal Moreover as pilot tones are not necessary for wavelet is equalized after DT-CWT stage. based OFDM system, they perform better in comparison to existing OFDM systems like 802.11a or HiperLAN, where 4 out of 52 sub-bands are used for pilots. This gives wavelet based OFDM system another 8% advantage over typical OFDM implementations [39]. We expected the OFDM based on DT-CWT will take all the advantages of WPM system. However, a major problem of the common discrete WPT (DWPT) is its lack of shift invariance; this means that on shifts of the input signal, the wavelet coefficients vary substantially. The signal Figure 3: DT-CWT modulation (DT-CWTM) information may even not be stationary in the sub- functional block diagram. bands so that the energy distribution across the sub- bands may change [15]. To overcome the problem of IDT-CWT works in a similar fashion to an IFFT shift dependence, one possible approach is to simply or IDWPT. It takes as the input QAM symbols and omit the sub-sampling causing the shift dependence. outputs them in parallel time-frequency Techniques that omit or partially omit sub-sampling “subcarriers”. In fig. (2) as the synthesis process, it are also known as cycle spinning, oversampled FBs can be shown that the transmitted signal, is or undecimated WT. However, these transforms are constructed as the sum of M waveform individually redundant [33], which is not desirable in multicarrier modulated with the QAM or PSK symbols [34], φ t modulation. As an alternative, we used a non- is the scaling function, ψ t is the wavelet function, redundant WT that achieves approximately shift and a is kth symbol, i 1, 2, … , N as follows: invariance [34], this transform yields to complex wavelet coefficients that modulate the data stream in . 9 the same way that WPM do. / 5 OFDM BASED ON DT-CWT . 10 , , , , In this study, simulations are focusing on using DT-CWT in the OFDM system as a non-redundant WT that can achieves approximately shift invariance [35 – 38]. Similar to the conventional OFDM and / , / , , , . 11 WPM systems, a functional block diagram of OFDM / based on DT-CWT is shown in fig. (3). At the transmitter an inverse DT-CWT (IDT-CWT) block is Where , is a constellation encoded data used in place of inverse FFT (IFFT) block in symbol modulating the DT-CWT function. conventional OFDM system or in place of inverse The IDT-CWT synthesis a discrete representation of DWPT (IDWPT) block in WPM system. At the the transmitted signal as sum of M waveforms UbiCC Journal, Volume 4, Number 3, August 2009 816 shifted in time that embed information about data sequence x n has high PAPR. Furthermore, to symbols. Those waveforms are built by successive demonstrate the similarities between power spectrum iterations of ^ , ^ and ^ , ^ . The DT-CWT at the density (PSD) characteristic of conventional OFDM, receiver recovers the transmitted symbols , WPM and the proposed scheme, the simulated PSD through the analysis formula exploiting orthogonality characteristics are presented in fig. 4. This fig. was properties of DT-CWT and schematically shows that the proposed scheme performs better than represented in fig. (1). the other two systems. In the baseband equivalent OFDM transmitter with The simulation parameters are documented as frame of N QAM symbols, , follows: Modulation type is 16-QAM; the number of 0,1, … , 1, the OFDM frame is given by: subcarriers is 64 subcarriers; a wavelet packet base is Daubechies-1 (DAUB-1); maximum tree depth (D = 7); PAPR threshold is 2dB; shaping filter is Raised / 12 Cosine (rolloff factor 0.001, upsampler = 4); DT- CWT using different filters (LeGall 5,3 tap filters (leg), Antonini 9,7 tap filters (anto), Near Symmetric While for WPM system, the transmitted signal 5,7 tap filters (n-sym-a), and Near Symmetric 13,19 is constructed as the sum of M wavelet packet tap filters (n-sym-b)) for the first stage of the FB and function individually modulated with the QAM (Quarter Sample Shift Orthogonal 10,10 tap filters symbols as the case in this paper‡. (q-sh-06) only 6,6 non-zero taps, Quarter Sample Shift Orthogonal 10,10 tap filters (q-sh-a) with 10,10 non-zero taps, unlike q-sh-06, Quarter Sample Shift , 13 Orthogonal 14,14 tap filters (q-sh-b), Quarter Sample Shift Orthogonal 16,16 tap filters (q-sh-c), and Quarter Sample Shift Orthogonal 18,18 tap filters (q- The construction of discrete versions of sh-d)) for the succeeding stages of the FB. transmitted waveforms for the conventional OFDM and WPM systems using (12) and (13) is quite 6 PAPR ANALYSIS RESULTS similar. For any time index n, both waveforms are sum of random symbols a or a , . Consider the simple case where all the sub- symbols are independently and identically distributed (i.i.d). then, by the CLT, the real and imaginary parts of the N-point IFFT output have mutually independent Gaussian probability distribution function with zero mean and standard deviation to σ . The instantaneous power of baseband signal , is defined by 14 We can characterize the instantaneous power as a chi-square distribution with two degrees of freedom [31] Figure 4: PSD of the Conventional OFDM, WPM and OFDM based on DT-CWT. 1 , 0 15 In order to achieve fair comparisons, same simulation parameters are used. The simulations If E | | is normalized to unity, then the CCDF were carried out for conventional OFDM with a 64 of the PAPR is given by: subcarriers using a 16 QAM modulation. The Daubechies-1 (Daub-1) wavelet packet bases were Pr 1 1 16 used to construct the wavelet packet trees in WPM system. For the proposed scheme, near symmetric 13,19 tap filters and quarter sample shift orthogonal Where N is the number of subcarriers. 14 tap filters were used to construct the real and the In order to analyze PAPR, we generate the imaginary part of DT-CWT respectively. From the transmitted waveforms using 16 QAM modulation CLT, x n is complex Gaussian distributed, and the with 64 subcarriers for all these systems. Fig. 5 shows, in the TD, the envelope of the proposed ‡ system. For the comparison, we also plotted the We use φ n for the wavelet packet function and ψ n for the envelope of the conventional OFDM and WPM DT-CWT function to avoid any confusion. UbiCC Journal, Volume 4, Number 3, August 2009 817 waveforms corresponding to the same information stage of the FB and quarter sample shift orthogonal symbol pattern. The transmitted envelopes for the (q-sh) 14 tap filters in the succeeding stages, OFDM conventional OFDM and WPM systems illustrate DT-CWT_2 using (n-sym 13,19 with q-sha 10 (10 approximately similar behavior, where the peak is non zero taps) filters), OFDM DT-CWT_3 using about 2.25, while the transmitted envelope for the (antonini (anto) 9,7 tap filters with q-sh0 10 (only 6 proposed system demonstrates better behavior than non zero taps) filters), OFDM DT-CWT_4 using the other two systems, where the peak is only about (anto 9,7 with q-sh 14 filters), OFDM DT-CWT_5 1.25 and this is the reason for that the proposed using (n-sym 5,7 with q-sh 14 filters), OFDM DT- system gives better result for PAPR than the other CWT_6 using (LeGall (leg) 5,3 tap filters with q-sh two systems. 14 filters), OFDM DT-CWT_7 using (n-sym 5,7 with q-sh 16 filters) and OFDM DT-CWT_8 using (leg 5,3 with q-sh 18 filters). The results in fig. 7 show that there is no observed degradation as a result of using different set of mismatching filters in the design of the proposed scheme. Figure 5. The Envelope of the Conventional OFDM, WPM and OFDM based on DT-CWT. Figure 7: The effect of using different set of filters in design of the OFDM based on DT-CWT. Figure 6: CCDF the Conventional OFDM, WPM and OFDM based on DT-CWT. The results for PAPR are best quantified using CCDF. In fig. 6, for 64 subcarriers with 16 QAM modulation, the CCDF plots for the proposed system, conventional OFDM and WPM system are shown. Figure 8: CCDF of PAPR for 16-QAM modulated conventional OFDM symbol with various values of This figure shows that the OFDM based on DT- subcarriers (N). CWT offers the best PAPR performance without using any reduction techniques. The proposed Again, the results for PAPR were repeated in scheme signal achieves about 3 dB improvement in both fig. 8 (for the conventional OFDM system) and PAPR over the traditional OFDM and WPM signals fig. 9 (for the proposed system) using different at 0.1% of CCDF while the other two systems, are numbers of subcarriers (64, 128, 256, 512, and 1024) approximately given same results of PAPR. with 16QAM modulation. We observe from these The simulation results for PAPR were also figures that the PAPR increases as the number of repeated with 16 QAM modulation and 64 subcarriers numbers (N) increases. As shown in fig. subcarriers (in fig. 7) using different set of filters. 6, 7 and in fig. 8, 9 the PAPR performance of DT- OFDM DT-CWT_1 illustrate the PAPR when using CWT based OFDM systems is better than the near-symmetric (n-sym) 13,19 tap filters in the first UbiCC Journal, Volume 4, Number 3, August 2009 818 conventional OFDM system or even WPM systems. As we saw in figure 5 showing the time-domain signal envelop of all the systems, this improvement in PAPR performance is explained from lower peaks of DTCWT systems observed in the fig. 5. Figure 11: The effect of using different type of filters in BER for OFDM based on DT-CWT. 8 CONCLUSION Figure 9: CCDF of PAPR for 16-QAM modulated OFDM based on DT-CWT symbol with various In this paper a new OFDM scheme that is based values of subcarriers (N). on DT-CWT is proposed. Comparing the proposed scheme in terms of PAPR and BER with the 7 BER ANALYSIS RESULTS traditional OFDM and WPM systems we see that the proposed scheme offers 3dB better PAPR The results given in this section compare the performance over the conventional OFDM and BER in the OFDM based on DT-CWT, with that for WPM systems at 0.1% of CCDF. While the traditional OFDM, and WPM. Also, same simulation conventional OFDM and WPM systems shows parameters are used to achieve a fair comparison. similar behavior. Simulation results shows that there The results of BER in OFDM based on DT-CWT is no observed PAPR and BER degradation as a using different set of filters are also shown in this result of using different set of mismatching filters in section. DT-CWT based system. The proposed scheme The results for BER are shown that the proposed outperforms the traditional OFDM and WPM scheme gives excellent improvements in BER over systems in term of BER. Also we found that the conventional OFDM and WPM systems. At the same conventional OFDM system gives better results of time the conventional OFDM outperform the WPM BER than WPM system. system in term of BER. As shown in fig. 10. The simulation results for BER were repeated using different set of filters (OFDM DT-CWT-1, ACKNOWLEDGMENTS OFDM DT-CWT-2, …, OFDM DT-CWT-8) and is Authors wish to thanks Prof. Nick G. Kingsbury shown in fig. 11. We see there is degradation of BER (University of Cambridge, United Kingdom) and Dr. as a result of using different set of mismatching Mohan Baro (Dalhousie University, Canada) whose filters in the design of the proposed scheme. comments and suggestions have largely contributed to improve this paper. APPENDIXES A. CCDF Approximations We can characterize the instantaneous power as a chi-square distribution with two degrees of freedom [40] 1 , 0 17 As a result, the cumulative distribution function (CDF) is defined as: Figure 10: BER performance of conventional OFDM, WPM and OFDM based on DT-CWT. UbiCC Journal, Volume 4, Number 3, August 2009 819 1 1 . 22 1 18 √2 √2 If E | | is normalized to unity, then the CCDF Note that the identity matrix on the right-hand side of of the PAPR is given by: (22) is twice the size of those on the left-hand side. Therefore if the two real DWTs are orthonormal transforms, then the DT-CWT satisfies . , 1 1 19 where * denotes the conjugate transpose. 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SIGNAL PROCESSING (SIP '09), Istanbul, [23] C. V. Bouwel, J. Potemans, S. schepers, B. Turkey, May 30 - June 1, 2009. Nauwelaers, and A. Van Caelle, “wavelet [38] Mohamed H. M. Nerma, Nidal S. Kamel, packet Based Multicarrier Modulation”, and Varun jeoti, “An OFDM System Based IEEE Communication and Vehicular on Dual Tree Complex Wavelet Transform Technology, SCVT 2000, pp. 131-138, (DT-CWT)” Journal: Signal Processing: 2000. An International Journal, Volume: 3, Issue: [24] Ivan W. Selesnick, Richard G. Baraniuk, 2, Pages: 14-21, May 2009. and Nick G. Kingsbury, “The Dual-Tree [39] M. K. Lakshmanan and H. Nikookar, “A Complex Wavelet Transform,” IEEE Signal Review of Wavelets for Digital Wireless Processing Mag, pp. 1053-5888, Nov 2005. Communication”, Wireless Personal [25] N.G. Kingsbury, “The dual-tree complex Communications Springer, 37: 387-420, wavelet transform: A new technique for Jan. 2006. shift invariance and directional filters,” in [40] R. Van Nee and A. De Wild, “reduction the Proc. 8th IEEE DSP Workshop, Utah, Aug. peak-to average power ratio of OFDM” 48th 9–12, 1998, paper no. 86. IEEE Vehicular Technology Conference, [26] N.G. Kingsbury, “Image processing with Ottawa, Canada, May 18-21, 1998; 2072- complex wavelets,” Philos. Trans. R. Soc. 2076, IEEE New York, USA. London A, Math. Phys. Sci., vol. 357, no. [41] H. Ochiai and H. Imai, “On the disitribution 1760, pp. 2543–2560, Sept. 1999. of the peak-to-average power ratio in [27] N.G. Kingsbury, “A dual-tree complex OFDM signals”, IEEE Trans. Commun. wavelet transform with improved 2001; 49, 282-289. orthogonality and symmetry properties,” in [42] S. wei, D. L. Goeckel, and P. E. Kelly “A Proc. IEEE Int. Conf. Image Processing, modern extreme value theory approach to UbiCC Journal, Volume 4, Number 3, August 2009 821 calculate the distribution of the peak-to- Nidal S. Kamel, received his average power ratio in OFDM systems”, Ph.D degree (Hons) in IEEE International Conference on Communications, New York, Apr. 28- May telecommunication and 2, 2002; vol. 3, 1686-1690; IEEE New statistical signal processing York, USA. from the Technical [43] H. Yu, M. Chen and G. wei “Distribution of University of Gdansk, PAPR in DMT systems”, Electron. Lett. 2003; 39, 799-801. Poland, in 1993. His research [44] R. Rajbanshi, A. M. Wyglinski and G. J. is focused on linear Minden, “Multicarrier Transceivers: Peak- estimation, noise reduction, to-average power ratio reduction”, IEEE pattern recognition, optimal filtering, and Commun. Society. WCNC 2008 telecommunications. Currently he is working for proceeding. Universiti Teknologi PETRONAS, Malaysia. He is senior member of IEEE. Varun Jeoti Jagadish, Mohamed H. M. Nerma, was received his Ph.D. degree born in Khartoum, Sudan. He from Indian Institute of received the B.Sc. degree in Technology Delhi India in Electrical Engineering 1992. He worked on several (Control) from Sudan sponsored R&D projects in University of Science and IIT Delhi and IIT Madras Technology (SUST), Sudan in during 1980 to 1989 1999. He received the M.Sc. developing Surface Acoustic degree in Communication Wave Pulse Compression filters, underwater optical Engineering from Karary Academy of Technology, receivers etc.. He was a Visiting Faculty in Sudan in 2002. From 2002 to 2006 he was lecturer in Electronics department in Madras Institute of the Sudan University of Science and Technology. He Technology for about 1 year during 1989 to 1990 is currently PhD. Student in University Technology and joined Delhi Institute of Technology for next 5 PETRONAS, Malaysia. years till 1995. He moved to Electrical & Electronic Engineering (E&E Engg) department of Universiti Sains Malaysia in 1995 and joined E&E Engg of Universiti Teknologi PETRONAS in 2001. His research interests are in Wireless LAN and MAN technologies, DSL technology and related signal processing. UbiCC Journal, Volume 4, Number 3, August 2009 822

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