Analytic comparison of using FFT and wavelet in IEEE a WLAN based OFDM technique

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1 Aalytic compariso of usig FFT ad wavelet i IEEE a WLAN based OFDM techique Habab Habib Alshammary, Abdel-Rahma Al-Qawasmi Abstract Modulatio techiques play a sigificat role i miimizig the effect of oise produced by oisy chaels, especially thermal oise produced due the heat effect i electroic commuicatio systems. The effect of oise has a sigificat value i wireless commuicatio systems ad ca affect the performace of systems ad be icreasig the probability of error. This icreasig of the probability of error will be over some acceptable values due the me\multiplexig techique used which will force the system to decrease the eeded data rate. OFDM meets requiremets of high data rates of mobile wireless commuicatios; the OFDM techology is to be a essetial techique for achievig the high data capacity ad spectral efficiecy requiremets for wireless commuicatio systems. I this paper a ivestigatio ito wavelet ad Fast Fourier Trasform (FFT) ad their effect o WLAN IEEE a system that implemets Orthogoal Frequecy Divisio Multiplexig OFDM aalyzed the effect of AWGN usig differet modulatio techiques parameters that simulated to study the performace of the proposed system such as BPSK, DPSK, QPSK, DQPSDK QAM16 ad QAM64. Results extracted i simulatio part presets a sufficiet privilege for DWT-OFDM pair. Idex Terms OFDM, wavelet, IFFT, IEEE , WLAN. T I. INTRODUCTION 1 he Fast Fourier Trasform (FFT) is a algorithm that Scietific use to compute the discrete Fourier trasform faster tha ca do discrete Fourier trasform or other algorithms [1]. The FFT is importat i it has a cetral place i differet applicatios such as image ad sigal processig due to its workig i the frequecy domai. The real equivalet versio of DFT Real ad Imagiary) is [2]. 1 This work was is submitted i 28\3\2016 ad supported i part by the Departmet of Electrical Egieerig College of Egieerig, Majmaah Uiversity, Majmaah 11952, Saudi Arabia. A. Al-Qawasmi is with the Majmaah Uiversity, Riyadh provice, KSA (a.alqawasmi@mu.edu.sa). Habab Habib Alshammary, Msc. E-learig maagemet ~ C (1) ~ C R I N 1 k 0 N 1 k 0 f f I ( k)cos( ) f R I ( k)si( ) R ( k)cos( ) f ( k)si( ) (2) M. Rahma metioed i his book [3], it is better to divide the trasform ito N/2 equal parts at each step. This algorithm is kow as a Cooley-Turkey algorithm that limits the power to power-of-two sizes. I this case, the umber of complex multiplicatios ad additios ca be reduced, ad the trasformatio will be fast. The Discrete Wavelet Trasform (DWT) deals with timedomai depedet fuctios of time ad it ca be writte as [4]: S m m / 2 m S( t)2 (2 t ) dt (3)

2 The Wavelet fuctio is: m m / 2 m S ( t) S 2 (2 t ) (4) m m Two scalig fuctios used with Wavelet trasform [4]: a m 1 m1 S( t) ( t) dt ad A m1 m1 ) a (5) S( t (6) m1 Practical sigals are limited i frequecy ad limited i time [8]. The frequecy aalysis i wavelet trasform is performed usig low frequecy while the aalysis is performed by applyig high-frequecy versios of the mother wavelet. Some issues are importat i desigig wavelet fuctios: Smoothess, Approximatio accuracy ad Size of the support of wavelets The pricipal differece betwee FFT ad DWT is that Fourier trasform localized i frequecy whereas Wavelet trasform is localized i both frequecy ad time. Also, Wavelets ofte give a better sigal represetatio usig Multiresolutio aalysis, with balaced resolutio at ay time ad frequecy. Orthogoal Frequecy Divisio Multiplexig (OFDM) is a covetioal form where all sub-carriers are orthogoal to each other. Due to the miimum frequecy distace betwee carriers, OFDM provides high data rate, high resistace to frequecy selective fadig ad reasoable complexity ad cost. The orthogoality requires that the sub-carrier spacig is: k f Hertz (7) T U where T U secods is the symbol duratio ad k is a positive iteger. A OFDM sigal is a sum of differet subcarriers that are modulated by usig Phase Shift Keyig (PSK) or Quadrature Amplitude Modulatio (QAM). The symbol ca be writte as: s( t) Re t N s 1 2 N s 2 s( t) 0, t t adt t T s d in s / 2 i 0.5 exp( j2 ( f c )( t ts )), ts t ts T T s OFDM sigals are typically produced digitally due to the challege of creatig huge baks of phase lock oscillators ad receivers i the aalog domai. Figure 1 shows the block diagram of a typical OFDM trasceiver [5]. Fig. 1. Block diagram showig a basic OFDM trasceiver Wireless Local Area Networks (WLAN) becomes familiar ad preferred etwork access amog users. The first of the IEEE Workshops o WLAN was held i 1991 [6]. At that time, iitial wireless LAN products had just appeared o the market, ad the IEEE committee had just begu its activities to develop a stadard for WLANs [6]. Wireless LAN provides more flexibility tha traditioal wired local area etworks stadards ad support data rate ragig from 1-2Mbps to 11Mbps ad 54Mbps depedig o the specificatios used. The IEEE committee is resposible for WLAN stadards icludig , a, g ad b together with other stadards that defie Quality of Service (QoS) ad Security for WLAN [7-8]. Primary types of equipmet used i WLAN system is listed i [9]. Each a/b/g device ca operate i oe of four possible modes [8]. Followig table is a summary of the etwork stadards. I this paper research, the IEEE (a) stadard will be used.the IEEE a is a Orthogoal Frequecy Divisio Multiplexig (OFDM) system very comparable to the Asymmetrical Digital Subscriber Loop (ADSL) Discrete Multi-Toe (DMT) modems sedig differet subcarriers i parallel usig the Iverse Fast Fourier Trasform (IFFT) ad receivig those subcarriers utilizig the Fast Fourier Trasform (FFT). I the IEEE a (8) 9

3 stadard, the trasmissio medium is wireless, ad the operatig frequecy bad is 5 GHz [10-11]. The IEEE a stadard system utilizes 52 subcarriers that are modulated usig biary or quadrature phase-shift keyig (BPSK/QPSK), 16 Quadrature Amplitude Modulatio (QAM), or 64 QAM. The pilot toes are used at the receiver to estimate ay residual phase error. Forward Error Correctio (FEC) codig (covolutioal codig) is used with a codig rate of 1/2, 2/3, or 3/4. The wavelet based OFDM modulator ad demodulator used is show i Figure 2, the overall system of OFDM is the same as i Figure 1; the oly differece is i the OFDM modulator ad demodulator. The processes of the S/P coverter, the sigal demapper ad the isertio of traiig sequece are the same as i the system of FFTOFDM. Also, the zeros will be added as i the FFT-OFDM model. After that the iverse discrete wavelet trasform (IDWT) will be applied to the sigal. The mai ad importat differece betwee FFT based OFDM ad DWT based OFDM is that the wavelet based OFDM will ot add a cyclic prefix to OFDM symbol. Therefore, the data rates i wavelet based OFDM ca surpass those of the FFT implemetatio. After that, the P/S coverter will covert the OFDM symbol to its serial versio ad will be set through the chael. At the receiver, the S/P coverts the OFDM symbol to parallel versio. Also, the zero pads will be removed, ad the other operatios of the chael estimatio, chael compesatio, sigal demapper ad P/S will be performed i a similar maer to that of the FFT based OFDM. Fig. 2. WT-OFDM modem System IFFT ad the FFT i the covetioal system are replaced by the discrete wavelet Trasform Wavelet Trasform (DW) ad the methods of the S/P coverter, the sigal demapper ad the isertio of traiig sequece are the same as i the OFDM system based FFT. Also, the zeros will be added as i the OFDM model based FFT. After that, the DWT will be applied to the sigal. The mai ad sigificat differece betwee OFDM based FFT ad the OFDM-based DWT is that the OFDM model based wavelet trasforms will ot add a cyclic prefix to the OFDM symbols. Therefore, the data rates i this system ca surpass those of the FFT implemetatio model. After that the P/S coverter will covert the OFDM symbol to its serial versio ad the sigals (data ad traiig) will be set through the chael to the receiver. At the receiver, the S/P coverts the OFDM symbol to the parallel versio, the, the DW will be applied to the received symbols. Also, the zero pads will be removed, ad the other operatios of the chael estimatio, chael compesatio, sigal demapper ad P/S will be performed i a similar maer to that of the OFDM-based FFT. The wavelet trasform divides the sigal ito the approximatio coefficiets ad detail coefficiets as show above. I a DWT based system, the wavelet trasform blocks, iverse discrete wavelet trasform (IDWT) ad discrete wavelet trasform (DWT) replace the IFFT ad FFT of FFT-OFDM system i modulatio ad demodulatio processes [12]. Oe of the advatages of applyig wavelet trasform is that due to the overlappig type of wavelet properties, the wavelet based OFDM does ot eed the cyclic prefix to deal with delay spreads of the chael. As a result, it has higher spectral cotaimet tha that of Fourier-based OFDM [13]. The iput iformatio is processed as per FFT-OFDM. However, the variatio is that the system does ot require CP to be added to the OFDM symbol. The output of the iverse discrete wavelet trasform (IDWT) ca be represeted as [14]: d(k) where m0 0 S m m / 2 m D 2 (2 ) (9) m k are the wavelet coefficiets ad (t) is the wavelet fuctio with compressed factor m times ad shifted times for each subscriber (umber k, 0 k N 1). The wavelet coefficiets are the represetatio of sigals i scale ad positio or time. X m at the receiver side, the process is iversed. The output of DWT is D N 1 m / 2 m m ( k)2 (2k ) k d (10) Multiresolutio aalysis of wavelet theory allows to represet wavelets ad scalig fuctios by great ad low pass filters (HPF ad LPF) sequetially with impulse resposes h[m] ad g[m]. Therefore, the wavelet trasform ca be easily implemeted usig discrete time filters. The OFDM performed by usig IFFT s ad FFT s have some difficulties. The OFDM suffers from

4 ISI (itersymbol iterferece) This is frequetly take care of by usig a addig a cyclic prefix larger tha the chael legth but this may ot always be possible. This process occurs due to loss of orthogoality due to chael effects. Time ad Frequecy Sychroizatio [15]. The OFDM eeds time ad frequecy sychroizatio to get a low bit error rate. Carrier Frequecy Offset- The offset betwee the carrier frequecy ad the frequecy of the local oscillator also creates a sigificat bit error rate. Due to these problems we wat to look at aother sort of modulatio to geerate the carrier. Oe of these is the wavelet trasform. Several authors suggest the wavelet trasform; it has a higher degree of side lobe suppressio ad the loss of orthogoality lead to lesser ISI ad ICI. I Wavelet OFDM, the FFT ad IFFT are replaced by DWT ad IDWT sequetially. For the Wavelet trasform, we observe that from the time-frequecy plot that the first Wavelet trasform gives mior flexibility tha the wavelet packet trasform. For the wavelet packet trasform, we ca costruct a algorithm to do the decompositio such that the effect due to the oise [16]. The above fig dispeses the case; the dark lies represet the oise. The top-left corer provides the usual wavelet decompositio. The bottom-left presets a carrier with o decompositio. The top-right shows a symmetrical tree structure while the bottom-right shows the select subcarrier decompositio. A subcarrier compares to a rectagle i the time-frequecy timig. Thus, if the maximum resolutio is defied, we ca have the same umber of subcarrier regardless of the tree structure. Paste Special Picture (with float over text uchecked). II. DISCUSSION AND PROBLEM FORMULATION There are differet applicatios of DWT. It has a wide applicatio i Digital Sigal Processig (DSP), Image Processig ad Idetificatio techiques. It ca be cosidered as a powerful tool for various aalyzes with may advatages as metioed before. I aalysis part, we will itroduce a simulatio pla ad theoretical aalyzes to show the IEEE a WLAN performace due to AWGN ad multipath effects. I simulatio part, a simulatio Matlab programs will be simulated ad preseted to show the performace of FFT- OFDM ad DWT-OFDM o IEEE a WLAN. The system model for FFT-based OFDM will ot be discussed i detail as it is well kow i the literature. Thus, we merely preset a brief descriptio of it. The data d k is first beig processed by a costellatio mappig. M- ary QAM modulator is utilized for this work to map the raw biary data to appropriate QAM symbols. These symbols are the iputted ito the IFFT block. This icludes takig N parallel streams of QAM symbols (N beig the umber of sub-carriers used i the trasmissio of the data) ad performig a IFFT operatio o this parallel stream [17]. A. DWT-OFDM IEEE a WLAN System: I DFT-based OFDM, a CP is combied to elimiate ISI. However, this ca miimize badwidth efficiecy greatly. Discrete alterative programs for replacig ID spectral cotaimet of the chaels is better sice it do DWT-based OFDM a advatage of badwidth efficiecy. The overall system of OFDM based discrete wavelet trasforms that will use i the simulatio is the same as FFT-OFDM. The IFFT ad the FFT i the covetioal system are replaced by the IDWT ad the DWT blocks. The processes of the S/P coverter, the sigal demapper ad the isertio of traiig sequece are the equivalet as i the OFDM system based FFT [18]. Also, the zeros will be added as i the OFDM model based FFT. After that, the IDWT will be applied to the sigal. The mai ad importat differece betwee OFDM based FFT ad the OFDM-based DWT or is that the OFDM model based wavelet trasform will ot add a cyclic prefix to the OFDM symbols. Therefore, the data rates i this system ca surpass those of the FFT implemetatio model. After that the P/S coverter will covert the OFDM symbol to its serial versio ad the sigals (data ad traiig) will be set through the chael to the receiver. At the receiver, the S/P coverts the OFDM symbol to the parallel versio, the, the DWT will be applied to the received symbols. Also, the zero pads will be removed, ad the other operatios of the chael estimatio, chael compesatio, sigal demapper ad P/S will be performed i a comparable maer to that of the OFDM-based FFT [18-20]. The traiig sequece will be used to estimate the chael frequecy respose [21]. The block diagram of OFDM system based o DWT is show i Figure 3 11

5 Fig. 3. The block diagram of OFDM system based o DWT B. Discussio: The simulatio process cotais two mai approaches: The first approach based o BER performace aalysis betwee FFT-OFDM ad DWT-OFDM depedig o three mai sources of disturbaces or distortio: AWGN, multipath effects ad delay spread. The secod simulatio approach cocetrated o the use of differet wavelet fuctios ad showed the effect of their implemetatio o the BER performace of DWT-OFDM system employed i IEEE a There several wavelet families: Daubechies, Haar Coiflets, Symlets. For a orthogoal wavelet, i the multiresolutio structure, we start with the scalig fuctio ϕ ad the wavelet fuctio ψ. Oe of the direct relatios is the twi-scale relatio [22]: 1 x ( x ) (11) 2 2 Z All the filters utilized i DWT ad IDWT are itimately related to the sequece. Clearly if ϕ is compactly istalled, the sequece (i) is fiite ad ca be viewed as a FIR filter. The scalig filter W is a low-pass. From filter W, we determie four FIR filters, of legth 2N ad orm 1, orgaized as follows: decompositio low-pass, decompositio high-pass, recostructio low-pass ad recostructio high-pass [22]. For FFT-OFDM Before ay receiver algorithms ca be employed, the timig must first be improved; that is, the system clock at the receiver must match sychroized with the trasmitter s clock, while takig ito accout the propagatio delay of the chael. Sice OFDM is a frequecy domai modulatio techique, it is required to have accurate estimates of the frequecy offset, produced by oscillator istability, at the receiver. The accuracy of the chael estimatio algorithm is also crucial to the overall system s performace. The phase correctio algorithm uses the pilot subcarriers to correct the rotatio of the OFDM symbols. This rotatio was itroduced by the residual frequecy offset of the carriers. The equalizatio is a ecessary step to recover the distorted sigal, due to multipath fadig. The the sigal is demodulated usig a soft decisio demodulator, that is, the demodulated bits retai additioal iformatio about the reliability of the decisio. To iclude this extra iformatio, the soft bits have various values: a large absolute value of the iitial bit ad a small value for the secod bit. I our simulatio, the sig of the soft coclusio idicates a 0 or 1 bit. The absolute value of each soft choice is the distace to the decisio boudary. This additioal iformatio ca sigificatly improve the performace of chael codig schemes. C. Performace of FFT-OFDM ad DWT-OFDM based IEEE a WLAN System Various trasmissio modes are defied i IEEE a/b/g WLAN stadards. A very few trasmissio modes are cosiderig for IEEE a/b/g i physical layer parameters ad wireless chael characteristics. I this thesis, we evaluated the performace of available trasmissio modes i IEEE a [1]. Nevertheless, the performace aalysis ca be doe straightforward usig the evaluatio of IEEE a. The performace of trasmissio modes is estimated by computig the probability of Bit Error Rate (BER) versus the Sigal Noise Ratio (SNR) followig the ofte used three wireless chael models (AWGN, Rayleigh ad Ricia). We examie the data modulatio ad data rate to ivestigate the performace that is BER vs. SNR. We also examie multipath received sigals. The simulatio results had cofirmed the performace of trasmissio modes uder several chael models ad the umber of ateas. Based o simulatio results, we observed that some trasmissio methods are ot efficiet i IEEE a. The evaluatio of performace verifies the icrease i the coverage area of the physical layer i the a WLAN devices [23].

6 The program cotais two mai parts: Part 1: Simulatio of FFT-OFDM IEEE a WLAN system with specific iput parameters show i table 4. This part cotais four subprograms simulatig the effect of AWGN, multipath effects, Doppler Effect ad delay spread o the BER. I this part, four modulatio techiques used: BPSK, DPSK, 16-QAM ad 64-QAM Part 2: Simulatio of DWT-OFDM IEEE a WLAN with specific parameters ad performace aalysis as simulated for FFT-OFDM. The differece here is the usig of differet Wavelet sigals to study differet results depedig o the sigal used. D. BER performace of FFT-OFDM IEEE a WLAN The BER performace of FFT- OFDM is compared with Discrete DWT Orthogoal Frequecy Divisio Multiplexig system (DWT- OFDM) usig BPSK as a modulatio techique over AWGN ad Multipath Rayleigh Fadig Eviromet. Usig MATLAB simulatio, we ca implemet a OFDM trasmissio. Usig the simulatio we ca easily modify the values of S/N ratio, ad the we ca ivestigate the results of each trasmissio ad see how the BER is chaged. I this paper, OFDM system is implemeted usig MATLAB simulatio, where each block of OFDM is simulated i scripts file. Figure 6 shows the block diagram of the OFDM. DWT-OFDM is obtaied by replacig IFFT at trasmitter ad FFT at the receiver by IDWT ad DWT respectively. We have recogized AWGN ad Multipath Rayleigh Fadig Chaels for comparig BER of FFTbased OFDM ad DWT-based OFDM. The followig OFDM system parameters are examied for the simulatio: E. Performace of FFT-OFDM based WLAN IEEE a Affected by AWGN: I this simulatio we used the Matlab program to simulate the effect of AWGN o the performace of WLAN system usig BPSK, QPSK, 16-QAM, ad 64- QAM. TABLE I SIMULATION OFDM SYSTEM MAIN PARAMETERS Parameters Value IFFT ad FFT Size 64-poit IDWT ad DWT Size 64-poit No. Of data sub carrier 52 Data symbol duratio (Td) 1µs Cyclic prefix duratio (Tcp) 16 Digital Modulatio BPSK, QPSK, 16-QAM ad 64- QAM FEC codes CRC, Covolutioal Covolutioal Code Rate 1/2 Iterleaver Size 35x1 SNR Rage (AWGN) 1-10 db Chaels AWGN, Rayleigh, Ricia OFDM Block size 8 Cyclic Prefix Legth 1 Doppler shift 20 Hz (a) 13

7 BPSK FFT-OFDM system has the best oise immuity compared to other modulatio techiques. As a additioal experimet, differet codes such as Kasami, Beroulli ad Gold codes are used as iput data. Results show i figure 5 shows that the effect is mior. The FFT-OFDM system processes the biary data i series fashio at before S/P. (b) (a) (c) (b) Fig. 5. BER of FFT-OFDM WLAN IEEE a, for various Codes: (a)qpsk (b)dqpsk (d) Fig. 4. BER of FFT-OFDM WLAN IEEE a (a) BPSK, (b) QPSK, (c) 16QAM ad (d) 64QAM Figure 4 shows that that the effect of AWGN o OFDM systems is ot sigificat comparig to the effect of multipath effects ad sychroizatio. Figure 6 shows that

8 F. Performace of FFT-OFDM based WLAN IEEE a Affected by Rayleigh multipath (a) (b) (d) Fig. 6. BER of FFT-OFDM WLAN IEEE a with a Rayleigh Chael a) BPSK, (b) QPSK, (c) QAM16 ad (d) QAM64 To check the performace of the FFT-OFDM WLAN IEEE a System through Rayleigh chael cosiderig the effect of AWGN, a Simulik Matlab program is used as show i figure 6. I this simulatio, it is observed that the BPSK ad QPSK modulatio techiques demostrate better performace i cotrast to others. O the other had, 16QAM ad 64QAM show more stability i chael behavior. I this case, the effect Doppler is take 20 Hz ad symbol duratio equals to 1 s. G. Performace of FFT-OFDM based WLAN IEEE a Affected by Ricia multipath: (C) Fig. 7. Effect of Multipath Ricia Chael o WLAN FFT-OFDM Figure 7 represets the effect of Ricia chael o the FFT-OFDM based WLAN IEEE a. It's clearly show that Jakes effect is less tha Gaussia effect. Next simulatio will cocetrate o the effect of AWGN ad multipath effects o DWT-OFDM based WLAN. 15

9 H. BER performace of DWT-OFDM IEEE a WLAN I Figure 8 the BER of DWT-OFDM performace ad differet spectrums are represeted. Here, BPSK modulatio is used ad Daubechies with order 2. (d) (a) (e) Fig. 8. the BER of DWT-OFDM ad spectrums i differet locatio i DWT-OFDM System (Daubechies with order 2). (b) I Figure 9 the BER of DWT-OFDM performace for BPSK modulatio ad Haar wavelet. Comparig BER i figure 8 (a) figure 9 the BER performace is very close. This result ca be explaied due to the same wavelet family (orthogoal) sigals. (c) Fig. 9. the BER of DWT-OFDM performace for BPSK modulatio ad Haar wavelet

10 III. CONCLUSION I this paper a OFDM IEEE a wireless etwork is ivestigated for Discrete wavelet (DWT) ad Fast Fourier Trasform (FFT) uder the effect of AWGN usig differet modulatio techiques parameters that simulated to study the performace of the proposed system such as BPSK, DPSK, QPSK, DQPSDK QAM16 ad QAM64. Results extracted i simulatio part presets a good privilege for DWT-OFDM pair REFERENCES [1] E. 0. Brigham, R. E. The fast Fourier trasforms, Morrow LTV Electro systems, Ic., IEEE spectrum DECEMBER 1967 [2] Duc Nguye, Discrete Fourier Trasform, Textbook otes o discrete Fourier trasform, Date May 1, [3] M. Rahma, Applicatios of Fourier Trasforms to Geeralized Fuctios, WIT Press, Ja 1, 2011 [4] C.S. Burrus, R.A. Gopiath, H. Guo, (1997) Itroductio to Wavelets ad Wavelet Trasforms, a Primer, Pretice Hall Ic. [5] Neha Pathak, OFDM (Orthogoal Frequecy Divisio Multiplexig) SIMULATION USING MATLAB, Iteratioal Joural of Egieerig Research & Techology (IJERT), Vol. 1 Issue 6, August 2012, ISSN: [6] The Secod IEEE Workshop o Wireless LANS: Summary, Worcester Polytechic Istitute. Available olie: ,March 16. [7] Eria Ferro ad Fracesco Potorti, Bluetooth ad WI-FI Wireless Protocols: A Survey ad Compariso. IEEE Wireless Commuicatio Magazie 2004, page 8 [8] Rob Flickeger (others) 2007; Wireless etworkig i the developig world. Hacker Friedly LLC. 2d editio. pp 4. pp55. [9] Garge, Vigay K. 2007; Wireless Commuicatio ad Networkig, Elsevier Ic. pp 717,181,715, 671, 671, [10] IEEE a, Wireless LAN Medium Access Cotrol (MAC) ad Physical Layer (PHY) specificatios: High-speed Physical Layer i the 5 GHZ Bad, IEEE Std a [11] V.NAVI THEJESH1, Performace Aalysis of IEEE a WLAN Stadard based o various Chaels PUBLICATIONS OF PROBLEMS & APPLICATION IN ENGINEERING RESEARCH PA Vol 04, Issue03; May-Jue [12] Swati Sharma ad Sajeev Kumar, BER Performace Evaluatio of FFT-OFDM ad DWT-OFDM, Iteratioal Joural of Network ad Mobile Techologies, ISSN Electroic Versio VOL 2 / ISSUE 2 / MAY [13] Cooley, James W.; Tukey, Joh W. (1965). "A algorithm for the machie calculatio of complex Fourier series". Math. Comput. 19 (90): doi: /s [14] Krisha Kumar, Garima Saii, Ber Performace Aalysis of Daubechies Wavelet I Dvb-T For Rayleigh Chael, Iteratioal Joural of Egieerig Research & Techology, Vol.1 - Issue 10 (December ) [15] va de Beek, J.-J & others, A time ad frequecy sychroizatio scheme for multiuser OFDM, Selected Areas i Commuicatios, IEEE Joural o, Year: 1999, Volume: 17, Issue: 11. [16] Sourabh Mahaja, Parvee Kumar,Aita Suma, Aalysis of OFDM ad OWDM System with various Wavelets Families, Iteratioal Joural of Egieerig Research ad Geeral Sciece Volume 2, Issue 3, April-May 2014 [17] Khaizura Abdullah ad Zahir M. Hussai, Simulatio of Models ad BER Performaces of DWT-OFDM versus FFT-OFDM, Computer ad Iformatio Sciece» Numerical Aalysis ad Scietific Computig» "Discrete Wavelet Trasforms - Algorithms ad Applicatios"., Chapter 4 [18] Sulaima M.Abbas Mohammed Nadhim Abbas Saifuldee A.Mohammed, SLANTLET TRANSFORM-BASED OFDM SCHEME, Joural of Egieerig, Number 3 Volume 13 September2006. [19] HAITHAM J. TAHA ad M. F. M. Salleh Multi-carrier Trasmissio Techiques for Wireless Commuicatio Systems: A Survey, WSEAS TRANSACTIONS o COMMUNICATIONS, Issue 5, Volume 8, May [20] Dr. Saad N. Abdul Majed, MULTICARRIER CODE DIVISION MULITPLE ACCESS BASED ON WAVELET, [21] Laith Ali Abdul-Rahaim; Hussei A. Lafta, Scramblig based o 2D-Compersed Wavelet Trasform ad permutatio Matrix i Commuicatios Systems, JOURNAL OF TELECOMMUNICATIONS, VOLUME 15, ISSUE 2, AUGUST [22] [23] Savita, BER Estimatio: Mitigatio Methods, Iteratioal Joural of Computer Applicatios ( ), Volume 48 No.25, Jue 2012 Eg. Habab H. Alshammary is a MSc holder i Electrical Commuicatios from Mutah Uiversity- Jorda. Dr. A. Al-Qawasmi. is a associate professor at Majmaah Uiversity- Electrical Egieerig Departmet. He received his Master PhD degrees from Kiev Uiversity of Civil Aviatio Ukraie i He published more tha 25 scietific papers i DSP ad Wireless Commuicatio systems. He was a Director of Computer ceter ( ) ad the head of Commuicatios ad Electroics departmet i Philadelphia Uiversity ( ). 17