Department of Electrical Engineering, COMSATS Institute of Information Technology, Lahore Pakistan

I. INTRODUCTION

IN recent years, the demand for high speed data services has focused the attention of researchers towards broadband communication.Orthogonal frequency division multiplexing(OFDM) is one of the multi-carrier modulation (MCM) techniques which is popular because of its robustness against multipath fading, low complexity and flexibility for multiple input and multiple output (MIMO)communications [1]. OFDM has been standardized in wireless communication as IEEE 802.11, HiperLAN/2 and in wired communication as ADSL, ADSL2+ [2, 3]. In OFDM,available bandwidth is divided into orthogonal subcarriers whereas in orthogonal frequency division multiple access (OFDMA) which is a multiple access technique, these subcarriers are distributed among different users. Though,OFDMA is an attractive technology to circumvent inter-symbol interference (ISI) however these systems are also very sensitive to high PAPR and carrier frequency offsets (CFO) [4,5]. OFDM employs rectangular waveform as a pulse shaping filter whose Fourier transform is a sinc function [6]. Therefore, OFDM system does not provide better spectral shaping to its sub-carriers due to its poor frequency localization and thus, makes it vulnerable to CFO [7].On the other hand, high PAPR leads to the requirement of expensive high power amplifier(HPA) with stringent linear range. Expensive HPA are practical for base stations but it would lead to expensive handsets. Therefore, to resolve the problem of high PAPR for uplink transmission, a new multiple access scheme“single carrier frequency division multiple access” (SCFDMA) was proposed. SCFDMA has been standardized in release 8 of 3rd Generation Partnership Project (3GPP) for Long term evolution (LTE) in which OFDMA is employed for downlink transmission, while SCFDMA is adopted for uplink transmission[8].

In this research work, a new transceiver design for SCFDMA based systems by replacing the conventional FFT with DWT is proposed.

SCFDMA systems, like OFDMA systems are also based on FFT for data modulation.However, the side-lobes in FFT based MCM systems is just 13 dB lower which makes it sensitive to adjacent channel interference and results in high out of band (OOB) radiations[9]. In addition to this, FFT based systems are considered spectrally inefficient due to the inclusion of cyclic prefix (CP). For OFDMA systems, extensive research proposes alternative solutions for these problems. One of the potential candidates to solve these issues in OFDMA system is to opt for discrete wavelet transform (DWT). DWT is implemented through filter banks with such tight filters that lower the side lobes up to 35 dB [10]. Implementation of OFDMA with DWT not only includes the advantages of FFT-OFDM but also provides additional benefits in the form of low PAPR, high spectral efficiency due to non-utilization of CP and strong resistance to CFO [10]. Wavelet OFDM (WOFDM) has been standardized as a modulation technique in IEEE P1901 for power line communication[10]. Inspite of different advantages of DWT for OFDMA, very few works are available which suggest application of DWT for SCFDMA systems [11]. Replacement of FFT with DWT for SCFDMA can bring different advantages in the same way as it brings for OFDMA systems in the form of low PAPR and OOB radiations along with higher spectral efficiency due to lack of CP. Therefore, this paper focuses on the utilization of DWT on SCFDMA systems that aims to improve the achievable BER and PAPR in comparison to OFDMA.

A large number of PAPR reduction techniques have been proposed for OFDM systems[12-15], including precoding based techniques,which are quite effective [16]. The basic idea of linear precoding (LP) is to spread information by using unitary transforms and improves the PAPR performance of the system. Since,SCFDMA is an uplink technique, so it is highly preferable to lower down the PAPR as much as possible. To reduce PAPR value in SCFDMA systems, different techniques have been proposed in the past [17-20], however;no work is available related to application of LP on DWT based SCFDMA for PAPR reduction, spectral efficiency (SE) improvement and bit error rate (BER) performance gain.

In this article, a new transceiver design is proposed for SCFDMA systems based on DWT for data modulation. To further enhance the performance of the proposed system,Walsh Hadamard transform (WHT) is also applied as a unitary transform for linear precoding to suppress the high PAPR values, to improve the SE of the proposed system and to improve the BER performance of the system.

This research work discusses the conventional FFT based SCFDMA system model in Section II. Section III and IV present the concept of DWT and WHT for linear precoding respectively. Section V describes the proposed DWT based transceiver structure for SCFDMA. Performance comparison of conventional FFT and WT based OFDMA and SCFDMA systems with precoded FFT and WT based OFDMA and SCFDMA systems is discussed in Section VI, while this article is concluded in Section VII.

II. CONVENTIONAL FFT BASED SCFDMA SYSTEM MODEL

Functional block diagram of conventional SCFDMA system is shown in Fig. 1. Processing of SCFDMA is similar to OFDMA with the additional blocks of FFT and subcarrier mapping at the transmitter side and IFFT and sub-carrier de-mapping at the receiver side.At the transmitter side, serial bit stream is converted into complex symbols by using one of the different conventional constellation mapping methods. These modulated complex symbols are now grouped into blocks with each block containingNsymbols.Npoint FFT is applied on these blocks to convert the time domain signal into frequency domain. The signal after the FFT processing is expressed as[11],

whereNis the FFT size andrepresents the time domain symbols. Then, theNsub-carriers are mapped by using any of the sub-carrier mapping methods details of which are given in Section V. After sub-carrier mapping,Mpoint inverse FFT (IFFT) is applied such thatto transform the sub-carrier amplitudes into time domain signal. The reason behindselection is that due to zero padding during sub-carrier mapping, the overall length of the frequency domain signal increases up toM. Therefore, amongMsub-carriers, onlyNsub-carriers are occupied by input data. Thus,the IFFT of the resultant zero padded signal is given as [11],

where,Mis the IFFT size.represents the frequency domain signal andshows the time domain symbols after IFFT. CP is appended at the resultant signal to mitigate the effects of multipath fading. The transmitted signal is then passed through the baseband communication channel. In this research work, we are considering block fading channel where the response of the channel remains constant over one block duration.

Since SCFDMA is an uplink MCM technique, hence the PAPR needs to be reduced to its lowest values. PAPR of the transmitted signalis defined as follows [22],

III. DISCRETE WAVELET TRANSFORM

Signals can be represented using two common transformation techniques, temporal or spectral representation. Time localization, in addition to the spectral components is signifi-cant in signal processing applications. In some applications, it is necessary to get the time localization along with the spectral components[23]. Wavelet transform (WT) gives both the time and frequency representation of signal at a given time.

DWT of any discrete signal is calculated by decomposing the signal into low frequency components and high frequency components providing approximate and detailed information about the signal respectively. Filter banks are employed to acquire the low and high frequency components of a signal in WT.Decomposition of signal into low pass filter(LPF) and high pass filter (HPF) components is named sub band coding [24]. When signal is passed through LPF, high frequency components above a certain band are blocked while HPF removes all frequencies that are below a certain band. When signal components are reduced, it directly affects the resolution of signal. Decomposition of signal with LPF and HPF can be expressed as given in (6) and (7)[25],

IV. WALSH HADAMARD TRANSFORM FOR LINEAR PRECODING

In literature, different techniques have been proposed for PAPR reduction of OFDM signal. These techniques can be divided into two categories: techniques with distortion and techniques without distortion [26]. Each technique has its own pros and cons where researchers achieve PAPR reduction gain at the expense of any other parameter in terms of transmission power or capacity etc [26].

The main idea of LP is to minimize PAPR value, by scrambling information symbols into system. This spreading breaks the autocorrelation between OFDM symbols which in return reduces the PAPR value. Different unitary or trigonometric transforms are used for this purpose. However, WHT as a simplest LP technique is proposed to reduce high PAPR value[27]. The simplicity of WHT lies in its kernel which takes only binary values. The Hadamard matrixis given as [28]

Fig. 2 Decomposition of signal using DWT

Signal after constellation mapping is multiplied with the kernel of the WHT and the input vectoris transformed into a new vectorexpressed as,

Multiplication of precoding matrix with the incoming signal spreads the information and reduces the autocorrelation of the signal which is the sole reason of high PAPR reduction gain. Thus, in this article, WHT is applied to reduce the PAPR of the FFT based SCFDMA systems and WT based SCFDMA systems.

V. PROPOSED TRANSCEIVER STRUCTURE FOR SCFDMA SYSTEM

The proposed transceiver structure is shown in Fig. 3. Our proposed system consists of DWT and inverse DWT (IDWT) for SCFDMA modulation. SCFDMA systems utilize two methods for subcarrier distribution among users. These two methods are: interleaved frequency division multiple access (IFDMA)and localized frequency division multiple access (LFDMA), shown in Fig 4. LFDMA allocates input data on consecutive sub-carriers whereas, in IFDMA input data are placed on entire subcarriers with zeros placed in unused subcarriers state. LFDMA incurs high PAPR as compared to IFDMA [29]. Therefore, in our proposed system, we have considered LFDMA for sub-carrier mapping to counter its inherent high PAPR problem.

However, before WT based SCFDMA modulator, linear precoder is applied in the form of WHT. Though different PAPR reduction techniques such as clipping, selective mapping(SLM), partial transmit sequence (PTS), tone reservation (TR) and tone injection (TI) are already available in the literature, however, they have their own pros and cons. Clipping results in the BER degradation whereas SLM and PTS have high implementation complexity [26].TR/TI has high complexity with bandwidth expansion because of the reserved sub-carriers for PAPR reduction [26]. Therefore, the selection of any PAPR reduction technique is the tradeoff between data rate loss, BER performance and complexity of implementation.The main motivation behind application of precoding technique in the form of WHT is the virtue of different characteristics associated with it. It does not require any bandwidth expansion [30]. Data rate is not lost because there is no transmission of side information and at the same time BER performance is also improved because of the additional benefit of diversity against frequency selective channels[30]. WHT also helps to boost the equalization gain of the transceiver by spreading the information into all sub-carriers [31]. Various transforms can be used as precoding matrix, it has been shown that WHT-based OFDM systems achieve satisfactory performance with simplicity in frequency selective channels by devising fast algorithms [27]. Moreover, WHT-OFDM systems also show better PAPR performance[32]. Other than this, WHT is also considered as the simplest precoding technique because the coefficients of Hadamard matrix are all composed of +1 and -1. This simplicity is very beneficial for uplink scenarios where battery of the user equipment is limited and we can’t afford PAPR reduction techniques with high complexity. Therefore, WHT is an appropriate option with low complexity and better performance for uplink by keeping in mind the limited battery life. Thus, it is believed that this research is the first work, which investigates the application of WHT for DWT based SCFDMA system.

Fig. 3 Proposed transceiver structure for Precoded WT based SCFDMA

We can summarize all steps of the transceiver processing in the following manner:First the serial data bits are mapped to complex symbolswheremis the total number of symbols. These complex symbols are subject to WHT for information spreading, generatingexpressed as,

To better understand this concept, let’s assume thatThe result of the WHT for this specific case is given as,

Fig. 4 Subcarriers mapping for IFDMA and LFDMA

The transformed signal is now passed to the WT based SCFDMA. Within SCFDMA modulation, DWT is employed using filter banks.DWT is implemented using 2-channel filter banks through a hierarchical algorithm known as the pyramidal algorithm [33]. The 2-channel filter bank splits the input signal into two parts by passing it through LPF, ‘h’ and HPF,‘g’. The forward discrete wavelet transform of a discrete signal requires scaling functionsand wavelet functionsfor its representation, whereandare the scaling and shift parameters whose values are adjusted as integer values [33]. Low values ofprovides coarse representation while higher values ofgives finer details.

Scaling function is associated withwhereas, wavelet function is associated withThe coefficients ofandare also termed as scaling filter coefficientsand wavelet filter coefficientsrespectively.Therefore, for our system scaling and wavelet transform coefficients forare given as[33, 34],

Fig. 5a Side lobes representation of different filter bank structures

Fig. 5b Filter bank subcarriers for OFDM-OQAM with variable levels of overlapping K

Application of WT in the proposed transceiver not only increases the spectral efficiency but also lowers the side lobes as shown in the Fig. 5a which shows the side lobe representation of different structures. Perfect reconstruction wavelet transform employs filter bank structure referred in literature, as cosine modulated filter banks (CMFB), paraunitary filter banks, biorthogonal filter banks, exponentially modulated filter banks. These filter banks exhibit much lower side lobe attenuation compared to discrete Fourier transform(DFT) filter banks. As shown in Fig. 5a, the DFT filter bank show higher amplitude side lobes, just 13 dB below the main lobe, thereby resulting in higher inter-carrier interference(ICI), whereas the CMFBs give a side lobe 38 dB below the main lobe [35]. Higher side lobe attenuation in these filter banks is attributed towards reduced interference scenario in communication systems [36]. Researchers have proposed an algorithm with reduced number of unknown variables for thenon-convex problem of prototype filter optimization, thereby giving lower value of stop band attenuation[37]. Fig 5b shows the response of subcarrier filter bank in orthogonal frequency division multiplexing-offset quadrature amplitude modulation (OFDM-OQAM) system for arbitrary variable levels of overlapping. It is seen that as the value ofKincreases from 1 to 4,the side lobe attenuation increases from 21.5 dB to 40 dB. In CMFBs,Mchannel banks are produced by shifting prototype filterwhile the biorthogonal filter banks are implemented using discrete time wavelet functions,resulting in perfect reconstruction of the transmitted signal through the synthesis-analysis filter bank structure, also known as the transmultiplexer. In paraunitary case, the synthesis filter bank is generated by time reversing the analysis filter bank and vice versa. However,in the exponentially-modulated filter banks,the transmit data consists of only the real part,while the imaginary part is not considered[38].

VI. SIMULATIONS AND DISCUSSIONS

In this section, performance of the proposed transceiver structure for WT based SCFDMA utilizing WHT is compared with the conventional SCFDMA system. Conventional and WT based OFDMA system is also simulated as a reference system. MATLAB is used to carry the simulations in Rayleigh fading channel. Performance of both transceivers is analyzed in terms of PAPR reduction, spectral efficiency and bit error rate. The simulation parameters are listed in Table I.

6.1 Analysis of PAPR reduction

Transmitted signal in the system is considered as a random variable so complementary cumulative distribution function (CCDF) is used to describe the statistical properties of the PAPR.CCDF of PAPR is defined as the probability of a function having a value greater than the threshold value [22]

Fig. 6 shows the CCDF comparison of conventional FFT and WT based MCM systems with precoded FFT and WT based MCM systems. In first analysis, FFT based OFDMA and SCFDMA with WT based OFDMA and SCFDMA systems are compared. At CCDF of 10-3, PAPR value for FFT based OFDMA is 11 dB while for SCFDMA system, PAPR value is 9dB. Thus, as compared to FFT based OFDMA, FFT based SCFDMA achieves PAPR reduction gain of 2 dB. Similarly, at CCDF value of 10-3WT based OFDMA system has PAPR value of 5.2 dB whereas for WT based SCFDMA system, PAPR value is 2.5 dB. Thus, in case of WT based, the system achieves a gain of 2.7 dB. On comparing the FFT based OFDMA with WT based OFDMA,PAPR reduction gain is 5.8 dB. Similarly,PAPR reduction gain for WT based SCFDMA is 6.5 dB as compared to FFT based SCFDMA. The better performance of WT based SC FDMA is attributed to the joint processing of WT and single carrier communication.

Moreover, the performance of FFT based WHT-OFDMA and FFT based WHT-SCFDMA can be compared with the conventional OFDMA and conventional SCFDMA. At CCDF of 10-3, PAPR value for conventional FFT based OFDMA and precoded FFT basedWHT-OFDMA is 11 dB and 9.6 dB respectively. It implies that the precoded OFDMA system has PAPR reduction gain of 1.4 dB.Similarly, for SCFDMA system, conventional system has PAPR value of 8.8 dB while precoded SCFDMA system has PAPR value of 8 dB. So, the achievable PAPR reduction gain is 0.8 dB. It clearly shows that the precoded systems are performing better than the conventional systems. It is mainly due to the spreading introduced in system due to WHT.

Table I Simulation Parameters

Fig. 6 CCDF comparison of FFT and WT based MCM systems with precoded FFT and precoded WT based MCM systems

CCDF comparison of conventional WT based OFDMA and SCFDMA with precoded WT based OFDMA and SCFDMA is also shown in Fig. 6. Probability that the PAPR value is greater than the threshold value of 10-3in conventional WT based OFDMA system and precoded WT based OFDMA system is 5.5 dB and 3.5 dB respectively. So, the achievable gain is 2 dB. In the same manner,in conventional WT based SCFDMA and in precoded WT based WHT-SCFDMA system,probability that the PAPR value is greater than the threshold value of 10-3is 2.25 dB and 1.75 dB respectively, which shows a gain of 0.5 dB.Thus, application of linear precoding matrix in MCM system increases the PAPR performance of the system without addition of any side information due to increase in transmission diversity which is a result of WHT processing before SCFDMA modulation. These results are supported by various previous findings in the literature, wherein WHT is used to reduce the PAPR of the system [39-41].

6.2 Improvement in spectral efficiency

The other performance metric which is considered is spectral efficiency. Capacity or spectral efficiency of OFDMA system in presence of AWGN and HPA distortion is given by [41],

LSCFDMArepresents the link loss in SCFDMA as compared to OFDMA. It occurs at high signal to noise distortion ratio (SNDR) due to frequency domain equalization. However, this loss can be recovered in presence of advanced receivers. Therefore, in this article for the sake of clarity and for fair comparison, we have assumedLSCFDMA=0 in the presence of advanced receiver so that the effect of HPA distortion can be specifically analyzed. If we considerLSCFDMA=0, (19) and (20) are same. However,SCFDMA is more resistant against distortion caused by HPA which leads to loweras compared to OFDMA. Thus, the achievable data rates in SCFDMA will be high as compared to OFDMA whereseverely disturbs the performance of the system. In case of WT based system, where CP is not used, the data rate is enhanced further as shown in the Fig. 7.

Fig. 7 gives the performance comparison of FFT based MCM systems and WT based MCM systems with precoded FFT based MCM systems and precoded WT based MCM systems. At SNDR of 20 dB, achieved data rate for FFT based OFDMA, FFT based SCFDMA, WT based OFDMA and WT based SCFDMA is 3.6 bps/Hz, 3.8 bps/Hz, 4.6 bps/Hz and 5.6 bps/Hz respectively. It can be inferred that the FFT based SCFDMA is attaining 0.2 bps/Hz more data rate as compared to FFT based OFDMA system whereas,WT based SCFDMA system is getting 1 bps/Hz more data rate as compared to WT based OFDMA system. Thus, due to presence of SCFDMA transceiver, the achievable data rates are getting higher as compared to OFDMA systems. Therefore, SCFDMA systems have more resistance against interference,noise and distortion and result in improved spectral efficiency.

In another analysis, FFT based conventional OFDMA and conventional SCFDMA systems are compared with FFT based precoded WHT-OFDMA and WHT-SCFDMA systems.At SNDR of 20 dB, data rate achieved by FFT based OFDMA is 3.6 bps/Hz whereas for precoded FFT based WHT-OFDMA system,achievable data rate is 3.8 bps/Hz. It means due to precoding, our system is performing better in presence of AWGN and distortion.Similarly, conventional FFT based SCFDMA is attaining data rate of 3.9 bps/Hz as compared to precoded FFT based WHT-SCFDMA where achievable data rate is 4 bps/Hz. Thus,FFT based precoded system achieves 0.1 bps/Hz improvement in spectral efficiency compared to the conventional FFT based systems.The increment in spectral efficiency is supported by the fact that diversity introduced in the system in the form of linear precoding improves the system performance in terms of spectral efficiency.

Fig. 7 also exhibits the behavior of WT based conventional and WT based precoded systems in terms of spectral efficiency. Conventional WT based OFDMA and SCFDMA systems attain spectral efficiency of 4.5 bps/Hz and 5.7 bps/Hz, whereas precoded WT based WHT-OFDMA and WHT-SCFDMA achieve data rate of 5.1 bps/Hz and 6.1 bps/Hz respectively. Thus, we can deduce that precoded WT based WHT-OFDMA and WHT-SCFDMA attain higher data rate of 0.6 bps/Hz and 0.4 bps/Hz as compared to their counterparts.

Fig. 7 Comparison of achievable data rates by FFT and WT based MCM systems with precoded FFT and precoded WT based MCM systems

Fig. 8 BER comparison of conventional and precoded OFDMA based systems

Fig. 9 BER comparison of conventional and precoded SCFDMA based systems

6.3 BER performance

Another performance metric to compare the overall performance of proposed transceiver with conventional transceivers in presence of AWGN and Rayleigh fading channel is BER.Fig. 8 shows the BER comparison of conventional FFT and WT based OFDMA systems with precoded FFT and WT based OFDMA systems. From the figure, it can be observed that for a BER of 10-3,required for FFT and WT based OFDMA system is 26 dB and 15 dB respectively. Thus, WT-OFDMA has a gain of 11 dB. Similarly, in the presence of WHT,FFT and WT based OFDMA systems requireequal to 16.5 dB and 6 dB which shows supremacy of WT based WHT-OFDMA system over FFT basedWHT-OFDMA with a gain of 10.5 dB.

BER comparison of conventional and precoded SCFDMA based systems can be analyzed in Fig. 9. For a BER of 10-3,values for FFT based SCFDMA and WT based SCFDMA based systems are 21 dB and 16 dB respectively, which gives a performance gain of 5 dB. For another analysis, BER comparison of precoded FFT based SCFDMA and our proposed transceiver i.e. precoded WT based SCFDMA are also shown in Fig. 9. FFT based WHT-SCFDMA achivesequal to 9 dB for a BER of 10-3while WT based WHT-SCFDMA acheivesequal to 5.5 dB. It shows 3.5 dB gain of our proposed system model as compared to the coventional FFT based architecture. High performance gains in the presence of WHT and WT is evident from the different works available in the literature [43, 44]. This advantage is due to the inherent property of constellation diversity in the system.

VII. CONCLUSION

In this research work, a new transceiver design for SCFDMA based systems by replacing the conventional FFT with DWT is proposed.Moreover, the application of WHT as a linear precoded technique to overcome the PAPR problem and to improve the spectral efficiency is also suggested. Precoded transceiver structure based on both FFT and DWT is simulated for OFDMA and SCFDMA systems. Perfor-mance of simulated systems is evaluated in terms of PAPR reduction, spectral efficiency and bit error rate. Results have shown the supremacy of our proposed precoded WT based structure on the conventional way of transmission. As a future work, authors are interested to apply the same concept for non-orthogonal multiple access systems.

[1] Y. Saito, Y. Kishiyama, A. Benjebbour, T. Nakamura, A. Li and K. Higuchi, “Non-orthogonal multiple access (NOMA) for cellular future radio access,”IEEE 77th Vehicular Technology Conference(VTC),pp. 1-5, 2013.

[2] T. Nawaz, A. Khan and S. Baig, “Evolution of Orthogonal Frequency Division Multiplexing Modulation to Discrete Wavelet Multitone”,International Conference on Frontiers of Information Technology (FIT), pp. 63-68, 2011.

[3] H.A. Latchman, S. Katar, L. Yonge and S. Gavette,Homeplug AV and IEEE 1901: A Handbook for PLC Designers and Users, John Wiley & Sons,2013.

[4] D. Falconer, S.L. Ariyavisitakul, A. Benyamin-Seeyar and B. Edison, “Frequency domain equalization for single-carrier broadband wireless systems,”IEEE Communication Magazine, vol.40, pp.58-66,2002

[5] F. Adachi, D. Garge, S. Takaoka and K. Takeda,“ Broadband CDMA techniques,”IEEE Wireless Communication, vol. 12, no. 2, pp.8-18,2005

[6] B.F. Boroujeny, “OFDM versus filter bank multicarrier,”IEEE Signal Processing Magazine, vol. 28,no.3, pp.92-112, 2011

[7] N. Debbabi, M. Siala and H. Boujemaa, “Optimization of the OFDM prototype waveform for highly time and frequency dispersive channels through a maximization of the SIR,” 12th IEEE International Conference on Electronics, Circuits and Systems, pp. 1-4, 2005

[8] J. Zyren and W. McCoy, Overview of the 3GPP long term evolution physical layer, Freescale Semiconductor, Inc., white paper, 2007.

[9] D. Karamehmedovic, M.K. Lakshmanan and H.Nikookar, “Optimal Wavelet Design for Multicarrier Modulation with Time Synchronization Error,”IEEE Conference on Global Telecommunication (GLOBECOM), pp. 1-6,2009.

[10] A. Khan, S. Baig and T. Nawaz, “DWMT transceiver equalization using overlap FDE for downlink ADSL,”Turkish Journal of Electrical Engineering & Computer Sciences, vol. 23, no. 3,pp. 681-697,2015

[11] F. Al-Kamali, M. Dessouky, B.M. Sallam, F. Shawki and F.A. El-Samie, “Transceiver scheme for single-carrier frequency division multiple access implementing the wavelet transform and peak-to-average-power ratio reduction methods,”IET Communications, vol. 4, no.1,pp. 69-79, 2010

[12] M. Bisht and A. Joshi, “Various Techniques to Reduce PAPR in OFDM Systems: A Survey,”International Journal of Signal Processing, Image Processing and Pattern Recognition, vol. 8, no.11, pp. 195-206, 2015

[13] T. Jiang and G. Zhu, “Complement block coding for reduction in peak-to-average power ratio of OFDM signals,”IEEE Communications Magazine,vol. 43, no. 9, pp. S17-S22, 2005

[14] S. Shu, D. Qu, L. Li and T. Jiang,” Invertible Subset QC-LDPC Codes for PAPR Reduction of OFDM Signals,”IEEE Transactions on Broadcasting, vol. 61, no. 2, pp. 290-298, 2015

[15] T. Jiang, C. Ni, C. Ye, Y. Wu and K. Luo, “A Novel Multi-Block Tone Reservation Scheme for PAPR Reduction in OQAM-OFDM Systems,”IEEE Transactions on Broadcasting, vol. 61, no. 4, pp.717-722, 2015.

[16] I. Baig and V. Jeoti, “ A Zadoff Chu Matrix Transform Precoding based Localized-OFDMA Uplink System: A PAPR Analysis with RRC Pulse Shaping,”Acta Electrotechnica et Informatica, vol. 11,no. 2, pp. 64-69, 2011

[17] Y. Xia and J. Ji, “ Reducing PAPR of SC-FDMA Signals through Simple Amplitude Predistortion,”ETRI Journal, vol. 37, no. 5, pp. 922-928,2015

[18] C. A. Azurdia-Meza, K. Lee and K. Lee, “PAPR Reduction in SC-FDMA by Pulse Shaping Using Parametric Linear Combination Pulses,”IEEE Communication Letters, vol. 16, no. 12, pp.2008-2011, 2012

[19] P. Yen, H. Minn and C. C. Chong, “PAPR reduction for bandwidth-aggregated OFDM and SC-FDMA systems,”IEEE Wireless Communications and Networking Conference, pp. 1363-1368, 2011

[20] P. Yen and H. Minn, “Low complexity PAPR reduction methods for carrier-aggregated MIMO OFDMA and SC-FDMA systems,”EURASIP Journal on Wireless Communications and Networking, vol. 2012, no. 179, pp. 1-13, 2012

[21] H.G. Myung, “Introduction to single carrier FDMA,”IEEE 15th European Signal Processing Conference, pp. 2144-2148, 2007.

[22] T. Jiang, C. Li and C. Ni, “Effect of PAPR reduction on spectrum and energy efficiencies in OFDM systems with class-A HPA over AWGN channel,”IEEE Transactions on Broadcasting, vol.59, no. 3,pp. 513-519, 2013

[23] N. J. Fliege,Multirate Digital Signal Processing,John Wiley and Sons, England, (1994).

[24] S.M. Kuo, B.H. Lee and W. Tian,Real-Time Digital Signal Processing: Fundamentals, Implementations and Applications, Wiley, 2013

[25] M. K. Lakshmanan, H. Nikookar, “A review of wavelets for digital wireless communication”,Wireless Personal Communications, vol. 37, no.3-4, pp. 387-420, 2006.

[26] .T. Jiang and Y. Wu, “An Overview: Peak-to-Average Power Ratio Reduction Techniques for OFDM Signals,”IEEE Transactions on Broadcasting, vol. 54, no. 2, pp. 257-268, 2008

[27] X. Ouyang, J. Jin, G. Jin and P. Li, “Low Complexity Discrete Hartley Transform Precoded OFDM System over Frequency-Selective Fading Channel,”ETRI Journal, vol. 37, no. 1, pp. 32-42, 2015

[28] T. Lukusa, K. Ouahada, A.R. Ndjiongue, H.C. Ferreira and A.J.H. Vinck, “Experimental Verification of Frequency Mappings with Hadamard Transform for Polwer Line Communications Channel,”18th IEEE International Symposium on Power Line Communications and its Applications, pp.190-195, 2014

[29] Y.S. Cho. J. Kim W.Y. Yang and C.G. Kang,MIMO-OFDM Wireless Communications with MATLAB, Wiley-IEEE Press, 2010

[30] N. Kaur and L. Kansal, “Reducing the Peak to Average Power Ratio of OFDM Signals through Walsh Hadamard Transform,”Global Journal of Researchers in Engineering, vol. 13, no. 1, pp.17-23, 2013

[31] Z. Dlugaszewski, and K. Wesolowski, “WHT/OFDM-an improved OFDM transmission method for selective fading channels,”Symposium on Communications and Vehicular Technology, pp.144-149, 2000.

[32] J. Mountassir, A. Isar and T. Mountassir, “Precoding techniques in OFDM systems for PAPR reduction,”16th IEEE Mediterranean Electrotechnical Conference, pp. 728-731, 2012.

[33] K. Lakshman, “Reconfigurable and Adaptive Wireless Communication Systems based on Wavelet Packet Modulators,” Ph.D. dissertation,EEMCS, Delft University of Technology, 2011.

[34] B.C. Sidney,Introduction to wavelets and wavelet transforms: a primer, Prentice Hall International,1998.

[35] S. Baig and M. J. Mughal, “Multirate signal processing techniques for high-speed communication over power lines,”IEEE Communications Magazine, vol. 47, no. 1, pp. 70-76, 2009

[36] A. Vishwakarma, A. Kumar and G.K. Singh, “Design of near-perfect-reconstructed transmultiplexer using different modulation techniques:A comparative study,”Journal of King Saud University - Engineering Sciences, pp. 1-7, 2016.

[37] D. Chen, D. Qu, T. Jiang and Y. He, “Prototype Filter Optimization to Minimize Stopband Energy With NPR Constraint for Filter Bank Multicarrier Modulation Systems,” inIEEE Transactions on Signal Processing, vol. 61, no. 1, pp. 159-169,Jan.1, 2013.

[38] J. Alhava and M. Renfors, “Exponentially-modulated filter bank transmultiplexer with finecoarse adaptive filtering,” 3rdInternationalSymposium on Communications, Control and Signal Processing, pp. 68-72, 2008

[39] E.V. Cuteanu and D. Isar, “Hybrid PAPR reduction scheme using Walsh Hadamard precoding and signal companding,”10th International Symposium on Electronics and Telecommunications,pp. 195-198, 2012

[40] F. Mangone, J. He, J. Tang, J. Xiao, M. Chen, F. Li and L. Chen, “A PAPR reduction technique using Hadamard transform combined with clipping and filtering based on DCT/IDCT for IM/DD optical OFDM systems,”O(jiān)ptical Fiber Technology,vol. 20, no. 4, pp. 384-390, 2014

[41] Z. Wang, S.Z. Zhang and B. Qiu, “ PAPR Reduction of OFDM Signal by Using Hadamard Transform in Companding Techniques,”IEEE 12th International Conference on Communication Technology, pp. 320-323, 2010

[42] F. Khan,LTE for 4G mobile broadband. Cambridge University Press, 2009

[43] R. F. Chisab, A.H. Ali, S.K. Abdullah, “ A Proposed PAPR and BER Reduction Method For 4G-LTE-SCFDMA Using The Multiwavelet Transform,”European Academic Research, vol. II, no.11, 2015

[44] W. Yan, Z. Lei and S. Sun, “Performance of Walsh-Hadamard Transformed STBC OFDM System,”IEEE 59th Vehicular Technology Conference, pp. 738-741, 2005