Professor Subhas Chandra Mukhopadhyay

Exeley Inc. (New York)

**Subject:** Computational Science & Engineering, Engineering, Electrical & Electronic

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Satwinder Kaur
/
Lavish Kansal
/
Gurjot Singh Gaba
** ^{*}**
/
Fahad Alraddady
/
Sandeep Kumar Arora

**Keywords : **
FBMC,
OFDM,
DST,
DCT,
PAPR

**Citation Information : **
International Journal on Smart Sensing and Intelligent Systems. Volume 13,
Issue 1,
Pages 1-10,
DOI: https://doi.org/10.21307/ijssis-2020-024

**License : **
(BY-NC-ND-4.0)

**Received Date : **16-July-2020
/
**Published Online: ** 04-September-2020

- ARTICLE
- FIGURES & TABLES
- REFERENCES
- EXTRA FILES
- COMMENTS

The filter bank multicarrier (FBMC) system suffers from the non-linear effects that arise due to a high peak-to-average power ratio (PAPR). Diverse precoding techniques are utilized to enhance the efficiency and robustness of FBMC. A high PAPR in the FBMC system can be overcome by a unique combination of precoding and conventional PAPR reduction techniques proposed in this paper. Different precoding schemes, discrete sine transform (DST) and discrete cosine transform (DCT), are combined with different PAPR reduction techniques, such as clipping and companding, to decrease the effects of the elevated PAPR in the FBMC system. The simulation results show a significant reduction in PAPR for both the transforms applied individually as well as in combination with conventional PAPR reduction methodologies. The MATLAB simulation outcome also depicts a substantial reduction in bit error rate (BER) in the range of 5 to 10 dB on the incorporation of DST/DCT precoding transforms in the conventional FBMC system.

Nowadays, orthogonal frequency division multiplexing (OFDM) is used for multicarrier modulation (MCM) in the fourth generation for communication. In OFDM, a cyclic prefix (CP) is used, but due to spectral efficiency decrease and out-of-band radiation problem is also there, so OFDM will not be the best candidate waveform for the fifth generation. The 5G telecommunication system is required to support the elevated data rate of up to 1 Gbps. Figure 1 depicts the basic architecture of 5G (Redana et al., 2019). The uppermost layer is the service-level layer that consists of the service lifecycle management loop, i.e. service assurance, service fulfillment, and service orchestration. It covers all the lifecycle phases such as the decommissioning phase, the runtime phase, the preparation phase, the configuration and activation phase, and the instantiation phase. The other two levels are the network and resource level and the function level.

The FBMC system is preferred over the OFDM system for 5G communications, as they have less out-of-band emission. Also, it is much more efficient than OFDM, as in OFDM, the cyclic prefix is inserted after every time slot, whereas in FBMC, it is inserted after every frame (Viholainen et al., 2009). Most of the 5G applications require high-speed data transmission for long-distance places with adequate signal strength; the presence of the high PAPR affects the signal quality as well as the coverage area. Because of the high PAPR, the distortion would be high, and in order to reduce the high PAPR, we may have to operate the high power amplifiers situated at the transmitter side with a moderate power level. The result of the same leads to a reduction in the coverage area of the system. Hence, we have incorporated new PAPR reduction techniques to reduce the effects of the high PAPR and provide a high-quality signal to the end users located in remote places. Some techniques such as coding, interleaving, companding, and signal distortion are not directly appropriate for FBMC due to the increased overlapping factor of the time-domain symbols. Both clipping and companding have low complexity, and these are less complex procedures for PAPR reduction. In this paper, two PAPR reduction schemes are suggested, i.e. clipping and companding, combined with precoding (DST and DCT) schemes. The organization of the manuscript is as follows: a literature review with respect to the proposed methodology is presented in the second section. The third section presents a brief idea about the transmitter and receiver section of the FBMC systems. PAPR and its reduction techniques are presented in the fourth section, which is followed by the fifth section depicting the simulation outcome for the suggested methodology. The sixth section exhibits the concluding remarks.

Kim et al. (2017) designed a novel waveform for the QAM-FBMC system. In the filter bank terminology, the filter bank that is related to the zero frequency carriers is termed as the prototype filter, and the other filters are realized from this first filter by frequency shifts. FBMC is a multicarrier technique, similar to OFDM, and can manage the scenarios where users are not synchronized. In CP-OFDM, the frequency domain faces out-of-band distortion, and therefore, to overcome the interference problem, various multicarriers are introduced, and FBMC is one of them. In FBMC, the fading effect reduces, and it achieves the appropriate BER performance in comparison to CP-OFDM. Renfors et al. (2010) provided some solutions for OFDM with the help of radio channels, as they provide efficiency, and multicarrier techniques can be used with multiple antenna sources and destinations. The frequency sub-bands have leakage, which has a grave effect on the outcome of FFT-based spectrum sensing. By using different frequency channels for each subcarrier, the interference problem has decreased (Xu et al., 2016).

Multicarrier modulation is the transmission technique utilized to segregate the channel bandwidth into many small channels. FBMC is an efficient candidate waveform in wireless communication. It has some advantages such as decent spectral efficiency and truncated out-of-band distortion, but this technique suffers from the high PAPR, which can be reduced by using some useful methods (Jeon et al., 2016; Nam et al., 2016; Zhai, 2016). To reduce PAPR, clipping and window methods are proposed (Rahim et al., 2009). The results are compared based on BER and spectral regrowth action. The effects of power amplifiers on multicarrier signals are also discussed. The two types of distortions used in it are in-band and out-of-band distortions. Both methodologies give the same BER performance in two different multicarrier systems. Another method used to check the BER performance is based on the synchronized and unsynchronized near−far effect; the unsynchronized method gives better results instead of the synchronized method. By using the unsynchronized method, an efficient BER has been achieved, making FBMC more efficient (Kaiming et al., 2015).

Elmaroud et al. (2014) combined the exponential companding transform and Hadamard transform techniques with a non-linear companding transform. The additive white Gaussian noise (AWGN) channel is utilized to remove the interference or noise from the system and make it efficient. The binary phase-shift keying (BPSK) modulation scheme is used to modulate the signal. The two combined approaches give a better PAPR, and in the end, its measured value is 4.1 dB. Gopal and Patra (2015) proposed the PAPR reduction methodologies such as tone injection (TI) and companding technique. To overcome the problem of the high PAPR, two different types of PAPR reduction techniques are used. The first technique is tone injection (TI); this method is used to reduce PAPR by adding extra constellation points to the original points. The second technique is the companding technique, in which a compander is used at the transmitter side and an expander is used at the receiver side. The compander can be of two types: A-law and μ-law. The TI-ACP algorithm is used to reduce PAPR in the system. The Blackman−Harris window and the PHYDAS filter are used to design a prototype filter. These combined TI and companding techniques are efficient and have low complexity at the receiver side. The PAPR reduction rate is very high from 16.4 to 3.7 dB with the same iterations, whereas the efficiency of the power amplifier has improved from 1.15 to 21.33%. By using these methods, PAPR has reduced and the performance of the system has also improved (Wang et al., 2016; Mohammed and Kostanic, 2018).

Shahenn et al. (2017) elaborated some methods to diminish the high PAPR issue, such as hybrid schemes used with precoding transform and μ-law companding techniques. Some precoding techniques, such as DST and DCT, are used with μ-law companding. Instead of other precoding techniques, DST gives better results when combined with μ-law, and the measured PAPR value is 2.88 dB in the FBMC system. The precoding technique can be used to minimize the autocorrelation of the input sequence to decrease the PAPR of the FBMC system and make it efficient (Nissel and Rupp, 2018; Zhao et al., 2018; Kansal et al., 2016, 2017, 2018, 2019; Kumar, 2019; Kumar and Rathore, 2019; Srivastava et al., 2020; Agarwal and Sharma, 2020; Kumar and Gupta, 2020; Cheng et al., 2020; Na and Choi, 2019).

In any of the literature work presented so far, the hybrid combination of discrete transforms and clipping and/or companding techniques to reduce the effect of PAPR has not been used for the FBMC system. Moreover, the BER analysis has not been carried out for the FBMC system on incorporating discrete transforms like such as DST and DCT. These research gaps motivate the authors to propose a new methodology, where the unique merger of the PAPR reduction technique with discrete transforms like DST/DCT will result in a significant improvement of the FBMC system in terms of PAPR and BER reduction, thus making it a suitable candidate for 5G applications.

Based on the detailed analysis of the proposed methodologies that are presented in the literature survey, the novelty aspects of the proposed work are addressed by the following points:

For the FBMC system, the DCT and DST transforms are utilized to realize an efficient PAPR reduction.

Existing PAPR reduction techniques such as clipping and companding are also incorporated to reduce PAPR for the FBMC system.

Further PAPR reduction is achieved on employing the hybrid combination of precoding techniques as well as conventional PAPR reduction techniques.

FBMC is deliberated as a candidate waveform for 5G in wireless transmissions. It has higher spectral efficiency and a well-designed localized spectrum. The baseband continuous-time model of the typical FBMC−OQAM modulated signal is given by the following equation:

$\begin{array}{}\text{(1)}& i(t)=\sum _{p=0}^{N-1}\sum _{q=-\infty}^{+\infty}{c}_{p,q}\phantom{\rule{.25em}{0ex}}g(t-qT/2){e}^{j\frac{2\pi}{T}pt}{e}^{j{\phi}_{p,q}},\end{array}$

(1)where The information data transmitted by the user are fed to the FBMC transmitter, as shown in Figure 2. The input data are mapped to the digital symbols by using the symbol mapping methodology. 16-QAM symbol mapping is utilized in the proposed methodology. OQAM processing has two processes, i.e. pre-processing and post-processing. In the pre-processing operation, the two complex values result in the formation of a single complex value. One is the real part and another is the imaginary part of the complex value. If the neighboring sub-channels are overlapped with each other, then the orthogonality is required. A filter bank that uses zero frequency carriers is called a prototype filter. It reduces the out-of-band distortions, which is essential to increase the number of coefficients in the time domain and frequency domain.

An input data stream is split into parallel data streams by using the serial-to-parallel conversion. In frequency spreading, the input data stream transmitted on a subcarrier is “spread” over a number of carriers equal to the number of non-zero samples of the prototype filter in the frequency domain. The frequency spreading gives accurate equalization with no further complexity increase in the case of non-flat sub-channels. The output of the frequency spreading block will be forwarded to the extended IFFT block. A parallel-to-serial conversion converts the parallel stream of the data into the serial form so that it can be forwarded to the receiver side through the transmission medium.

At the receiver side, the incoming data are first forwarded to the serial-to-parallel block, which converts the serial data into the parallel form, as shown in Figure 3. The high data rate stream is divided into lower data rate streams at the encoding stage; after that, they are changed to a complex form at the QAM mapping block in real and imaginary parts. The parallel data are then forwarded to the extended FFT block, which comprises of filter banks. The output of the extended FFT block is then sent to the frequency despreading block. The despreading block data are then forwarded to the OQAM post-processing block through the parallel-to-serial conversion block. After the poly-phase ﬁlters, the upsampling by an element of *N*/2 is performed. Through the speciﬁc blend of deferrals and adders, the subsequent examples from the parallel branches experience a parallel-to-serial transformation (Zhai, 2016). The demodulator part, the analysis filter bank (AFB). The outputs of the parallel branches are the OQAM symbols, which must go through the OQAM post-processing, which reverses the procedure. The conversion of real into complex for both even and odd symbols is carried out by the OQAM post-processing block in the FBMC receiver. The symbol demapping block then recovers the original information bit from the data provided by the OQAM post-processing block.

In a multicarrier modulation system, the output symbol is the summation of symbols modulated on different subcarriers. This results in very high peak power in comparison to the average power of the symbols. In the FBMC system, PAPR is presented as the ratio of peak power to the average power, as presented in the following equation:

$$\begin{array}{}\text{(2)}& \mathrm{PAPR}=(\frac{\mathrm{max}\phantom{\rule{.25em}{0ex}}\{|T[n]{|}^{2}\}}{E\{|T[n]{|}^{2}\}}),\end{array}$$

(2)where In dB, the peak-to-average ratio can be given in the following equation:

$$\begin{array}{}\text{(3)}& \mathrm{PAPR}(\mathrm{dB})=10\phantom{\rule{.25em}{0ex}}\mathrm{log}\phantom{\rule{.25em}{0ex}}10(\mathrm{PAPR}).\end{array}$$

The complementary cumulative density function (CCDF) plot is used to measure the peak-to-average power ratio performance of PAPR reduction schemes, as presented in Equation (4). In FBMC, the increased number of subcarriers is similar to OFDM:

$$\begin{array}{}\text{(4)}& \mathrm{CCDF}=\mathrm{Probability}(\mathrm{PAPR}>\mathrm{PAPR}\xb0),\phantom{\rule{.25em}{0ex}}\end{array}$$

(4)where
$\mathrm{PAPR}\xb0$PAPR° is the threshold PAPR.The proposed methodologies for PAPR reduction in the FBMC system are as follows.

Clipping is a simple method to decrease PAPR in the FBMC system, as presented in Figure 4. Clipping is a form of distortion that limits the signal if it exceeds the threshold point. As the name suggests, clipping means cutting that part which is not suitable to enter the saturation region in the system. The clipped signal *x*
^{
c
} is presented in the following equation:

$$\begin{array}{}\text{(5)}& \phantom{\rule{.25em}{0ex}}{x}^{c}=\{\begin{array}{c}x,x\u2a7d{A}_{\mathrm{max}}\\ {A}_{\mathrm{max}},x{A}_{\mathrm{max}}\end{array},\end{array}$$

(5)where Companding is a low complexity method to reduce PAPR. It does not reduce BER performance, similar to the clipping method. In the companding methodology, the transmitter is equipped with a compressor and the receiver is equipped with an expander. They are used to amplify the small signal, improve the power of the FBMC signal, and then decrease the high peak value, as presented in Figure 5. It has two types:

A-law companding is a regular companding algorithm, used in Europe. It is used to change the dynamic range of an analog signal for digitizing. It is one of the two versions of G.711, and the other version is the same as mu-law, used in Japan and North America. In Europe,

*A*= 87.6, where*A*is known as the compression parameter. The equation of A-law encoding is presented in Equation (6), where*x*is the input signal and*F*(*x*) is the companded version of the input signal:$$\begin{array}{}\text{(6)}& F(x)=sgn(x)\{\begin{array}{c}\frac{A\left|x\right|}{1+\phantom{\rule{.25em}{0ex}}\mathrm{log}(A)},\phantom{\rule{.25em}{0ex}}\left|x\right|<\frac{1}{A}\\ \frac{1+\phantom{\rule{.25em}{0ex}}\mathrm{log}(A\left|x\right|)}{1+\phantom{\rule{.25em}{0ex}}\mathrm{log}(A)},\phantom{\rule{.25em}{0ex}}\frac{1}{A}<\left|x\right|\u2a7d1\end{array}.\end{array}$$μ-law companding is another companding algorithm. It is used in United State and Japan for audio companding. The μ-law encoding principle is presented in the following equation:

$$\begin{array}{}\text{(7)}& \phantom{\rule{.25em}{0ex}}F(x)=sgn(x)\frac{\mathrm{ln}(1+\mu \left|x\right|)}{\mathrm{ln}(1+\mu )}\phantom{\rule{.25em}{0ex}}-1\u2a7dx\u2a7d1,\end{array}$$

(7)where In this paper, two types of precoding schemes are used, i.e. DST and DCT.

DST is a linear transform related to the Fourier transform. The

*N*real numbers*x*_{0}, …,*x*_{ N−1}are transformed into the*N*real numbers*X*_{0}, …,*X*_{ N−1}according to the following equation:$$\begin{array}{}\text{(8)}& X\phantom{\rule{.25em}{0ex}}(k)=\phantom{\rule{.25em}{0ex}}\sum _{n=0}^{N-1}x(n)sin[\frac{\pi}{N+1}(n+1)(K+1)],\end{array}$$(8)where*k*= 0, …,*N*−1;*x*(*n*) is the input signal and*X*(*k*) is the output signal.DCT uses only real numbers and is related to the Fourier transform. There are eight types of DCT variants, and four of them are common. The basic formula of DCT-1 is presented in the following equation:

$$\begin{array}{}\text{(9)}& X\phantom{\rule{.25em}{0ex}}(k)=\phantom{\rule{.25em}{0ex}}\sum _{n=0}^{N-1}x(n)\mathrm{cos}[\frac{\pi (2n+1)}{2N}k],\end{array}$$

(9)where The impact of using PAPR reduction and precoding schemes on the CCDF vs PAPR analysis of the FBMC system is depicted in this paper through MATLAB simulations. In the simulation work, DCT and DST precoding schemes are used for the assessment of the performance of the FBMC system incorporated with PAPR reduction schemes. The BER analysis is also carried out over the AWGN and Rayleigh fading channel for the DCT and DST precoded FBMC systems. Simulation parameters utilized in MATLAB simulations are presented in Table 1.

Figure 6A, B depicts the PAPR reduction analysis for FBMC on incorporating diverse transforms, i.e. DCT and DST, as precoding, which then combines with the conventional PAPR reduction technique, i.e. clipping. This combination of precoding with FBMC improves PAPR from 13.9 to 12.1 dB. When clipping is combined with FBMC, a reduction in PAPR is observed and the performance of the system is enhanced. By combining precoding and clipping with FBMC, PAPR is reduced and the response of the system is much better than others. DCT gives better PAPR results as compared to DST.

Figure 7A, B depicts the PAPR reduction analysis for FBMC on incorporating diverse transforms, i.e. DCT and DST, as precoding, which then combines with the conventional PAPR reduction technique, i.e. companding. This combination of precoding with FBMC improves PAPR from 14 to 12.1 dB. When A-law companding is combined with FBMC, a reduction in PAPR is observed and the performance of the system is enhanced. By combining precoding and A-law companding with FBMC, PAPR is reduced and the response of the system is much better than others. DCT gives better PAPR results as compared to DST.

Figure 8A, B depicts the PAPR reduction analysis for FBMC on incorporating diverse transforms, i.e. DCT and DST, as precoding, which then combines with the conventional PAPR reduction technique, i.e. companding. This combination of precoding with FBMC improves PAPR from 14 to 12.1 dB. When μ-law companding is combined with FBMC, a reduction in PAPR is observed and the performance of the system is enhanced. By combining precoding and μ-law companding with FBMC, PAPR is reduced and the response of the system is much better than others. DCT gives better PAPR results as compared to DST.

From Figures 6-8, it is observed that in DST with clipping, DST with A-law companding, DST with μ-law companding, DCT with clipping, DCT with A-law companding, and DST with μ-law companding, DCT gives better performance than DST in the cases of clipping and A-law companding, while for μ-law companding, DST gives better results.

The BER analysis of the FBMC system with and without percoding is presented in Figure 9A, B. It is very evident from Figure 9A, B and Table 2 that the BER performance of the FBMC system incorporated with precoding is better than the conventional FBMC system; the DST precoded FBMC system performs better than the DCT precoded FBMC system. BER reduction in the cases of DCT and DST is due to the fact that both the transforms work on the real numbers and also under the finite boundary conditions. DCT uses only the cosine functions, whereas DST uses the sine functions.

FBMC is the multicarrier modulation scheme regarded as a candidate waveform for 5G. The performance of the FBMC system is analyzed in terms of PAPR reduction by using clipping and companding PAPR reduction schemes combined with precoding techniques, i.e. DST and DCT.

These techniques reduce the PAPR values up to a great extent. Of all the above-discussed techniques, precoding combined with the PAPR reduction technique like clipping or companding provides the least PAPR. These PAPR reductions are evaluated for both DST and DCT. These methods may increase the computational complexity, but along with that, they also increase the capacity of the system. The proposed strategies make the FBMC methodology a prominent contender for 5G. MATLAB simulation results show that the PAPR value has decreased from 14 to 3.7 dB and the efficiency of the power amplifier has increased. It is also very evident from the BER analysis that the precoded FBMC has superior BER performance than that of the conventional FBMC system.

In the future, the proposed model can also be evaluated for other discrete transforms such as discrete wavelet transform and discrete fractional Fourier transform. The methodology can be extended to study the performance of a hybrid combination of FBMC and massive MIMO/multi-user MIMO systems.