Proceedings of ICWN'19...technique takes attention in the uplink LTE communication system, because...

Effect of Companding Techniques to Enhance the Performance of SC-FDMA Systems

Sarah M. Farid1, Hesham Elbadawy2and khaled Shehata3

1Electronics and Communications Department, Faculty of Engineering, Modern Academy, Cairo, Egypt

2Electronics and Communications Department, Faculty of Engineering, Arab Academy of Science and Technology, Cairo, Egypt

3Electronics and Communications Department, Faculty of Engineering, Arab Academy of Science and Technology, Cairo, Egypt

Abstract - Single Carrier Frequency Division Multiple Access technique takes attention in the uplink LTE communication system, because of its lower Peak to Average Power Ratio (PAPR).Even though it offers higher execution in PAPR reduction than Orthogonal Frequency Division Multiple Access, A wide range that handle the PAPR problem still remains. Many techniques were used in SC-FDMA systems for minimizing PAPR, but most of them need to transmit extra information or they are more complex such as Partial Transmit Sequence and Selective Mapping. In this paper, the performance of several advanced companding techniques like tangent rooting companding, Absolute exponential companding and logarithmic companding techniques in SC-FDMA system was tested with respect to PAPR reduction and BER system performance. So according to some simulation and analysis we did, it was found that the Absolute Exponential Companding technique gave much better system performance compared with the conventional SC-FDMA and other companding techniques.

Keywords: LTE, SC-FDMA, AEXP, PAPR reduction, Companding, CCDF

1 Introduction The third Generation Partnership Project (3GPP) in Long Term Evolution (LTE) for uplink communication has implemented Single Carrier Frequency Division Multiple Access (SC-FDMA) [1]. SC-FDMA signal has a less Peak to Average Power Ratio (PAPR) than Orthogonal Frequency Division Multiple Access (OFDMA) signal because of lower signal envelope swings. However, there is a need for more progress in PAPR in localized SC-FDMA systems, especially for high modulation order [2]. Highly linear power amplifiers and Digital to Analog (D/A) converters are needed to meet the large PAPR demands, but unfortunately the cost will be increased, also the power efficiency will be decreased and that will require an additional complexity. At the same time the mobile terminals are limited in the power, so this problem is a critical issue in the uplink transmission [3].

In the literature, several methods have been proposed to minimize PAPR such as: coding techniques, probabilistic techniques, signal distortion and multiple signaling techniques [4]. However the non-linear companding techniques were considered from the simplest signal distortion methods that don’t require transmission of extra side information like other reduction techniques and also have a low implementation complexity. The most famous companding techniques for reducing PAPR in communication systems are A-law and μ-law companding. Hence, the output companded signal average power will be much higher because of increasing the small amplitudes and will not affect the large amplitudes of the signal [5].

The authors in [6] proposed μ- law companding in SC-FDMA system, and the system was improved by 3.25 dB at complementary cumulative distribution function (CCDF) = 10-4 than conventional system at μ=4. Moreover, as the companding coefficient (μ) increased, BER performance is degraded, however PAPR performance was improved more than conventional system. In [7], the PAPR at CCDF =10-3, when using Selective Mapping (SLM) and Partial Transmit Sequence (PTS), was equal to 6.6 dB and 5.6dB, respectively. Also, the simulation results in [8] showed that the system performance was improved by using an absolute exponential companding.

In this paper, a hybrid Absolute Exponential Companding technique SC-FDMA system (AEXP-SCFDMA) is proposed in the LTE uplink systems to enhance the PAPR reduction with acceptable BER system performance. The proposed system outperforms better in both of PAPR reduction and BER when compared to the conventional SC-FDMA system, μ-Law, PTS, SLM, tangent rooting companding technique (TanhR) and logarithmic companding technique (logR) as will be shown in the simulation outcomes.

The rest of the paper is organized as follows: Section two includes the PAPR problem, (SC-FDMA) system block diagram and a briefly discussion about the advanced companding techniques. In section three, the proposed (AEXP-SCFDMA) system is presented and simulated.

Int'l Conf. Wireless Networks | ICWN'19 | 51

ISBN: 1-60132-504-5, CSREA Press ©

Simulation outcomes are analyzed and illustrated in section four. Finally, the conclusions are stated in section five.

2 SC-FDMA System Model In this section, the ordinary LTE SC-FDMA system

block diagram is presented, as shown in Figure 1. SC-FDMA is an upgraded structure of OFDMA system which would be viewed as Discrete Fourier Transform (DFT)-spreading OFDMA, in which data is converted from time domain into frequency domain by DFT before entering OFDMA system [9].

The input stream of bits (X) at the transmitter of the SC-FDMA system was mapped by applying QPSK, 16-QAM, and 64-QAM modulation techniques separately. Whereas, the output from the mapper X(s) is a sequence of a complex numbers, where s is the sample index and X(s) is the data symbol. After that, it was subjected to serial to parallel converter (S/P) block to get data blocks Xn, in which each of them contains M number of symbols. After that, these data blocks are represented in frequency domain X(K) by passing them into M-point DFT [8] as defined in equation (1), (1)

Fig. 1: Conventional SC-FDMA system [4].

The DFT-block output X(K) is applied to the subcarrier mapping block to map one by one of the M-DFT outputs into N different orthogonal subcarriers, where M must be greater than M by a factor called spreading factor (Q) [8] as in equation (2),

(2)

In SC-FDMA system, there are two famous schemes of subcarrier mapping allocations: The Interleaved-FDMA (IFDMA), which is a type of the Distributed-FDMA (DFDMA) and the Localized-FDMA Access (LFDMA). The LFDMA maps the data into adjacent subcarriers and pads the other subcarriers with zeroes. Whereas the (IFDMA) maps the data through the whole band with equidistance, while the other subcarriers are also padded with zeroes. By comparing LFDMA and IFDMA, the LFDMA has proved higher PAPR than IFDMA. The output from subcarrier mapper block used in LFDMA is represented by XL which is computed using equation (3),

(3)

After the subcarrier mapping block, an output of N complex subcarriers amplitudes are applied to IFFT block that

converts N subcarriers into Xm time domain signals, which is represented in equation (4),

(4)

Then the output Xm is passed through parallel to serial block to transmit the data sequentially. Inverse steps are done at the receiver to get the data. The current work will try to develop the LTE system performance by improving the PAPR. PAPR is defined as the ratio between the peak amplitude of the signal to the average power. Peak power of the signal occurs when N modulated symbols with the same phase are added together [4]. PAPR of Xm can be mathematically represented by equation (5):

(5)

Where, (E) stands for the expectation value (mean square value). Further, some companding techniques will be mentioned briefly to be compared with the proposed technique (AEXP-SCFDMA) in the uplink system.

2.1 Tangent Companding Technique (TanhR) TanhR is one of the companding techniques that works on the transformation of the signal distribution into tangent

Channel

Destination De-Mapper

P/S Converter

IDFT M-Point

Remove CP/ADC

S/P Converter

FFT N-Point

Subcarrier De-Mapper

Binary Inputs

Mapper

S/P Converter

DFT M-Point

P/S Converter

IFFT N-Point

Subcarrier Mapper

Add CP/DAC

{X} {X(S)} {Xn} {Xk} {Xl} {Xm}

52 Int'l Conf. Wireless Networks | ICWN'19 |


distribution using the hyperbolic function (Tanh) [10] as in equation (6):

(6)

Where, the positive number k represents the companding degree level for the signal envelope (x) which ranged from 5 to 25. y is also a positive number, ranged from 0.2 to 1, that controls effectively the PAPR and sgn(x) to determine the phase of the SC-FDMA signal.

Although TanhR Companding has reduced the PAPR and system complexity it has an disadvantage in the BER of the system especially, when it is applied for a system with a high modulation order like 16-QAM and 64-QAM. It controls the level of PAPR reduction by adjusting the two factors K and y at the transmitter [11].

The recovered signal at the receiver after the expanding process can be extracted by using equation (7):

(7)

2.2 Logarithmic Companding Technique (LogR)

LogR companding is a low complexity companding technique with good system performance in PAPR reduction [12]. The logarithmic companding function can be represented as in equation (8):

(8)

Where, a positive number k represents the companding degree level for the signal envelope (x) and sgn(x) to determine the phase of the SC-FDMA signal.

At the receiver end the de-companding function is represented in equation (9):

3 Proposed Technique In this section, a new hybrid technique in the uplink

mobile communication system instead of the conventional SC-FDMA system is introduced. This hybrid technique is done by combining the conventional SC-FDMA system with one of the nonlinear companding schemes which are named as Absolute Exponential Companding (AEXP), Tangent rooting companding (TanhR) and Logarithmic companding (LogR), as illustrated in Figure 2.

The proposed hybrid scheme (AEXP-SCFDMA) has an effective role, not only in reducing the PAPR for different modulation techniques of the transmitted companded signal, but also BER will be improved by keeping the average power of the transmitted companded signal at the same level with the input signal.

Fig. 2: (SC- FDMA) system with companding.

This will prevent the system from exceeding the saturation region of the power amplifier. This may be achieved by converting the signal amplitudes into uniform distribution companded signal by the manipulation of both small and large amplitudes, which differs from other

companding techniques, like μ-Law technique that is based mainly on enlarging only the small signals.

At the transmitter, the companding function h(x), in consistence with [8] which changes the amplitudes of the



input signal which is expressed in equation (10). Where (d) is the degree of the exponential companding that controls signal companded factor (α), to control the average power of the output companded signals. α will be used for keeping the output average power at the same level of the input signals. So, the h(x) companding function may be represented as follows:

(10)

Where α is the positive constant value that controls the average power of the output companded signal which is mathematically given as in equation (11). At which

is the sign function, α2 is the input modulated signal variance, and x is the IFFT output signal.

(11)

At the receiver, the inverse companding operation is applied by using inverse function h-1(x) that can be expressed as in equation (12),

(12)

4 Simulation Results and Analysis Excessive simulations are done for evaluating the system

performance by using several modulation techniques and different FFT sizes. The result was showed that the proposed AEXP companding technique outperforms the conventional system, TanhR companding and LogR companding. The proposed model does not only prove better PAPR reduction, but also it improves the obtained BER system performance than the conventional system and other companding techniques, especially for high modulation orders. The parameters of the system are summarized in Table I.

The Complementary Cumulative Distribution Function (CCDF) of the proposed companding technique was introduced in order to study the effect of BER performance and PAPR by varying (d) for 16-QAM and 64-QAM in simulations. Figure 3 shows the obtained CCDF of PAPR for different (d) and 16-QAM modulation technique. On the other hand, Figure 4 illustrates the obtained BER against the (d) for different SNR levels of 16-QAM system.

As shown in Figure 3 and 4, by increasing d, the obtained PAPR increases whereas BER decreases. So, there

will be a local minimum that gives the lowest BER as well as the lowest PAPR.

TABLE I Simulation Parameters

PARAMETER DESCRIPTION Number Of Subcarrier Mapping(M) 64,128 Subcarrier Mapping Localized Number Of Symbols 1000 Number Of Bits (N) 64000,128000 Modulation Technique QPSK,16-QAM,64-QAM FFT size (n) 128,256,512 Spreading factor (q) 3,4 Cyclic prefix length 0.25*FFT size Channel model AWGN Companding factor (d) From 0.2 to 2

Fig. 3: PAPR for different d values, 16-QAM.

Fig. 4: BER for different d values, 16-QAM.

4.1 PAPR Results and Analysis The proposed AEXP-SCFDMA system was compared with TanhR companding technique, LogR companding technique and against conventional SC-FDMA system for different sizes of FFT and different modulation techniques by (CCDF), as illustrated in Figure 5 and 6.



Fig. 5: PAPR Reduction Performance for AEXP, TanhR, LogR and

SC-FDMA for M=256 and different modulation techniques.

Fig. 6: BER PAPR Reduction for AEXP and SC-FDMA for M=512 and different modulation techniques.

From Figure 5 and 6, it was observed that the proposed (AEXP-SCFDMA) reduces the PAPR much better than the traditional SC-FDMA. Also, as the number of subcarriers (FFT size) increases the PAPR is improved. This improvement is achieved because of the hybrid proposed technique, as it combines the advantage of reducing the PAPR from the companding technique and the pre-coding technique. Table II shows the analysis of Figure 5 and it was noticed that AEXP has an improvement in PAPR for QPSK, 16-QAM and 64-QAM about 3.94 dB, 4.45 dB and 4.76 dB respectively.

Also, Figure 5 shows that TanhR companding technique outperforms better than AEXP and LogR for QPSK modulation by 1.75 dB and 2.2 dB respectively.

TABLE II PAPR Analysis for FFT=256.

Different PAPR AEXP-SCFDMA SCFDMA

PAPR at 10-3 for QPSK 3.61 dB 7.55 Db

PAPR at 10-3 for 16-QAM 4 dB 8.45 dB

PAPR at 10-3 for 64-QAM 4.01 dB 8.77 dB

Table III shows the analysis of Figure 6 for AEXP Companding. From this table we can notice that there is also an improvement in PAPR for QPSK, 16-QAM and 64-QAM about 4.18 dB, 4.7 dB and 4.92 dB respectively.

TABLE III PAPR Analysis for FFT=512

Different PAPR AEXP-SCFDMA SCFDMA

PAPR at 10-3 for QPSK 3.52 dB 7.7dB



Another comparison was done between our proposed technique and the New Error Function (NEF) companding technique, PTS and SLM. It was found that our proposed (AEXP-SCFDMA) method had a slightly better performance in PAPR reduction than (NERF) companding technique [13] by 0.05 dB at QPSK modulation technique and M=512.

Table IV illustrates the difference between our system performance with PTS and SLM in [7], where we found that the PAPR reduction achieved by the proposed AEXP-SCFDMA at PAPR=10-1 was much better than PTS and SLM by 1.9 dB and 2.9 dB respectively. And so, depending on the results, the performance of AEXP-SCFDMA system is better than the performance of NERF, PTS and SLM.

TABLE IV

PAPR Reduction Results Achieved by AEXP-SCFDMA, PTS and SLM.

PAPR Value AEXP-SCFDMA PTS SLM

PAPR at 10-1 for 16-QAM 3.7 dB 5.6 dB 6.6 dB

4.2 BER Results and Analysis This section shows the SC-FDMA system performance

with respect to BER, taking into consideration that there is a trade-off between it and PAPR. The BER for (AEXP-SCFDMA) proposed system, conventional system, TanhR and LogR companding techniques has been presented in Figure 7.

From Figure 7, it was observed that for BER=10-4 and QPSK modulation technique, the proposed AEXP technique having SNR= 6, which is the same as the traditional (SC-FDMA), and for 16-QAM modulation the proposed one was degraded a little as it had SNR=14 and (SC-FDMA) have SNR=12.2. This degradation is due to introduction the companding technique with the conventional system so the whole system BER increases at the same SNR ratio level.



Fig. 7: Bit Error Rate (BER) versus (SNR).

For TanhR and LogR, the BER curves meet with each other at BER=10-4 with SNR=6.2 for QPSK modulation which is worse than the proposed AEXP-SCFDMA and conventional SC-FDMA system. The most degradation happened when using high order modulation techniques like 16-QAM and 64-QAM.

Also a comparison was done between our proposed method (AEXP-SCFDMA) and both the approximated de-companding (ADC) and the no de-companding (NDC) function companding techniques in [14]. Table V shows that our proposed technique had better BER performance than NDC and ADC by 2.69 and 3.79 respectively.

TABLE V

BER analysis by AEXP-SCFDMA, NDC and ADC.

BER=10-4 AEXP-SCFDMA NDC ADC

SNR 14.1 16.79 17.89

5 Conclusions In this paper, advanced companding techniques were tested within the LTE uplink SC-FDMA system and compared with each other in terms of PAPR and BER system performance. This was done by performing excessive simulations and analysis for evaluating the systems. The best companding technique was our proposed (AEXP-SCFDMA) technique, as it had a promising PAPR reduction with an acceptable little BER degradation than conventional system for all modulation orders and subcarrier sizes. TanhR and LogR techniques were having a good PAPR reduction with less complexity but at the other side they had a very high BER system degradation, especially for high modulation orders. The results showed that our proposed (AEXP-SCFDMA)

technique achieved better system performance with respect to both PAPR reduction and BER system performance than other state-of-the-art PAPR reduction techniques like PTS, NERF, TanhR, LogR and SLM.

6 References [1] E. U. T. R. Access, “Long Term Evolution (LTE) physical layer; General description,” in 3rd Generation Partnership Project (3GPP),TS 36.201, 2007.

[2] Wu, Kun, Guangliang Ren, and Maixin Yu. "PAPR reduction of SC-FDMA signals using optimized additive pre-distortion." IEEE Communications Letters 19, no. 8, 1446-1449, 2015.

[3] Deepak, N. R., and S. Balaji, "Uplink Channel Performance and Implementation of Software for Image Communication in 4G Network." In Software Engineering Perspectives and Application in Intelligent Systems, pp. 105-115. Springer, Cham, 2016.

[4] F. Sandoval, “Hybrid Peak-to-Average Power Ratio Reduction Techniques : Review and Performance Comparison,” IEEE Access, vol. 5, pp. 27145–27161, 2017.

[5] V. N. Sonawane and S. V. Khobragade, “Comparative Analysis between A- law & μ -law Companding Technique for PAPR Reduction in OFDM,” Int. J. Adv. Res. Comput. Commun. Eng., vol. 2, no. 5, pp. 2210–2214, 2013.

[6] F. E. Abd El-Samie, F. S. Al-Kamali, M. I. Dessouky, B. M. Sallam, and F. Shawki, “Performance enhancement of SC-FDMA systems using a companding technique,” Ann. des Telecommun. Telecommun., vol. 65, no. 5–6, pp. 293–300, 2010.

[7] Jameel, Ahmed J, "PAPR reduction of localized single carrier FDMA using partial transmit sequence in LTE systems." International Journal of Computing and Network Technology", 5, no. 01, pp. 21-26, 2017.

[8] I. A. A. Shaheen, A. Zekry, F. Newagy, and R. Ibrahim, “Absolute Exponential Companding to Reduced PAPR for FBMC/OQAM,” Proc. - 2017 Palest. Int. Conf. Inf. Commun. Technol. PICICT 2017, pp. 60–65, 2017.

[9] El-Samie, Fathi E. Abd, Faisal S. Al-Kamali, Azzam Y. Al-Nahari, and Moawad I. Dessouky. “SC-FDMA for mobile communications”, CRC press, 2016.

[10] A. Kumar and Y. Y. K. Prajapati, “PAPR Minimization of Clipped OFDM Signals Using Tangent Rooting Companding Technique,” Wirel. Pers. Commun., no. 0123456789, 2019.



[11] D. P. K and A. Prasad, “Effect of PAPR reduction techniques on BER Performance of OFDM System,” Int. J. Recent Adv. Eng. Res., vol. 03, no. 07, 2017.

[12] Kareem, Ali N., Sinan M. Abdul Satar, Mohammed A. Husein, Liqaa A. Al-Hashime, and Ghaida A. Al-Suhail. "Performance Improvement Of OOFDM Systems Based On Advanced Logarithmic Companding Technique." Transactions on Networks and Communications 6, no. 5 (2018).

[13] Ramtej, K. Shri, and S. Anuradha. "New error function companding technique to minimize PAPR in LTE uplink communications." In 2017 Twenty-third National Conference on Communications (NCC), pp. 1-5. IEEE, 2017.

[14] S. R. Kondamuri and A. Sundru, “Performance analysis of hybrid PAPR reduction technique for LTE uplink communications,” Phys. Commun., vol. 29, pp. 103–111, 2018.



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