[EEE/OSA/[APR International Conference on [nfonnatics, Electronics & Vision

Partial Companding as a P APR Reduction Technique of an OFDM System

Tabassum Haque, Subaha Mahmuda, Feroz Ahmed School of Engineering and Computer Science

Independent university Bangladesh Dhaka, Bangladesh

katha I16@yahoo.com, subaha2007@yahoo.com, feroz _ ahmed _ 2002@yahoo.com

Abstract-In this paper, a new technique of BER minimization in a companding based PAPR reduction scheme is proposed. In this approach, the conventional companding scheme is only applied for those OFDM signals whose amplitude exceeds a predefined threshold level, which results in lower BER and lower computational time. Though for the proposed scheme, improvement of the PAPR is less than the conventional companding technique, however, BER performance is improved significantly.

Keywords- Orthogonal Frequency Division Multiplexing

(OFDM), Peak-to-Average Power Ratio (PAPR), Bit Error Rate

(BER), Complementary Cumulitive Distribution Function (CCDF)

I. INTRODUCTION

OFoM is widely adopted as a multicarrier modulation system in different sectors of wireless applications due to high bandwidth efficiency and its inherent resistance to Inter Symbol Interference (ISI).With insertion of guard interval (01) and cyclic prefix (CP), the system gets extremely low lSI and almost flat frequency selective fading, which is caused by multipath effect. Only a simple equalizer in the receiver is enough to recover the signal from the fading channel. The implementation of the system is relatively less complex and inexpensive since it only needs a few Fast Fourier Transform (FFT) blocks. These advantages make an OFoM system suitable for implementation in Digital Audio Broadcasting (DAB), Digital Video Broadcasting (DVB), Wimax, WiFi, Long Term Evolution (LTE), and OFDM-MIMO, among others [1-4].

One of the major disadvantages of OF OM system is its high PAPR. This means, the output amplifier at the transmitter has to be linear over a large dynamic range. Linear amplifier is not efficient and increases the power requirement of the transmitter. The high P APR decreases the efficiency of the system by preventing the system to use high efficiency mostly used non-linear amplification devices [5]. High Power Amplifier (HP A) with large linear region is required to amplify this kind of signal and to prevent spectral growth. However, HPA with large linear region is really expensive. That is why, P APR reduction is essential for OFDM signal.

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To overcome the high PAPR problem of OFDM system, a number of techniques are proposed which include amplitude clipping and filtering [6-7], companding [8-9], block coding [10], partial transmit sequence (PTS)[ 11-13], selective mapping [14-15], tone reservation [5], peak windowing [5], among others.

Among the mentioned P APR reduction schemes, the companding technique is relatively simple and suitable for implementation. However, high BER limits the performance of the OFDM system by highly amplifying low level signal which causes out-of-band radiation. In this paper, the newly proposed partial companding technique minimizes this out-of­band radiation problem by applying the conventional companding scheme on OFDM signal where amplitudes exceed a predefined threshold level. The signals lower than the threshold level are remain unchanged, which results in lower BER and less computational time.

[I. THEORITICAL FORMULATION

A. Characteristic of OFDM signal OFDM system is the sum of independent signals which are

of equal bandwidth. The subcarriers which carry the independent signals maintain the rule of orthogonality. Which means, the subcarrier frequencies are equally spaced with [n = nfj.[, where fj.[ == liNTs. Ts is the symbol duration. [n this system, A block of N transmitted symbols are demonstrated as Xn {n=O, I, 2 . . . . , N- I} and each symbol is modulated with M-PSK or M-QAM to one of the set of subcarriers of tn. OF OM signal is simply the Inverse FFT (IFFT) of the N modulated signals and the resulting signal can be expressed as,

(1)

The P APR is the ratio of the maximum power and the mean power of an OFDM system. In dB it can be written as,

ICIEV 2012

IEEE/OSA/IAPR International Conference on Infonnatics, Electronics & Vision

[PAPR] B = 1010 1 lMaxlxct)12j

d g 0 E[lx(t)12] (2)

Since, IFFT is a linear operation; the transmitted signal x(t) follows a complex Gaussian distribution. Large number of N results to a high PAPR.

When the transmitted signal is passed through HPA the signal suffers with significant non-linear distortion which degrades the system performance by causing in-band distortion and out-of-band radiation.

B. The CCDF o{PAPR The performance of P APR can be evaluated with

Cumulative Distribution Function (CDF) of OFDM system; the most frequently used criteria of measuring the efficiency of PAPR. The CDF can be expressed as [5],

F(A) = 1 - eA (3)

In practical use, the Complementary CDF (CCDF) is used instead of CDF which denotes the PAPR of a certain data block exceeds a given threshold. For a large number of subcarriers (N) the CCDF of the PAPR can be expressed as,

Pr(PAPR > A) = 1- (F(A)t = 1 - (1 - e-A)N (4)

C. Conventional Companding Scheme

Companding is a technique, which reduces the dynamic range of a signal by increasing the average power. In this case, low level signals are highly amplified in compare to the high level signals. The P APR is reduced to an extent if dynamic range is reduced [8-9, 12].

Xc(t)

Figure 1. An OFDM system with conventional companding scheme

684

Figure 1 depicts the block diagram of an OFDM system which utilizes the conventional companding scheme. Additive White Gaussian Noise (A WGN) channel is used as the noise channel. The ,u-Iaw companding is basically used as the non­linear companding technique. The value of ,u is varied for different levels of compression. The value of ,u=255 gives the standard compressed signal.

The OFDM signals are companded before they are converted to analog signal and transmitted through the A WGN channel. In the case of ,u-Iaw companding; for a selected,u. the baseband signal can be compressed as follows [16],

0.8

0.6

0. 4

0.2 '" -" " c 0 '" � -0.2

-0. 4

-0.6

-0.8

-1 0

In[ 1+/l IX(t)l ] X (t) = sgn[x(t)] Xmax Xmax C lnIH/l]

, I I , • � , ( II I - I II • I •

I I

I I L I

I L L I 1 LI \ 'I \

I

t

1 0 20 30 40 Time Index

(5)

� , I I

50 60

Figure 2. Time domain output of un companded and companded envelope of a baseband OFDM signal

III. PROPOSED PARTIAL COMPANDING TECHNIQUE

The original transmitted signal is compared first with the predefmed threshold magnitude level. If the magnitude of the OFDM signal is higher than the predefined threshold level, conventional companding technique is applied to compand the signal. Otherwise signal is transmitted through the A WGN channel without any change. Since, the amplitudes of the low level signals are unchanged in this technique, so the signal distortion is decreased. Result in lower BER. In the receiving end, decompression is applied only for the compressed signals.

The threshold level decides the performance of the P APR and BER. Lower threshold level gives higher improvement in P APR, however BER is increased.

We have chosen the threshold as the factor of maximum

peale For example, as a factor, f=': means threshold value is 3

xmax X .:; where, xmax is the maximum peak value of the 3

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[EEE/OSA/[APR International Conference on [nfonnatics, E[ectronics & Vision

OFDM signal. Some of the possible threshold position is shown at figure 3.

�!r= 0.9 ,------,----

.

--r .•. -

..

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...

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-

.

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-. . • -.--r. , -• . • -----,------, 0.8 ......... ,.... K········�·

,.,.,."."." .• """"", .. " "" , " .""""., . f=1/3 ········ V · 0.7

0.6 1 \ .... -

] 0.5

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� 04

0.3 pJ" . tJ··MX . 0.2 V N :. .. . . - .

.. _ .'"'J .. V . vtf)'/

0.1 1-_...;....-1-+_...;.... _. ,,_,, _. " .... " _" ---'r------I1f-" .;...'.' ._,,_. " _""",IL;;.."_"......" ° 0·L- -�10�-2� 0-�3�0--4� 0 -�50L--�60��7�0-�80

Time Index

Figure 3. Different threshold levels of partial companding technique

In the transmitter side the expression of partial companding is as follows,

{X(t), Xc(t) = compand ( x(t)), x(t) < xr(t) x(t) 2:: xr(t) (6)

Where, compand (.) is the same function which is shown in Eq. 5 and xr(t) is the threshold amplitude of the original signal.

In the recelvmg end, the received signal in Eq. 4 is decompanded as follows,

{ RxCt), RAt) < RxrCt) X Ct) = d decompand ( RxCt)), RAt) ;?: RxrCt) (7)

Where, decompand (.) is the same function which is shown in Eq. 7 and RxrCt) is the threshold amplitude of the received signal.

[V. SIMULATION RESULTS AND DISCUSSION

Here, we present the results of computer simulations used to evaluate PAPR reduction capability and BER performance of the proposed scheme. An OFDM system with a sub-carrier of N=64 and 16-QAM modulation is considered in this simulation.

Figure 4 shows the CCDF performance of a companding algorithm for PAPR reduction [17-[8]. At CCDF=10-3, the

values of P APR of partial companding with factors �,�, � ,� 3 6 10 20

are respectively 10db, 7db, 6.2db and 5.7db. That means, the

probability of exceeding the P APR 10 db for factor � is 3

685

10-3.By analyzing this graph it can be seen, as the threshold goes lower the P APR is reduced more.

� 1 0-2 -+-Without companding o o ----B----- Conventional Companding

-+- Partial Companding,f=1 !3 --+-- Partial Companding,f=1 f6 . -B--Partial Companding,f=1 /1 0

.

1 0.3 L---'----L----:'---4:>---'---+-:IB--4----:'-�4!_I--,J. ·4 ·2 4 1 2

PAPRO(db) Figure 4. Comparisons of the CCDF for different companding factors

The signal amplitudes greater than the threshold value is companded and the amplitudes below the threshold remain unchanged.

a: w co

BER vs SNR 1 00

cc: .:-c_ : .,"", : :'"": :c--:: :c--:: :eT: . ,:-C:: _:-c_

: :'"": :c--:: :c--:: :c--:: :T:: .. :-c.: .,"", : :c--:: :c--:: :c--:: :-:-:-: :TC.-: .c:-.: :'"": :c--:: :c--:: :-:-:-: :-:-:1: : ,:-c. :'"": :c--:: :c--:: :c--:: :-:-:-: :eT: "c:-.: .,"""C--;"C--:, ,-:-:-:-:-:J

1 0-1 :::::::::::::,"

1 0.2 _Without companding ---.e.- Conventional Companding ---&-- Partial Companding ,1=1 !3 --e-- Partial Companding ,1=1 f6 - Partial Companding ,1=1 11 0 ---;0-- Partial Companding ,1=1 120

1 0.3 t===:::C::==�:::::L:�=::::1.. __ ---.l---.1-.Lk...;L_---.J o 5 1 0 15

SNR (dB) 20 25 30

Figure 5, Comparisons of the BER performance for different companding factor

The results in figure 4 are showing the performance of BER for different companded signals. At BER= 10-3, the

values of SNR of partial companding with factors �,�, � , � 3 6 10 20

are respectively 21.5db, 22.5db, 24and 25.2db. The value of conventional companding for the same level of BER is 25.5db.

That means; for factor f=�, to keep the BER at 10-3, the 3

required SNR is 21.5db. With lowering the threshold level the BER reaches near to the BER of conventional companding technique.

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IEEE/OSA/IAPR International Conference on Infonnatics, Electronics & Vision

Comparing with the P APR of the original signal and companding by a factor of 1110 of the maximum peak of the signal, the P APR is decreased from approximately 11.0dB to 6.0dB whereas, the BER is increased from approximately IS.OdB to 24.0dB at BER=10-3• However, when BER is reduced to 21.SdB for companding by a factor of 1/3, PAPR gets increase to 7.0dB. This denotes there is a tradeoff between BER and PAPR in this technique. Improvement of both is not possible. We have to select a certain factor of maximum peak with the specification of the system. It means system should be optimized to meet a specific application by selecting a certain threshold level.

20

- - - PSD of Partial Companding .1=1 /1 0

15 -- PSD of conventional companding '"

I 10

� � '" c '" 0 '" u '" Q. (j)

� -10 0 0-

-15

-20 -60 -40 -20 o 20 40 60

Normalized Frequency(pi rad/sample)

Figure 6. Power spectral density of partial companding and conventional companding

From the power spectral density output of conventional companding scheme and partial companding scheme shown in

figure 6, we can see; for factor, f= 2.. the side-lobs are reduced 10 than the conventional companding technique. As a result, out-of-band radiation decreases thus BER is also decreased.

V. CONCLUSION

A new technique of minimizing BER in conventional PAPR reduction scheme has been proposed and numerically analyzed. Though it can be applied to any companding scheme, we only applied it on conventional companding technique for simplicity. The improvement of the BER has been achieved by reducing the out-of-band radiation of the companded OFDM signal. On top of that its low implementation complexity, easy recovery process and lower computational time make the proposed technique attractive for real life implementation.

REFERENCES

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[4] Yajun Kou, Wu-Sheng Lu and Andreas Antoniou, "A new peak-to­average power-ratio reduction algorithm for OF OM systems via constellation extension", IEEE Trans. Wireless Communications, vol. 6, no. 5, pp. 1823-1832, May 2007.R. Nicole, "Title of paper with only first word capitalized," J. Name Stand. Abbrev., in press.

[5] Y. Yorozu, M. Hirano, K. Oka, and Y. Tagawa, "Electron spectroscopy studies on magneto-optical media and plastic substrate interface," IEEE Transl. 1. Magn. Japan, vol. 2, pp. 740-741, August 1987 [Digests 9th Annual Conf. Magnetics Japan, p. 301, 1982].

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[12] Y. Xiao, X. Lei, Q. Wen, and S. Li, "A class of low complexity PTS techniques for PAPR reduction in OF OM systems," IEEE Signal Proc. Lett., vol. 14, no. 10, pp. 680-683, Oct.2007.M. Young, The Technical Writer's Handbook. Mill Valley, CA: University Science, 1989.

[13] S. H. MUller and J. B. Huber, "OFDM with reduced peak-to--average power ratio by optimum combination of partial transmit sequences," Elect. Lett., vol. 33, no. 5, pp. 368-369, Feb. 1997.

[14] Imran Baig and Varun Jeoti, "OCT Precoded SLM Technique for PAPR Reduction in OFDM Systems",The 3rd International Conference on Intelligent & Advanced Systems (ICIAS2010) June 15-17, 2010, Kuala lumpur, Malaysia.

[15] Robert Bauml, Robert F. H. Fischer and Johannes B. Huber, "Reducing the Peak-to-Average Power Ratio of Multicarrier Modulation by Selected Mapping," Elect. Letters. vol. 32, no. 22, Oct. 1996.Y. Xiao, X. Lei, Q. Wen, and S. Li, "A class of low complexity PTS techniques for PAPR reduction in OFDM systems," IEEE Signal Proc. Lett., vol. 14, no. 10, pp. 680-683, Oct.2007.M. Young, The Technical Writer's Handbook. Mill Valley, CA: University Science, 1989.

[16] Thomas G. Pratt, Nathan Jones, Leslie Smee, and Michael Torrey, Thesis on " OFDM Link Performance with Companding for PAP Ratio Reduction in the Presence of Non-Linear Amplification", Georgia Tech Research Institute

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