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(IJCSIS) International Journal of Computer Science and Information Security,Vol. 9, No. 6, June 2011 

Compensation of Nonlinear Distortion in OFDM

Systems Using an Efficient Evaluation Technique

Dr. (Mrs.).R.Sukanesh, 

Professor, Department of ECE,Thiagarajar College of Engineering,

Madurai - 15, India.

R.Sundaraguru, 

Research Scholar, Department of ICE,Anna University Chennai,

Chennai-25, India. 

 Abstract— Orthogonal Frequency Division Multiplexing (OFDM)

signal with larger peak to average power ratio (PAPR) will cause

the undesirable spectrum re-growth and performance

degradation in bit error rate (BER), both due to the inter-

modulation products occurring in the nonlinear amplifier at the

transmitter. This paper proposes a new approach to compensate

the nonlinearity introduced by the HPA. By approximating the

attenuation coefficient of HPA model, the distortion is estimated,

and then it is subtracted from the received symbol at the receiver.

By performing several iterations, the estimation of the distortionbecomes more accurate, and cancels the nonlinear distortion. Simulation results show that the presented scheme is more

efficient to compensate the nonlinear distortion in OFDM

systems.

 Keywords— Orthogonal Frequency division Multiplexing (OFDM),

  Nonlinear Distortion (NLD), High Power Amplifier (HPA), Bit

 Error Rate (BER), Peak to Average Power Ratio (PAPR).

I.  INTRODUCTION

OFDM has attracted considerable interest among

communication system designers because of its high spectrumefficiency and robustness to severe multipath fading and it is

widely used in high speed digital communications such as

digital video broadcasting (DVB), digital audio broadcasting

(DAB), digital subscriber line (DSL) and digital HDTV broadcasting systems [1], [2], [3]. However, due to the large

dynamic range of the modulated signal, OFDM is very

sensitive to nonlinear distortions both in the high power 

amplifier (HPA) stages of the transmitter and in the channel.The nonlinearity causes (i) spectral-spreading of the OFDM

signal and (ii) intermodulation between subcarriers which

seriously degrade the system performance. To overcome the

linearization challenges at the transmitter, several digital

 predistortion schemes have been proposed [4], [5]. The basicidea behind these techniques relies on modeling the

nonlinearity in HPA and its inverse function first and then

  passing the transmitted signal (before HPA) through theinverse nonlinearity (pre-distorter). However, in order to

implement the adaptive predistortion technique in OFDM

systems, a large amount of RAM is required, whose contents

are updated with low convergence speeds. One recent solutionof this problem is decision-added compensation method

  proposed in [6], which compensates the nonlinearity at the

receiver, but the channel response isn’t accurate. Thealgorithm proposed in [7] can mitigate the nonlinear distortion

and gives better BER performance with the assumption of 

attenuation coefficient is equal to 1, which is not true

according to Bussgang’s theorem. In this paper a new adaptive

method is proposed, in which the BER performance improvedwith moderate complexity in the system.

The remainder of this paper is organized as follows. InSection II, the OFDM transmission system model with

nonlinearity is discussed. The proposed compensationtechnique is introduced in Section III. Section IV presents the

simulation results. Conclusions are drawn in section V.

II.  OFDM SYSTEM MODEL

Fig.1 Baseband equivalent OFDM system

Fig.1 shows the baseband-equivalent functional block 

diagram of the OFDM transmission system. The QAM signalgenerator produces complex symbols with independent,

identically distributed random in-phase and quadrature

components from the finite alphabet set. The serial-to-parallel

 block converts the QAM input data stream into a block of  N 

symbols, which in turn modulate the corresponding subcarrier.

The Nyquist rate sampled OFDM signal is described as,

 ,S  N 

 ,N  , ,n N 

π kn j N 

k 

k n  ,e s 110

21

0

1−=

⎟ ⎠

 ⎞⎜⎝ 

⎛ −

=

∑= L

(1)

According to the central limit theorem if the number of 

subcarriers is large, the signal can be approximated as a

Gaussian distributed random variable. Using Bussgang’s

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(IJCSIS) International Journal of Computer Science and Information Security,Vol. 9, No. 6, June 2011 

theorem the signal at the output of nonlinearity can be written

as the sum of an attenuated input replica and an uncorrelated

distortion term [8], [9].

nd 

nα s

n s +=~

(2)

where d n is the distortion term, and ‘α’ is the attenuation

coefficient, which is described as,

⎭⎬⎫

⎩⎨⎧

∗

=2

~

n

nn

 s E 

 s s E α

(3)

The transmitter and receiver shaping filters have the frequency

response Gt  and Gr respectively,

( ) ( ) ( ), f G f r G f t G ==(4)

where G(f) denotes a raised-cosine Nyquist pulse. The

spectrally shaped signal at the output of the transmit filter is

fed through the HPA and the channel. The auto-correlationfunction of the output signal can be written as,

dd  R

 ss Rα

 s s R +=

2~~

(5)

Equation (5) can be used to derive the power of distortion for 

different subcarriers. At the receiver, the output of the FFT block gives a set of decision variables.

k  D

k S 

k S  += α 

~

(6)

 N 

kn j

 N 

n

nk  e s N 

S 

π  21

0

1 −−

=

∑=(7)

 N 

π kn j

 N 

n

nk  ed  N  D

21

0

1 −−

=∑=

(8)

( ) ( )k 

nnhn

d nhn

α sn

r  +∗+∗=~

(9)

where h(n) is the channel response assumed to be perfectly

known, and nk  is the channel noise. Therefore the equivalent

linear model of the OFDM transmission with nonlinearity

consists of a complex gain ‘α’, and an uncorrelated additive

Gaussian distortion [10], [11]. The performance of this system

is evaluated in the same way as an AWGN channel.

III.  PROPOSED MODEL

Fig. 2 shows the block diagram of a proposed compensationtechnique. The receiver works in an iterative fashion that theattenuation coefficient ‘α’ of transmitting HPA model is

estimated using the training sequence, which gives theimitation of nonlinear distortion components, at last use the

replica to cancel the nonlinear distortion components in the

received symbols.

Fig.2 Proposed Model to Compensate Nonlinear Distortion

Based on the proposed system the nonlinear signal can be

expressed as the sum of the attenuated linear signal α sn and the

nonlinear distortion d n.

nnn α s sd  −= ~(10)

The estimated nonlinear distortion term d n is subtracted

from the current channel observation to obtain the refined

channel signal. By taking the advantage of training sequence,

it is possible to get more accurate channel response. So the

output after nonlinear compensation is represented as,

( )nhd r  s nnn ∗−=(11)

Finally the proposed adaptive algorithm will be moreeffective and compensate the nonlinear distortion. 

IV.  SIMULATION RESULTS

Only AWGN is assumed to be present in the channel.

The numbers of IFFT and sub-carriers points are 1024 and 512respectively. A widely accepted HPA model is a nonlinear 

memoryless model, in which transformation carried between

the complex envelope of the input and output signals [11],[12]. It can be defined as f[  ρ ] = A[  ρ ] ·e  jΦ[  ρ ], where the function  A [·] and Φ [·] represents the AM/AM and AM/PM

conversions, respectively. Two nonlinear HPA models have been adopted for simulation. A travelling wave tube amplifier 

(TWTA) with strong AM/AM and AM/PM conversions, are

given by [12],

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[ ]2

 Α2

 ρ

 ρ2 Α ρ Α

 sat 

 sat +

= (12)

[ ]2

 sat  A2

 ρ

2 ρ

3

π  ρΦ

+= (13)

and for solid state power amplifier (SSPA)

[ ]( )[ ]

,212

1 ρ ρ

o A ρ

 ρ ρ A

+

=(14)

[ ] 0= ρΦ (15)

where  A sat  is the input saturation voltage,  Ao is the output

saturation voltage, and ‘ρ’ is the parameter that controls the

smoothness of the transition from linear region to saturation

region. In the case of TWTA, Ao = A sat  / 2 and for SSPA, Ao =

 A sat  / 2 . The effect of the nonlinear amplifier depends on theoperating point, which is the average power of the input

signals. Input backoff (IBO) and output backoff (OBO) [8] are

two common parameters to verify the nonlinear distortion.

in P 

 s A IBO

2

log10= (16)

out  P 

o A IBO

2

log10= (17)

where 2 s A  is the input power at the saturation point, P in is the

average input power,2o A is the maximum output power, and

 P out is the average output power.

Fig.3 BER versus SNR for 16QAM when IBO=1dB

Fig.3 shows the BER performance under the ideal AWGNchannel without SSPA. With SSPA, the performance of the

SNR is improved about 5 dB compared with algorithm in [7]. 

Fig. 4 BER versus SNR for 16QAM when IBO=8dB

Fig. 4 shows the BER performance under the ideal AWGN

channel without TWTA. With TWTA, the SNR performance

is improved more than 6 dB compared with algorithm in [7].

Fig. 5 BER versus IBO for 16QAM when SNR =20dB

In Fig. 5, it is observed that the IBO of the compensatedsignals with SSPA can be improved more than 1 dB compared

with the algorithm proposed in [7].

Fig. 6 BER versus IBO for 16QAM when SNR =25dB

Fig.6 shows the IBO of the compensated signals with

TWTA can be improved about 2 dB compared with algorithm

 proposed in [7].

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V.  CONCLUSIONS

In this paper, a new adaptive algorithm is proposed at the

receiver to compensate the nonlinearity of the HPA in OFDM

systems. By performing several iterations, the estimated

distortion becomes more accurate and it is subtracted from the

received signal. This paper presented various computer simulation results to verify the effectiveness of proposed

method. From the computer simulation results, it is confirmedthat the presented method could achieve the higher transmission data rate with better BER performance.

For future works, these techniques will be applied to more

complex MIMO systems.

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digital terrestrial TV broadcasting," IEEE Commun. Mag., vol. 33, pp.100-109, Feb. 1995.

[2]  B. Le Floch, R. Halert-Lasalle and D. Castellain, “Digital audio

 broadcasting to mobile receivers," IEEE Trans. Consumer Electronics.,vol. 35, pp. 493-503, Aug. 1989.

[3]  R. Van Nee and R. Prasad, “OFDM Wireless Multimedia

Communications," Artech House, 1999.[4]  H. Kang, Y. Cho and D.Youn, “On compensating nonlinear distortions

of an OFDM system using an efficient adaptive predistorter," IEEETrans. Commun., vol. COM-47, no. 4, pp. 522-526, Apr. 1999.

[5]  G. Karam and H. Sari, “A data predistortion techniques with memory for QAM radio systems," IEEE Trans. Commun., vol. COM-39, pp. 336-

344, Feb. 1991.

[6]  Shouyi Yang, Jiangtao Xi, Fang Wang, Xiaomin Mu and HideoKobayashi “Decision aided compensation of residual frequency offset

for MIMO-OFDM systems with nonlinear channel” Proceedings of ‘International Symposium on Intelligent Signal processing and

Communication Systems,’ pp.113-116, Dec 2005.

[7]  Jing Yang, Xiaomin Mu, Shouyi Yang, Lin Qi, “Algorithm of nonlinear compensation in OFDM system,” IEE International conference on

Signal Processing for Communications. Hangzhou, China, pp. 939-942,

 Nov 2006.

[8]  P. Banelli and S. Cacopardi “Theoretical analysis and performance of 

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Communications, vol. 48, no. 3, pp. 430–441, March 2000.[9]  A. Papoulis   Probability, random variables, and stochastic processes,

3rd ed. New York: McGraw-Hill, 1991.

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Svensson and H. Zirath “System implications in designing a 60 GHz

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[11]  E. Costa and S. Pupolin “M-QAM-OFDM system performance in the

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[12]  A.A.M. Saleh, “Frequency-independent and frequency-dependent

nonlinear models for TWT amplifiers,”   IEEE Transactions onCommunications, vol-COM -29, no.11, pp.1715–1720, Nov.1981.

AUTHORS PROFILE

Dr.R.Sukanesh- Professor, Department of Electronics and Communication

Engineering, working at Thiagarajar College of Engineering, affiliated to

Anna University of Technology, Madurai. She is doing research in the area of 

neural network based parameter identification applied to bio-medical systems.

R.Sundaraguru - PhD research scholar in Information and Communication

Engineering field, doing research at Anna University Chennai. His area of 

interest is interference suppression in wireless OFDM systems. 

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