Compensation of Nonlinear Distortion in OFDM Systems Using an Efficient Evaluation Technique

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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, R.Sundaraguru,
Professor, Department of ECE, Research Scholar, Department of ICE,
Thiagarajar College of Engineering, Anna University Chennai,
Madurai - 15, India. Chennai-25, India.

Abstract— Orthogonal Frequency Division Multiplexing (OFDM) proposed in [6], which compensates the nonlinearity at the
signal with larger peak to average power ratio (PAPR) will cause receiver, but the channel response isn’t accurate. The
the undesirable spectrum re-growth and performance algorithm proposed in [7] can mitigate the nonlinear distortion
degradation in bit error rate (BER), both due to the inter- and gives better BER performance with the assumption of
modulation products occurring in the nonlinear amplifier at the
transmitter. This paper proposes a new approach to compensate
attenuation coefficient is equal to 1, which is not true
the nonlinearity introduced by the HPA. By approximating the according to Bussgang’s theorem. In this paper a new adaptive
attenuation coefficient of HPA model, the distortion is estimated, method is proposed, in which the BER performance improved
and then it is subtracted from the received symbol at the receiver. with moderate complexity in the system.
By performing several iterations, the estimation of the distortion The remainder of this paper is organized as follows. In
becomes more accurate, and cancels the nonlinear distortion. Section II, the OFDM transmission system model with
Simulation results show that the presented scheme is more nonlinearity is discussed. The proposed compensation
efficient to compensate the nonlinear distortion in OFDM technique is introduced in Section III. Section IV presents the
systems. simulation results. Conclusions are drawn in section V.
Keywords— Orthogonal Frequency division Multiplexing (OFDM),
Nonlinear Distortion (NLD), High Power Amplifier (HPA), Bit
Error Rate (BER), Peak to Average Power Ratio (PAPR). II. OFDM SYSTEM MODEL

I. INTRODUCTION

OFDM has attracted considerable interest among
communication system designers because of its high spectrum
efficiency and robustness to severe multipath fading and it is
widely used in high speed digital communications such as Fig.1 Baseband equivalent OFDM system
digital video broadcasting (DVB), digital audio broadcasting
(DAB), digital subscriber line (DSL) and digital HDTV Fig.1 shows the baseband-equivalent functional block
broadcasting systems [1], [2], [3]. However, due to the large diagram of the OFDM transmission system. The QAM signal
dynamic range of the modulated signal, OFDM is very generator produces complex symbols with independent,
sensitive to nonlinear distortions both in the high power identically distributed random in-phase and quadrature
amplifier (HPA) stages of the transmitter and in the channel. components from the finite alphabet set. The serial-to-parallel
The nonlinearity causes (i) spectral-spreading of the OFDM block converts the QAM input data stream into a block of N
signal and (ii) intermodulation between subcarriers which symbols, which in turn modulate the corresponding subcarrier.
seriously degrade the system performance. To overcome the The Nyquist rate sampled OFDM signal is described as,
linearization challenges at the transmitter, several digital
predistortion schemes have been proposed [4], [5]. The basic
N−1

∑
idea behind these techniques relies on modeling the ⎛ j 2πkn⎞
⎜ ⎟
nonlinearity in HPA and its inverse function first and then 1 ⎝ N ⎠
sn = Sk e , n = 0,1,L,N − 1,
passing the transmitted signal (before HPA) through the N (1)
inverse nonlinearity (pre-distorter). However, in order to k=0
implement the adaptive predistortion technique in OFDM
systems, a large amount of RAM is required, whose contents According to the central limit theorem if the number of
are updated with low convergence speeds. One recent solution subcarriers is large, the signal can be approximated as a
of this problem is decision-added compensation method Gaussian distributed random variable. Using Bussgang’s

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ISSN 1947-5500
(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 linear model of the OFDM transmission with nonlinearity
as the sum of an attenuated input replica and an uncorrelated consists of a complex gain ‘α’, and an uncorrelated additive
distortion term [8], [9]. Gaussian distortion [10], [11]. The performance of this system
is evaluated in the same way as an AWGN channel.
~ = αs + d
s
n n n (2) III. PROPOSED MODEL

where dn is the distortion term, and ‘α’ is the attenuation
Fig. 2 shows the block diagram of a proposed compensation
coefficient, which is described as,
technique. The receiver works in an iterative fashion that the

{ }
attenuation coefficient ‘α’ of transmitting HPA model is
∗
E ~n s n
s estimated using the training sequence, which gives the
α= imitation of nonlinear distortion components, at last use the
⎧ 2⎫ replica to cancel the nonlinear distortion components in the
E⎨ sn ⎬
received symbols.
⎩ ⎭ (3)

The transmitter and receiver shaping filters have the frequency
response Gt and Gr respectively,

Gt ( f ) = G r ( f ) = G ( f ),
(4)

where G(f) denotes a raised-cosine Nyquist pulse. The
Fig.2 Proposed Model to Compensate Nonlinear Distortion
spectrally shaped signal at the output of the transmit filter is
fed through the HPA and the channel. The auto-correlation
Based on the proposed system the nonlinear signal can be
function of the output signal can be written as,
expressed as the sum of the attenuated linear signal αsn and the
nonlinear distortion dn.
2
R ~~ = α R + R
ss ss dd (5) d n = ~n − αs n
s
(10)
Equation (5) can be used to derive the power of distortion for
different subcarriers. At the receiver, the output of the FFT The estimated nonlinear distortion term dn is subtracted
block gives a set of decision variables. 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
S = αS + D
k k k (6) output after nonlinear compensation is represented as,

s n = rn − d n ∗ h(n )
(11)
N −1

∑
2πkn
1 −j
Sk = sn e N Finally the proposed adaptive algorithm will be more
N effective and compensate the nonlinear distortion.
(7)
n =0
IV. SIMULATION RESULTS

N −1

∑
2 πkn Only AWGN is assumed to be present in the channel.
1 −j
The numbers of IFFT and sub-carriers points are 1024 and 512
Dk = dne N
N respectively. A widely accepted HPA model is a nonlinear
(8)
n =0 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
~ = αs ∗ h(n ) + d ∗ h(n ) + n
r A [·] and Φ [·] represents the AM/AM and AM/PM
n n n k (9) conversions, respectively. Two nonlinear HPA models have
been adopted for simulation. A travelling wave tube amplifier
where h(n) is the channel response assumed to be perfectly (TWTA) with strong AM/AM and AM/PM conversions, are
known, and nk is the channel noise. Therefore the equivalent given by [12],

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ISSN 1947-5500
(IJCSIS) International Journal of Computer Science and Information Security,
Vol. 9, No. 6, June 2011
ρ
[ ] 2
Α ρ = Α sat
2 2
(12)
ρ + Α sat

2
π ρ
[ ]
Φ ρ = (13)
2
3 ρ 2 + A sat

and for solid state power amplifier (SSPA)

[ ]= ρ (14)
[1 + ( ρ ]
A ρ ,
2ρ 1 2ρ
Ao ) Fig. 4 BER versus SNR for 16QAM when IBO=8dB

Φ [ρ ] = 0 (15) 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].
where Asat 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 = Asat / 2 and for SSPA, Ao =
Asat / 2 . The effect of the nonlinear amplifier depends on the
operating 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.

2
As (16)
IBO = 10 log
Pin

2
Ao (17)
IBO = 10 log Fig. 5 BER versus IBO for 16QAM when SNR =20dB
Pout

2
where As is the input power at the saturation point, Pin is the In Fig. 5, it is observed that the IBO of the compensated
2
signals with SSPA can be improved more than 1 dB compared
average input power, Ao is the maximum output power, and with the algorithm proposed in [7].
Pout is the average output power.

Fig.3 BER versus SNR for 16QAM when IBO=1dB Fig. 6 BER versus IBO for 16QAM when SNR =25dB

Fig.3 shows the BER performance under the ideal AWGN Fig.6 shows the IBO of the compensated signals with
channel without SSPA. With SSPA, the performance of the TWTA can be improved about 2 dB compared with algorithm
SNR is improved about 5 dB compared with algorithm in [7]. proposed in [7].

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V. CONCLUSIONS for MIMO-OFDM systems with nonlinear channel” Proceedings of
‘International Symposium on Intelligent Signal processing and
In this paper, a new adaptive algorithm is proposed at the Communication Systems,’ pp.113-116, Dec 2005.
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systems. By performing several iterations, the estimated compensation in OFDM system,” IEE International conference on
Signal Processing for Communications. Hangzhou, China, pp. 939-942,
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received signal. This paper presented various computer [8] P. Banelli and S. Cacopardi “Theoretical analysis and performance of
simulation results to verify the effectiveness of proposed OFDM signals in nonlinear AWGN channels,” in IEEE Transactions on
method. From the computer simulation results, it is confirmed Communications, vol. 48, no. 3, pp. 430–441, March 2000.
that the presented method could achieve the higher [9] A. Papoulis Probability, random variables, and stochastic processes,
transmission data rate with better BER performance. 3rd ed. New York: McGraw-Hill, 1991.
[10] A. Behravan, F. Munier, T. Svensson, M. Flament,T. Eriksson, A.
For future works, these techniques will be applied to more Svensson and H. Zirath “System implications in designing a 60 GHz
complex MIMO systems. WLAN RF frontend,” in Proc. GHz2001 Symposium, Lund, Sweden,
Nov. 2001.
REFERENCES [11] E. Costa and S. Pupolin “M-QAM-OFDM system performance in the
presence of a nonlinear amplifier and phase noise,” in IEEE
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[4] H. Kang, Y. Cho and D.Youn, “On compensating nonlinear distortions
Dr.R.Sukanesh- Professor, Department of Electronics and Communication
of an OFDM system using an efficient adaptive predistorter," IEEE
Engineering, working at Thiagarajar College of Engineering, affiliated to
Trans. Commun., vol. COM-47, no. 4, pp. 522-526, Apr. 1999.
Anna University of Technology, Madurai. She is doing research in the area of
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[6] Shouyi Yang, Jiangtao Xi, Fang Wang, Xiaomin Mu and Hideo Engineering field, doing research at Anna University Chennai. His area of
Kobayashi “Decision aided compensation of residual frequency offset interest is interference suppression in wireless OFDM systems.

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