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X. Cheng, W. Li, and T. Znati (Eds.): WASA 2006, LNCS 4138, pp. 416 423, 2006. © Springer-Verlag Berlin Heidelberg 2006 A Novel Analog Pre-distorter of TWTA Non-linearity in High Power Satellite Transmitters Rafik Zayani 1,2 and Ridha Bouallegue 2,3 1 Institut Supérieur d’Informatique / ISI 2 Unité de recherches Systèmes de Télécommunications / 6’Tel à Sup’Com 3 Ecole Nationale d’Ingénieur de Sousse / ENISo [email protected] [email protected] http://membres.lycos.f/ridhabouallegue Abstract. OFDM systems are susceptible to HPA non-linearities in particular because of their large peak-to-average power ratios (PAPR). Several pre- distortion or post-distortion schemes for compensation these effects of nonlinearities in communications systems have been studied recently. In this paper, we present a new analog pre-distorter to enhance the power efficiency of satellite OFDM transmitters using TWT amplifiers. This conceptually simple technique can in linearize a HPA system quite well, if the pre-distorter and main amplifier are sufficiently well matched. In addition, the performance of the new pre-distortion scheme for OFDM systems is evaluated in terms of spectrum and total degradation BER. Simulation results also show that our pre-distortion scheme is efficient in compensating the non-linear distortion of HPAs. Keywords: OFDM, Pre-distorter, HPA, TWTA, SSPA. 1 Introduction Currently, orthogonal frequency division multiplexing (OFDM) is utilized as an essential part for asymmetric digital subscriber line (ADSL) and digital audio broadcasting (DAB) [1], [2]. Moreover, OFDM is expected to be a strong candidate for wireless multimedia systems [3]. However, multicarrier systems such as OFDM show great sensitivity to nonlinear distortion. The OFDM structure requires a summation of a large number of sub- carriers for multicarrier modulation, and as a result of this summation, large signal envelope fluctuations occur. These fluctuations cause OFDM systems to be very sensitive to nonlinear distortion introduced by the high power amplifier (HPA) at the transmitter. This distortion can be mitigated by backing off the HPA from saturation; however, back off reduces the HPA output power [4] [5]. A complicated pre-distortion technique was proposed for systems using high power amplifiers (HPA) to compensate for the non-linearity. The concept is to distort the input signals to the HPA with an inverse function of the HPA non-linearity and to generate linearly amplified signals at the HPA output.

[Lecture Notes in Computer Science] Wireless Algorithms, Systems, and Applications Volume 4138 || A Novel Analog Pre-distorter of TWTA Non-linearity in High Power Satellite Transmitters

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Page 1: [Lecture Notes in Computer Science] Wireless Algorithms, Systems, and Applications Volume 4138 || A Novel Analog Pre-distorter of TWTA Non-linearity in High Power Satellite Transmitters

X. Cheng, W. Li, and T. Znati (Eds.): WASA 2006, LNCS 4138, pp. 416 – 423, 2006. © Springer-Verlag Berlin Heidelberg 2006

A Novel Analog Pre-distorter of TWTA Non-linearity in High Power Satellite Transmitters

Rafik Zayani1,2 and Ridha Bouallegue2,3

1 Institut Supérieur d’Informatique / ISI 2 Unité de recherches Systèmes de Télécommunications / 6’Tel à Sup’Com

3 Ecole Nationale d’Ingénieur de Sousse / ENISo [email protected]

[email protected] http://membres.lycos.f/ridhabouallegue

Abstract. OFDM systems are susceptible to HPA non-linearities in particular because of their large peak-to-average power ratios (PAPR). Several pre-distortion or post-distortion schemes for compensation these effects of nonlinearities in communications systems have been studied recently.

In this paper, we present a new analog pre-distorter to enhance the power efficiency of satellite OFDM transmitters using TWT amplifiers.

This conceptually simple technique can in linearize a HPA system quite well, if the pre-distorter and main amplifier are sufficiently well matched.

In addition, the performance of the new pre-distortion scheme for OFDM systems is evaluated in terms of spectrum and total degradation BER. Simulation results also show that our pre-distortion scheme is efficient in compensating the non-linear distortion of HPAs.

Keywords: OFDM, Pre-distorter, HPA, TWTA, SSPA.

1 Introduction

Currently, orthogonal frequency division multiplexing (OFDM) is utilized as an essential part for asymmetric digital subscriber line (ADSL) and digital audio broadcasting (DAB) [1], [2]. Moreover, OFDM is expected to be a strong candidate for wireless multimedia systems [3].

However, multicarrier systems such as OFDM show great sensitivity to nonlinear distortion. The OFDM structure requires a summation of a large number of sub-carriers for multicarrier modulation, and as a result of this summation, large signal envelope fluctuations occur. These fluctuations cause OFDM systems to be very sensitive to nonlinear distortion introduced by the high power amplifier (HPA) at the transmitter. This distortion can be mitigated by backing off the HPA from saturation; however, back off reduces the HPA output power [4] [5].

A complicated pre-distortion technique was proposed for systems using high power amplifiers (HPA) to compensate for the non-linearity.

The concept is to distort the input signals to the HPA with an inverse function of the HPA non-linearity and to generate linearly amplified signals at the HPA output.

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A Novel Analog Pre-distorter of TWTA Non-linearity 417

Therefore, some schemes for non-linear compensation is desirable to simultaneously reduce nonlinear distortion and the amount of back off required. Pre-distortion is one way to achieve these goals.

In this paper, we present a new analog pre-distortion scheme for compensation of nonlinear distortion in OFDM systems. The proposed pre-distortion technique connects a pre-distorting amplifier in front of the main amplifier. Compared to the compressive main amplifier, the additional has the opposite output distortion characteristic.

The results also demonstrate that our pre-distortion scheme can compensate nonlinear distortion effectively with a simple structure.

The remainder of this paper is organized as follows. In section 2, we present a description of the proposed scheme. In section 3 and 4, we describe the non-linear model for high power amplifier and pre-distorter model respectively. Section 5 presents and discusses the simulation results. The last section shows the conclusions.

2 Proposed OFDM System

The basic idea of OFDM is to transmit data on parallel QAM (Quadrature Amplitude Modulation) or QPSK (Quadrature Phase Shift Keying) modulated sub-carriers. Let N be the number of sub-carriers, Ck, k=0…N-1 the N complex symbols to be transmitted simultaneously, and TS the OFDM symbol duration. The complex envelope of the ODFM base band signal is:

1 2

0

( )tN i k

Tsk

k

S t C eπ−

=

=∑ (1)

Fig. 1. Transmitter of an OFDM system with pre-distorter

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418 R. Zayani and R. Bouallegue

The OFDM symbol can be easily generated using a IFFT algorithm, and the reception can be done with a FFT to recover the Ck symbols. The most interesting property of OFDM is that the channel equalization can be done in the frequency domain, after the FFT, and is a simple multiplication of the Ck

symbols. The OFDM system under consideration has a pre-distorter in the transmitter to

compensate for nonlinear distortion of the HPA as indicated in Fig1. The following figure presents the instantaneous amplitude of an OFDM signal

(with 16-QAM modulation).

Fig. 2. Instantaneous amplitude of an OFDM system with 16-QAM modulation

3 Non-linearity Models

Power amplifiers are typically the most power-hungry components of RF transceivers. The design of PAs, especially for linear, low-voltage operations, remains a difficult problem defying an elegant solution. Two type’s amplifiers are mostly used in communication: TWT and SSPA. TWT is mostly used for high power satellite transmitters while SSPA is used in many other applications including mobile transmitters because of its small size. Several previous papers used saleh’s model to analyze the HPA [6,7].

The complex output of RF with non-linear distortion can be expressed as:

[ ] { }( ) ( ( ))( ) ( )

j t tx t f t e

ϕ φ ρρ

+= (2)

Where ( )tρ and ( )tϕ are the amplitude and phase of the input signal. The

measured AM/AM and AM/PM for TWT is well presented by saleh’s model [3] as:

Page 4: [Lecture Notes in Computer Science] Wireless Algorithms, Systems, and Applications Volume 4138 || A Novel Analog Pre-distorter of TWTA Non-linearity in High Power Satellite Transmitters

A Novel Analog Pre-distorter of TWTA Non-linearity 419

2

2 2

( ( )) ( ) /(1 ( ) )

( ( )) ( ) /(1 ( ) )

⎧ = +⎪⎨

= +⎪⎩

A Af t t t

t t tφ φ

ρ α ρ β ρ

φ ρ α ρ β ρ (3)

While SSPA’s AM/AM and AM/PM can be captured by [8,9]:

[ ][ ]

2 1/ 2max( ) ( ) /[1 ( ( ) / ) ]

( ) 0

p pf t t t A

t

ρ ρ ρφ ρ

⎧ = +⎪⎨

=⎪⎩ (4)

Here maxA is the maximum output amplitude and the parameter p controls the

smoothness of the transition from the linear region to the limiting region. [4] Among the models available, here we will concentrate in describing the well-

known Saleh Model for TWT memory-less HPAs, which is in fact the most commonly used in the literature and thence will be applied later in our Pre-distorter model.

3.1 Saleh Model for TWT HPAs

In the expressions above, we choose to set the signal gain term to 2Aα = , while

1A φβ β= = and / 3φα π= , so that the input saturation voltage 1/s AA β=

and the maximum output amplitude [ ]{ }max max ( ) / 2A sA f x t Aα= = .

The corresponding AM/AM and AM/PM curves so scaled are depicted in the following figure.

Fig. 3. AM/AM and AM/PM normalized transfer characteristics of the Saleh model for memory-less TWT HPAs

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420 R. Zayani and R. Bouallegue

4 Analog Pre-distorter

The analog pre-distortion technique connects a pre-distorting amplifier in front of the main amplifier. Compared to the compressive main amplifier, this additional amplifier has the opposite output distortion characteristic, i.e. its nonlinearity is expansive, not compressive. These two nonlinear distortions cancel each other when summed, resulting in a linear and distortion-free output from the main RF amplifier.

Fig. 4. Simplified pre-distorter for linearization of HPA with memory

As in figure 4, the purpose of pre-distortion is to find another pre-distortion function ( )g x , so that the overall effect of signal output will be linear as,

( ) ( ( )) ( ( ( )) ( )y t f x t f g s t Cs t= = ≈% (5)

The formulation of the pre-distortion, is obtained by replacing the saturation input

amplitude 1/s AA β= in the expression (3). This gives

2

22

( )( ( ))

( )s A

s

A x tf x t

A x t

α=+

(6)

Whence we can find an AM/AM transfer inverse function [ ]1 .f − by solving (7) for

1( ( ))x f f x−= . Some straightforward algebraic steps lead us to directly obtain:

221 2( ) 1 1

2A s

tA s

A sf s

s A

αα

−⎡ ⎤⎛ ⎞⎢ ⎥= − − ⎜ ⎟⎢ ⎥⎝ ⎠⎣ ⎦

(7)

Where it is important to note that this inversion will be valid only within the

interval{ } { }0 / 2 0 1A ss A sα≤ ≤ ≡ ≤ ≤ .

As show in figure 2, the maximal amplitude of an OFDM signal doesn't pass 1,

{ }0 ( ) 1s t≤ ≤ .

Page 6: [Lecture Notes in Computer Science] Wireless Algorithms, Systems, and Applications Volume 4138 || A Novel Analog Pre-distorter of TWTA Non-linearity in High Power Satellite Transmitters

A Novel Analog Pre-distorter of TWTA Non-linearity 421

Wherein the AM/PM correction requires that:

( )1( )x f x−⎡ ⎤Ψ = −Φ ⎣ ⎦ (8)

The corresponding AM/AM and AM/PM transfer characteristics of pre-distorter,

valid for the normalized Saleh’s HPA model in the interval{ }0 1, , is shown in the

following figure.

Fig. 5. AM/AM et AM/PM theoretical pre-distortion characteristics for the Saleh model

5 Simulations and Results

To simulate an OFDM system, the Matlab tool has been chosen at the level by reason of her performances of calculation and her suppleness.

The performance of the proposed pre-distorter is analyzed in an OFDM system with 48 carriers (which corresponds to the used modulation in the networks HiperLan/2) [7] and 512 carriers. We used 16-QAM modulation scheme.

We also used the model in (3) with 2 1= =A Aandα β in the model of TWT

amplifier. The Bit Error Rate (BER) of such system vs. the Signal to Noise Ratio (SNR) is

presented in the following figure, by the bend 'with corr'. The curve by the bend 'without corr' presents the BER of the same system without pre-distorter whereas the 'theory' curve concerns linear systems.

Page 7: [Lecture Notes in Computer Science] Wireless Algorithms, Systems, and Applications Volume 4138 || A Novel Analog Pre-distorter of TWTA Non-linearity in High Power Satellite Transmitters

422 R. Zayani and R. Bouallegue

Fig. 6. Bit Error Rate of the OFDM system vs. SNR: a QAM16 modulation is used on 48 carriers

Fig. 7. Bit Error Rate of the OFDM system vs. SNR : a QAM16 modulation is used on 512 carriers

Page 8: [Lecture Notes in Computer Science] Wireless Algorithms, Systems, and Applications Volume 4138 || A Novel Analog Pre-distorter of TWTA Non-linearity in High Power Satellite Transmitters

A Novel Analog Pre-distorter of TWTA Non-linearity 423

We note a real improvement of the quality of the transmission using the corrector which brings a gain of 12 dB for BER = 10-1.

While increasing the number of carriers, we determine by simulation that our pre-distorter still be efficient that is for 512 carriers.

6 Conclusion

We have proposed a non-linear per-distorter to compensate non-linearity in OFDM satellite transmitters using TWT amplifier.

This conceptually simple technique can in linearize a HPA system quite well, if the pre-distorter and main amplifier are sufficiently well matched. Because of its open-loop nature, there are no stability issues and the usable bandwidth is much greater than that of closed-loop feedback systems. Because of its simplicity, this technique can be applied to microwave circuits without too great difficulties.

Simulation shows promising performance in terms of spectrum and BER.

References

[1] L. J. Cimini, «Analysis and simulation of a digital mobile channel using orthogonal frequency division multiplexing», IEEE Trans. Communications, vol. 33, no. 7, pp. 665–675, July 1985.

[2] S. Chang and E. J. Powers, «A simplified predistorter for Compensation of nonlinear distortion in OFDM Systems», IEEE transaction 2001.

[3] N. D’Andrea, V. Lottici and R. Reggiannin, «Nonlinear Predistortion of OFDM Signals over Frequency-Selective Fading Channels», IEEE Transactions on Communications. Vol. 49. N° 5. pp. 837-843. 2001.

[4] A. E. Jones, T. A. Wilkinson, S. K. Barton, «Block Coding Scheme for Reduction of Peak to Mean Envelop Power Ratio of Multicarrier Transmission Schemes», IEE Electronics Letters, vol. 30, no. 25, pp. 2098-2099, 1994

[5] R. zayani, S. Zid, R. Bouallegue, « Simulateur des non-linéarités HPA sur un système OFDM » OHD Conference, septembre 2005.

[6] Lei Ding, «Digital Predistortion of Power Amplifiers for Wireless Applications», a Thesis presented to the Academic Faculty, March 2005.

[7] V. Ahirwar and B. S. Rajan, « Tradeoff between PAPR Reduction and Decoding complexity in transformed OFDM System», IEEE transaction 2005.

[8] R. J. Baxley, « Analyzing Selected Mapping for Peak-to-Average Power Reduction in OFDM», a Thesis presented to the Academic Faculty, May 2005.

[9] J. G. WÄohlbier, «Nonlinear Distortion and Suppression In Traveling Wave Tubes: Insights And Methods », a Thesis presented to the Academic Faculty, 2003.�