Digital predistortion for RSOAs as external modulators in radio over fiber systems

Digital predistortion for RSOAs as external modulators in radio over fiber systems

Zhansheng Liu, Manuel Alberto Violas,* and Nuno Borges Carvalho

Instituto de Telecomunicações, Dep. Electrónica Telecomunicaçãoes e Inofrmática, Universidade de Aveiro, Campus Universitário de Santiago, Aveiro 3810-193, Portugal

*[email protected]

Abstract: Reflective semiconductor optical amplifiers (RSOAs) can be used as external modulators in radio over fiber (RoF) links due to their amplification and modulation characteristics and colorless property. The nonlinear distortion of RSOA, however, limits its dynamic range. In this paper we demonstrate digital predistortion (DPD) linearization techniques to improve the linearity of RSOA external modulators. 64 quadrature amplitude modulation (QAM) signals are utilized to extract the model parameters. The dynamic AM/AM and AM/PM characteristics and power spectral densities of the modulated signals from the RSOA are demonstrated without and with DPD. Experimental results show clearly that the nonlinear distortion of RSOA external modulators in RoF links can be compensated using DPD linearization techniques.

©2011 Optical Society of America

OCIS codes: (060.0060) Fiber optics and optical communications; (230.4110) Modulators; (250.5980) Semiconductor optical amplifiers.

References and links

1. D. Wake, A. Nkansah, and N. J. Gomes, “Radio over fiber link design for next generation wireless systems,” J. Lightwave Technol. 28(16), 2456–2464 (2010).

2. M. J. Crisp, S. Li, A. Wonfor, R. V. Penty, and I. H. White, “Demonstration of radio over fibre distributed antenna network for combined in-building WLAN and 3G coverage,” in National Fiber Optic Engineers Conference, OSA Technical Digest Series (CD) (Optical Society of America, 2007), paper JThA81.

3. A. Hekkala, M. Lasanen, I. Harjula, L. C. Vieira, N. J. Gomes, A. Nkan, S. Bittner, F. Diehm, and V. Kotzsch, “Analysis of and compensation for non-ideal RoF links in DAS [Coordinated and Distributed MIMO],” IEEE Wireless Commun. 17(3), 52–59 (2010).

4. G. de Valicourt, M. A. Violas, D. Wake, F. Van Dijk, C. Ware, A. Enard, D. Maké, Z. Liu, M. Lamponi, G. H. Duan, and R. Brenot, “Radio over fiber access network architecture based on new optimized RSOA devices with large modulation bandwidth and high linearity,” IEEE Trans. Microw. Theory Tech. 58(11), 3248–3258 (2010).

5. X. Yu, T. Gibbon, and I. Monroy, “Bidirectional radio-over-fiber system with phase-modulation downlink and RF oscillator-free uplink using a reflective SOA,” IEEE Photon. Technol. Lett. 20(24), 2180–2182 (2008).

6. D. Wake, A. Nkansah, N. J. Gomes, G. de Valicourt, R. Brenot, M. Violas, Z. Liu, F. Ferreira, and S. Pato, “A comparison of radio over fiber link types for the support of wideband radio channels,” J. Lightwave Technol. 28(16), 2416–2422 (2010).

7. Z. Liu, M. Sadeghi, G. de Valicourt, R. Brenot, and M. Violas, “Experimental validation of a reflective semiconductor optical amplifier model used as a modulator in radio over fiber systems,” IEEE Photon. Technol. Lett. 23(9), 576–578 (2011).

8. E. Udvary and T. Berceli, “Improvements in the linearity of semiconductor optical amplifiers as external modulators,” IEEE Trans. Microw. Theory Tech. 58(11), 3161–3166 (2010).

9. J. Kim and K. Konstantinou, “Digital predistortion of wideband signals based on power amplifier model with memory,” Electron. Lett. 37(23), 1417–1418 (2001).

10. A. Zhu, P. J. Draxler, J. J. Yan, T. J. Brazil, D. F. Kimball, and P. M. Asbeck, “Open-loop digital predistorter for RF power amplifiers using dynamic deviation reduction-based Volterra series,” IEEE Trans. Microw. Theory Tech. 56(7), 1524–1534 (2008).

11. L. Guan and A. Zhu, “Low-cost FPGA implementation of Volterra series-based digital predistorter for RF power amplifier,” IEEE Trans. Microw. Theory Tech. 58(4), 866–872 (2010).

12. H. Cao, H. M. Nemati, A. S. Tehrani, T. Eriksson, J. Grahn, and C. Fager, “Linearization of efficiency-optimize dynamic load modulation transmitter architectures,” IEEE Trans. Microw. Theory Tech. 58(4), 873–881 (2010).

13. L. Ding, G. T. Zhou, D. R. Morgan, Z. Ma, J. S. Kenney, J. Kim, and C. R. Giardina, “A robust digital baseband predistorter constructed using memory polynomials,” IEEE Trans. Commun. 52(1), 159–165 (2004).

14. D. R. Morgan, Z. Ma, J. Kim, M. G. Zierdt, and J. Pastalan, “A generalized memory polynomial model for digital predistortion of RF power amplifiers,” IEEE Trans. Signal Process. 54(10), 3852–3860 (2006).

#150272 - $15.00 USD Received 30 Jun 2011; revised 4 Aug 2011; accepted 13 Aug 2011; published 23 Aug 2011(C) 2011 OSA 29 August 2011 / Vol. 19, No. 18 / OPTICS EXPRESS 17641

1. Introduction

Future wireless systems will need to provide the terminal users with larger transmission bandwidth coverage, higher data rates and higher mobility. Radio-over-fiber (RoF) distributed antenna systems (DAS) have been widely investigated because they satisfy the requirements of the next generation wireless access systems [1–3]. RoF links are used to connect between a central unit (CU) and a number of remote antenna units (RAUs) in DAS. The distributed antennas are linked directly to RAUs in order to enable the greatest flexibility for the accommodation of future radio systems and services. RoF links also create opportunity to offer low loss and transparent characteristics of radio signal transmission.

Reflective semiconductor optical amplifiers (RSOAs) have been proposed as colorless external modulators in wavelength division multiplexing (WDM) systems [4–7]. The optical modulator is the primary source of nonlinear distortion in the RoF links. Performance degradation of the optical links will occur due to the inherent nonlinearity of the electrical-to-optical (E/O) conversion process in external modulators [8]. Thus the nonlinearity of RSOA becomes the main limitation on the maximum signals that can be transmitted. An alternative strategy is to employ linearization techniques for the RSOA. Most linearization techniques have been widely proposed and used to compensate for the nonlinearity effects of radio frequency (RF) power amplifiers [9–12]. Digital predistortion (DPD) is the most commonly used, simple and robust method for improving linearity of nonlinear devices [13,14]. Memory effects are usually considered in most of the DPD models to improve the linearization performance.

In this paper we first improve the linearity of the RSOA external modulators by DPD linearization techniques. The DPD is basically based on the generalized memory polynomial model [14]. The dynamic AM/AM and AM/PM characteristics of the RSOA without and with the DPD are demonstrated. Experimental results show clearly that the improvement of the linearity of the RSOA is obtained.

2. Digital predistortion and generalized memory polynomial model

The diagram of digital predistortion is shown in Fig. 1. In order to extract the model parameters the baseband input and output signals of the device under test (DUT) (see Fig. 2) should first be measured. As the pth-order pre-inverse transfer function is identical to the pth-order post-inverse transfer function [10], the input and output of the DUT can be regarded as the output and input of the DPD model to invert the characteristics of the DUT. Thus the coefficients of the model can be simply extracted with an offline process.

Fig. 1. Diagram of digital predistortion.

In order to compensate the nonlinear distortion of the RSOA external modulator in RoF links, we use a generalized memory polynomial [14] as a DPD model, which is given by


( ) ( ) ( ) ( ) ( )

( ) ( )

1 11

1 0 1 0 1

1

1 0 1

+

a a b b b

c c c

K L K L Mk k

kl klm

k l k l m

K L Mk

klm

k l m

u n a y n l y n l b y n l y n l m

c y n l y n l m

− −−

= = = = =

−

= = =

= − − + − − −

− − +

∑∑ ∑∑∑

∑∑∑

ɶ ɶ ɶ ɶ ɶ

ɶ ɶ

(1)

where ( )u nɶ and ( )y nɶ are the complex envelopes of the input and output of the DUT,

respectively; aK , b

K and cK are the order of nonlinearity; aL , b

L , cL , b

M and cM are the

memory lengths; kla , klm

b , and klmc are the corresponding coefficients of the DPD.

As the model is linear in the coefficients, the linear least-squares error minimization method can be used to estimate the coefficients of the model, which is described by

( ) 1ˆ H H

−=h Y Y Y u (2)

where ( )H⋅ denotes the complex conjugate transpose; Y and u are output signal matrix (N ×

P) and input signal vector (N × 1) of the DUT, respectively, a a b b b c c c

P K L K L M K L M= + + ;

h is the estimated vector (P × 1) of the coefficients, this is, the coefficient vector of the DPD.

10 11 ( 1) 101 102 ( 1) 101 102 ( 1)ˆ

a a b b b c c c

T

K L K L M K L Ma a a b b b c c c− − − = h ⋯ ⋯ ⋯ .

The matrix Y and vector u are described in details by following equations

1

1

1

(0) ( ( 1)) ( ( 1)) (0) ( 1)

( ) ( ( 1)) ( ( 1)) ( ) ( 1)

( 1) ( 1 ( 1)) ( 1 ( 1)) ( 1) ( 1 1)

( ( 1)) ( ( 1) ) (0

a

a

a

b

K

a a

K

a a

K

a a

K

b b b

y y L y L y y

y n y n L y n L y n y n

y N y N L y N L y N y N

y L y L M y

−

−

−

− − − − −= − − − − − − − − − − − − − − −

− − − − −

Y

ɶ ɶ ɶ ɶ ɶ⋯ ⋯

⋮ ⋮ ⋮


⋮ ⋮ ⋮


ɶ ɶ ɶ ) (1) ( ( 1)) ( ( 1) )

( ( 1)) ( ( 1) ) ( ) ( 1) ( ( 1)) ( ( 1) )

( 1 ( 1)) ( 1 ( 1) ) ( 1) ( 1 1) ( 1 ( 1)) ( 1 ( 1) )

c

b c

b c

K

c c c

K K

b b b c c c

K K

b b b c c c

y y L y L M

y n L y n L M y n y n y n L y n L M

y N L y N L M y N y N y N L y N L M

− − − − +

− − − − − + − − − − +

− − − − − − − − − + − − − − − − +

ɶ ɶ ɶ⋯

⋮ ⋮ ⋮

ɶ ɶ ɶ ɶ ɶ ɶ⋯

⋮ ⋮ ⋮

ɶ ɶ ɶ ɶ ɶ ɶ⋯

(3)

[ ](0) ( ) ( 1)T

u u n u N= −u ɶ ɶ ɶ⋯ ⋯ (4)

where ( )T⋅ denotes the transpose.

In order to obtain the predistorted RF input signal of the DUT, the predistorted baseband

output signal of the DPD u can be first obtained by

ˆˆ =u Xh (5)

where X is the baseband input signal matrix (N × P) of the DPD, which is also the desired output signal of the DUT.

3. Experimental setup

The experimental setup is shown in Fig. 2. The test baseband signals were designed in Matlab and fed into a vector signal generator (VSG) to be up-converted to RF domain with a carrier frequency of 1 GHz. A commercial broadband amplifier (AMP), ZHL-42W, was used to drive the DUT. A vector signal analyzer (VSA) was used to obtain the baseband input and output signals of the DUT. This was realized by a switch. For instance, the direct connection between the output of AMP and VSA enables us to obtain the measurements of the input signals for the


DUT. The VSG and VSA were connected to a computer controller using general purpose interface bus (GPIB) cables. A 10 MHz reference and trigger signals between the VSG and VSA were used in order to synchronize and trigger multi measurement events. Any error in the generation acquisition synchronization could lead to poor repeatability of measurements.

A commercial distributed feedback (DFB) laser, which was biased at 30 mA and had a wavelength of 1550 nm, was used as the seed light of the RSOA. The input optical power of

the RSOA was set to −7 dBm by adjusting a tunable optical attenuator. The RSOA was biased at 90 mA. The forward and reverse signals of the RSOA were separated by an optical circulator. A photodiode (PD) with a responsivity of 0.8 A/W was used as a detector to convert optical signals to electrical ones.

Fig. 2. The experimental test bench.

4. Experimental results

In order to extract the coefficients of the DPD and generate the predistorted signal for the RSOA external modulator, two random 64 quadrature amplitude modulation (QAM) signals with 20 Msymbol/s, which were filtered with a square root raised cosine (RRC) filter with the

roll-off factor of 0.22α = , were generated in Matlab. One of them was used to estimate the

parameters of the DPD. The complex baseband QAM signal with a sampling rate at 80 MHz was fed into the VSG memory to be up-converted to 1 GHz and passed through the DUT. In this case the average RF input power of the DUT was set up to 13 dBm with a peak-to-average power ration (PAPR) of around 5.42 dB, which was the input 1 dB compression point (P1dB) of the RSOA. The complex baseband input and output signals of the DUT were obtained from the VSA. After time alignment and phase correction, 10,000 samples were used to estimate the coefficients of DPD as mentioned in Section 3. In our work we set

5a b cK K K= = = (only odd order considered, this is, k = 1,3,5 for aK , b

K and cK in this work),

2a b cL L L= = = and 2b c

M M= = (30 coefficients total). Once the coefficients were obtained,

they were used to predistort the other random 64-QAM signal according to Eq. (5). The predistorted signal had a PAPR of approximately 8.38 dB, which was about 3 dB more than the original signal’s. The predistorted signal was fed into the VSG and passed through the system. The output of the RSOA with the DPD was obtained from the VSA.


The dynamic AM/AM and AM/PM performances of RSOA external modulator without and with the DPD are shown in Fig. 3. The phase shift was obtained by calculating the difference between complex output signals and complex input signals of the RSOA. From these figures we can clearly see that the nonlinear distortion and memory effect have been successfully compensated. The normalized power spectral density without and with the DPD and the transmitted signal (output of the AMP) are shown in Fig. 4. The 3rd order intermodulation distortion was improved by 17 dB with the DPD when compared to the situation without the DPD.

Fig. 3. Dynamic characteristics of RSOA without and with DPD (a) AM/AM; (b) AM/PM.

-50 -40 -30 -20 -10 0 10 20 30 40 50-80

-70

-60

-50

-40

-30

-20

-10

0

Norm

aliz

ed p

ow

er

spectr

al density (

dB

)

Frequency offset (MHz)

transmitted

without DPDwith DPD

Fig. 4. Normalized output power spectra of RSOA without and with DPD and spectrum of transmitted signal.

After demodulation process in Matlab, the constellations without and with the DPD and for the transmitted symbols are shown in Fig. 5. It can also be clearly seen that the nonlinearity effects of the RSOA have been successfully compensated. To evaluate the performance of the DPD, the error vector magnitude (EVM) is used as a figure of merit. The EVMs without and with the DPD are 6.1% and 2.0%, respectively, which were calculated by


2

1

2

1

( ) ( )

( )

N

n

N

n

y n s n

EVM

s n

=

=

−=∑

∑ (6)

where ( )s n is the reference transmitted symbol; ( )y n is the received symbol; N is the number

of samples.

-1 -0.8 -0.6 -0.4 -0.2 0 0.2 0.4 0.6 0.8 1

-1

-0.8

-0.6

-0.4

-0.2

0

0.2

0.4

0.6

0.8

1

In-phase

Quadra

ture

Fig. 5. Normalized constellation (blue ‘x’ for without DPD, green ‘•’ for with DPD, and red ‘+’ for the transmitted symbol).

5. Conclusion

In this paper we have utilized the DPD linearization technique to compensate the nonlinear distortion of the RSOA external modulator in RoF links. The experimental results show that the nonlinear distortion and memory effects of the RSOA have been successfully compensated by the DPD based on the generalized memory polynomial model. The large modulated signal can be transmitted by RoF systems with the DPD. The 3rd order intermodulation distortion of the RSOA has been improved by 17 dB with the DPD. The EVMs without and with the DPD are 6.1% and 2.0%, respectively.

We will focus on implementing the digital predistortion for the RSOA external modulator by field programmable gate arrays (FPGAs) for practical applications. The coefficients of the DPD will be dynamically updated by sampling the output signal of the RSOA.

Acknowledgments

This work was supported by the project CROWN PTDC/EEA-TEL/115828/2009. Z. Liu is sponsored by the Fundação para a Ciência e Tecnologia (FCT) under Ph.D Grant SFRH/BD/68376/2010, whose support is gratefully acknowledged.


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Digital predistortion for RSOAs as external modulators in radio over fiber systems