Abstract

This article proposes an optimized version of a canonical piece-wise-linear (CPWL) digital predistorter in order to enhance the linearity of a radio-over-fiber (RoF) LTE mobile fronthaul. In this work, we propose a threshold allocation optimization process carried out by a genetic algorithm (GA) in order to optimize the CPWL model (GA-CPWL). Firstly, experiments show how the CPWL model outperforms the classical memory polynomial DPD in an intensity modulation/direct detection (IM/DD) RoF link. Then, the GA-CPWL predistorter is compared with the CPWL model in several scenarios, in order to verify that the proposed DPD offers better performance in different optical transmission conditions. Experimental results reveal that with a proper threshold allocation, the GA-CPWL predistorter offers very promising outcomes.

© 2017 Optical Society of America

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References

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  1. T. Pfeiffer, “Next generation mobile fronthaul architectures,” in Optical Fiber Communications Conf. 2015 (Optical Society of America, 2015), paper M2J.7.
  2. Y. Xu, X. Li, J. Yu, and G. Chang, “Simple and reconfigured single-sideband OFDM RoF system,” Opt. Express 24(20), 22830–22835 (2016).
    [Crossref] [PubMed]
  3. D. Waken, A. Nkansah, and N. J. Gomes, “Radio over fiber link design for next generation wireless systems,” J. Lightwave Technol. 28(16), 2456–2464 (2010).
    [Crossref]
  4. S. E. Alavi, M. R. K. Soltanian, I. S. Amiri, M. Khalily, A. S. M. Supaat, and H. Ahmad, “Towards 5G: a photonic based millimeter wave signal generation for applying in 5G access fronthaul,” Scientific Reports,  6, 19891 (2016).
    [Crossref] [PubMed]
  5. J. Zhou, S. Fu, F. Luan, J. H. Wong, S. Aditya, P. P. Shum, and K. E. K. Lee, “Tuneable multi-tap bandpass microwave photonic filter using a windowed Fabry-Pérot filter-based multi-wavelength tuneable laser,” J. Lightwave Technol. 29(22), 3381–3386 (2011).
    [Crossref]
  6. N. Alic, “Cancellation of nonlinear impairments in fiber optic transmission systems,” in Optical Fiber Communications Conf. 2016 (Optical Society of America, 2016), paper Tu2E.1.
  7. J. Amstrong, “OFDM of optical communications,” J. of Lightwave Technology 27(3), 189–204 (2009).
    [Crossref]
  8. Y. Pei, K. Xu, J. Li, A. Zhang, Y. Dai, Y. Ji, and J. Lin, “Complexity-reduced digital predistortion for subcarrier multiplexed radio over fiber systems transmitting sparse multi-band RF signals,” Opt. Express 21(3), 3708–3714 (2013).
    [Crossref] [PubMed]
  9. C. Han, S. Cho, H. S. Chung, and J. H. Lee, “Linearity improvement of directly-modulated multi-IF-over-fiber LTE-A mobile fronthaul link using shunt diode predistorter,” in European Conference and Exhibition on Optical Communications 2015 (Optical Society of America, 2015), paper We.4.4.4.
  10. A. Zhu, “Decomposed vector rotation-based behavioral modeling for digital predistortion of RF power amplifiers,” IEEE Trans. Microwave Theory Tech. 63(2), 737–744 (2015).
    [Crossref]
  11. P. Guo, X. Wang, and Y. Han, “The enhanced genetic algorithms for the optimization design,” in Proc. of IEEE Conference on Biomedical Engineering and Informatics 2010 (IEEE, 2010), pp. 2990–2994.
  12. A. Zhu, P. J. Draxler, J. J. Yn, 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. Microwave Theory Tech.,  56(7), 1524–1534 (2008).
    [Crossref]
  13. L. Ding, G. TongZhou, D. T. 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).
    [Crossref]
  14. L. O. Chua and S. M. Kang, “Section-wise piecewise-linear functions: canonical representation, properties and applications,” Proc. of the IEEE 65(6), 915–929 (1977).
    [Crossref]
  15. 3GPP TSGRAN, “User equipment (UE) radio transmission and reception (FDD),” Technical Specification ETSI TS136.101 V9.4.0 (2010).
  16. M. Aziz, M. Rawat, and F. M. Ghannouchi, “Low complexity distributed model for the compensation of direct conversion transmitter’s imperfections,” IEEE Trans. Broadcast. 60(3), 568–574 (2014).
    [Crossref]
  17. C. H. Cox, G. E. Betts, and L. M. Johnson, “An analytic and experimental comparison of direct and external modulation in analog fiber-optic links,” IEEE Trans. Microwave Theory Tech.,  38(5), 501–509 (1990).
    [Crossref]

2016 (2)

Y. Xu, X. Li, J. Yu, and G. Chang, “Simple and reconfigured single-sideband OFDM RoF system,” Opt. Express 24(20), 22830–22835 (2016).
[Crossref] [PubMed]

S. E. Alavi, M. R. K. Soltanian, I. S. Amiri, M. Khalily, A. S. M. Supaat, and H. Ahmad, “Towards 5G: a photonic based millimeter wave signal generation for applying in 5G access fronthaul,” Scientific Reports,  6, 19891 (2016).
[Crossref] [PubMed]

2015 (1)

A. Zhu, “Decomposed vector rotation-based behavioral modeling for digital predistortion of RF power amplifiers,” IEEE Trans. Microwave Theory Tech. 63(2), 737–744 (2015).
[Crossref]

2014 (1)

M. Aziz, M. Rawat, and F. M. Ghannouchi, “Low complexity distributed model for the compensation of direct conversion transmitter’s imperfections,” IEEE Trans. Broadcast. 60(3), 568–574 (2014).
[Crossref]

2013 (1)

2011 (1)

2010 (1)

2009 (1)

J. Amstrong, “OFDM of optical communications,” J. of Lightwave Technology 27(3), 189–204 (2009).
[Crossref]

2008 (1)

A. Zhu, P. J. Draxler, J. J. Yn, 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. Microwave Theory Tech.,  56(7), 1524–1534 (2008).
[Crossref]

2004 (1)

L. Ding, G. TongZhou, D. T. 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).
[Crossref]

1990 (1)

C. H. Cox, G. E. Betts, and L. M. Johnson, “An analytic and experimental comparison of direct and external modulation in analog fiber-optic links,” IEEE Trans. Microwave Theory Tech.,  38(5), 501–509 (1990).
[Crossref]

1977 (1)

L. O. Chua and S. M. Kang, “Section-wise piecewise-linear functions: canonical representation, properties and applications,” Proc. of the IEEE 65(6), 915–929 (1977).
[Crossref]

Aditya, S.

Ahmad, H.

S. E. Alavi, M. R. K. Soltanian, I. S. Amiri, M. Khalily, A. S. M. Supaat, and H. Ahmad, “Towards 5G: a photonic based millimeter wave signal generation for applying in 5G access fronthaul,” Scientific Reports,  6, 19891 (2016).
[Crossref] [PubMed]

Alavi, S. E.

S. E. Alavi, M. R. K. Soltanian, I. S. Amiri, M. Khalily, A. S. M. Supaat, and H. Ahmad, “Towards 5G: a photonic based millimeter wave signal generation for applying in 5G access fronthaul,” Scientific Reports,  6, 19891 (2016).
[Crossref] [PubMed]

Alic, N.

N. Alic, “Cancellation of nonlinear impairments in fiber optic transmission systems,” in Optical Fiber Communications Conf. 2016 (Optical Society of America, 2016), paper Tu2E.1.

Amiri, I. S.

S. E. Alavi, M. R. K. Soltanian, I. S. Amiri, M. Khalily, A. S. M. Supaat, and H. Ahmad, “Towards 5G: a photonic based millimeter wave signal generation for applying in 5G access fronthaul,” Scientific Reports,  6, 19891 (2016).
[Crossref] [PubMed]

Amstrong, J.

J. Amstrong, “OFDM of optical communications,” J. of Lightwave Technology 27(3), 189–204 (2009).
[Crossref]

Asbeck, P. M.

A. Zhu, P. J. Draxler, J. J. Yn, 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. Microwave Theory Tech.,  56(7), 1524–1534 (2008).
[Crossref]

Aziz, M.

M. Aziz, M. Rawat, and F. M. Ghannouchi, “Low complexity distributed model for the compensation of direct conversion transmitter’s imperfections,” IEEE Trans. Broadcast. 60(3), 568–574 (2014).
[Crossref]

Betts, G. E.

C. H. Cox, G. E. Betts, and L. M. Johnson, “An analytic and experimental comparison of direct and external modulation in analog fiber-optic links,” IEEE Trans. Microwave Theory Tech.,  38(5), 501–509 (1990).
[Crossref]

Brazil, T. J.

A. Zhu, P. J. Draxler, J. J. Yn, 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. Microwave Theory Tech.,  56(7), 1524–1534 (2008).
[Crossref]

Chang, G.

Cho, S.

C. Han, S. Cho, H. S. Chung, and J. H. Lee, “Linearity improvement of directly-modulated multi-IF-over-fiber LTE-A mobile fronthaul link using shunt diode predistorter,” in European Conference and Exhibition on Optical Communications 2015 (Optical Society of America, 2015), paper We.4.4.4.

Chua, L. O.

L. O. Chua and S. M. Kang, “Section-wise piecewise-linear functions: canonical representation, properties and applications,” Proc. of the IEEE 65(6), 915–929 (1977).
[Crossref]

Chung, H. S.

C. Han, S. Cho, H. S. Chung, and J. H. Lee, “Linearity improvement of directly-modulated multi-IF-over-fiber LTE-A mobile fronthaul link using shunt diode predistorter,” in European Conference and Exhibition on Optical Communications 2015 (Optical Society of America, 2015), paper We.4.4.4.

Cox, C. H.

C. H. Cox, G. E. Betts, and L. M. Johnson, “An analytic and experimental comparison of direct and external modulation in analog fiber-optic links,” IEEE Trans. Microwave Theory Tech.,  38(5), 501–509 (1990).
[Crossref]

Dai, Y.

Ding, L.

L. Ding, G. TongZhou, D. T. 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).
[Crossref]

Draxler, P. J.

A. Zhu, P. J. Draxler, J. J. Yn, 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. Microwave Theory Tech.,  56(7), 1524–1534 (2008).
[Crossref]

Fu, S.

Ghannouchi, F. M.

M. Aziz, M. Rawat, and F. M. Ghannouchi, “Low complexity distributed model for the compensation of direct conversion transmitter’s imperfections,” IEEE Trans. Broadcast. 60(3), 568–574 (2014).
[Crossref]

Giardina, C. R.

L. Ding, G. TongZhou, D. T. 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).
[Crossref]

Gomes, N. J.

Guo, P.

P. Guo, X. Wang, and Y. Han, “The enhanced genetic algorithms for the optimization design,” in Proc. of IEEE Conference on Biomedical Engineering and Informatics 2010 (IEEE, 2010), pp. 2990–2994.

Han, C.

C. Han, S. Cho, H. S. Chung, and J. H. Lee, “Linearity improvement of directly-modulated multi-IF-over-fiber LTE-A mobile fronthaul link using shunt diode predistorter,” in European Conference and Exhibition on Optical Communications 2015 (Optical Society of America, 2015), paper We.4.4.4.

Han, Y.

P. Guo, X. Wang, and Y. Han, “The enhanced genetic algorithms for the optimization design,” in Proc. of IEEE Conference on Biomedical Engineering and Informatics 2010 (IEEE, 2010), pp. 2990–2994.

Ji, Y.

Johnson, L. M.

C. H. Cox, G. E. Betts, and L. M. Johnson, “An analytic and experimental comparison of direct and external modulation in analog fiber-optic links,” IEEE Trans. Microwave Theory Tech.,  38(5), 501–509 (1990).
[Crossref]

Kang, S. M.

L. O. Chua and S. M. Kang, “Section-wise piecewise-linear functions: canonical representation, properties and applications,” Proc. of the IEEE 65(6), 915–929 (1977).
[Crossref]

Kenney, J. S.

L. Ding, G. TongZhou, D. T. 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).
[Crossref]

Khalily, M.

S. E. Alavi, M. R. K. Soltanian, I. S. Amiri, M. Khalily, A. S. M. Supaat, and H. Ahmad, “Towards 5G: a photonic based millimeter wave signal generation for applying in 5G access fronthaul,” Scientific Reports,  6, 19891 (2016).
[Crossref] [PubMed]

Kim, J.

L. Ding, G. TongZhou, D. T. 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).
[Crossref]

Kimball, D. F.

A. Zhu, P. J. Draxler, J. J. Yn, 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. Microwave Theory Tech.,  56(7), 1524–1534 (2008).
[Crossref]

Lee, J. H.

C. Han, S. Cho, H. S. Chung, and J. H. Lee, “Linearity improvement of directly-modulated multi-IF-over-fiber LTE-A mobile fronthaul link using shunt diode predistorter,” in European Conference and Exhibition on Optical Communications 2015 (Optical Society of America, 2015), paper We.4.4.4.

Lee, K. E. K.

Li, J.

Li, X.

Lin, J.

Luan, F.

Ma, Z.

L. Ding, G. TongZhou, D. T. 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).
[Crossref]

Morgan, D. T.

L. Ding, G. TongZhou, D. T. 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).
[Crossref]

Nkansah, A.

Pei, Y.

Pfeiffer, T.

T. Pfeiffer, “Next generation mobile fronthaul architectures,” in Optical Fiber Communications Conf. 2015 (Optical Society of America, 2015), paper M2J.7.

Rawat, M.

M. Aziz, M. Rawat, and F. M. Ghannouchi, “Low complexity distributed model for the compensation of direct conversion transmitter’s imperfections,” IEEE Trans. Broadcast. 60(3), 568–574 (2014).
[Crossref]

Shum, P. P.

Soltanian, M. R. K.

S. E. Alavi, M. R. K. Soltanian, I. S. Amiri, M. Khalily, A. S. M. Supaat, and H. Ahmad, “Towards 5G: a photonic based millimeter wave signal generation for applying in 5G access fronthaul,” Scientific Reports,  6, 19891 (2016).
[Crossref] [PubMed]

Supaat, A. S. M.

S. E. Alavi, M. R. K. Soltanian, I. S. Amiri, M. Khalily, A. S. M. Supaat, and H. Ahmad, “Towards 5G: a photonic based millimeter wave signal generation for applying in 5G access fronthaul,” Scientific Reports,  6, 19891 (2016).
[Crossref] [PubMed]

TongZhou, G.

L. Ding, G. TongZhou, D. T. 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).
[Crossref]

Waken, D.

Wang, X.

P. Guo, X. Wang, and Y. Han, “The enhanced genetic algorithms for the optimization design,” in Proc. of IEEE Conference on Biomedical Engineering and Informatics 2010 (IEEE, 2010), pp. 2990–2994.

Wong, J. H.

Xu, K.

Xu, Y.

Yn, J. J.

A. Zhu, P. J. Draxler, J. J. Yn, 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. Microwave Theory Tech.,  56(7), 1524–1534 (2008).
[Crossref]

Yu, J.

Zhang, A.

Zhou, J.

Zhu, A.

A. Zhu, “Decomposed vector rotation-based behavioral modeling for digital predistortion of RF power amplifiers,” IEEE Trans. Microwave Theory Tech. 63(2), 737–744 (2015).
[Crossref]

A. Zhu, P. J. Draxler, J. J. Yn, 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. Microwave Theory Tech.,  56(7), 1524–1534 (2008).
[Crossref]

IEEE Trans. Broadcast. (1)

M. Aziz, M. Rawat, and F. M. Ghannouchi, “Low complexity distributed model for the compensation of direct conversion transmitter’s imperfections,” IEEE Trans. Broadcast. 60(3), 568–574 (2014).
[Crossref]

IEEE Trans. Commun. (1)

L. Ding, G. TongZhou, D. T. 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).
[Crossref]

IEEE Trans. Microwave Theory Tech. (3)

A. Zhu, “Decomposed vector rotation-based behavioral modeling for digital predistortion of RF power amplifiers,” IEEE Trans. Microwave Theory Tech. 63(2), 737–744 (2015).
[Crossref]

C. H. Cox, G. E. Betts, and L. M. Johnson, “An analytic and experimental comparison of direct and external modulation in analog fiber-optic links,” IEEE Trans. Microwave Theory Tech.,  38(5), 501–509 (1990).
[Crossref]

A. Zhu, P. J. Draxler, J. J. Yn, 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. Microwave Theory Tech.,  56(7), 1524–1534 (2008).
[Crossref]

J. Lightwave Technol. (2)

J. of Lightwave Technology (1)

J. Amstrong, “OFDM of optical communications,” J. of Lightwave Technology 27(3), 189–204 (2009).
[Crossref]

Opt. Express (2)

Proc. of the IEEE (1)

L. O. Chua and S. M. Kang, “Section-wise piecewise-linear functions: canonical representation, properties and applications,” Proc. of the IEEE 65(6), 915–929 (1977).
[Crossref]

Scientific Reports (1)

S. E. Alavi, M. R. K. Soltanian, I. S. Amiri, M. Khalily, A. S. M. Supaat, and H. Ahmad, “Towards 5G: a photonic based millimeter wave signal generation for applying in 5G access fronthaul,” Scientific Reports,  6, 19891 (2016).
[Crossref] [PubMed]

Other (5)

T. Pfeiffer, “Next generation mobile fronthaul architectures,” in Optical Fiber Communications Conf. 2015 (Optical Society of America, 2015), paper M2J.7.

C. Han, S. Cho, H. S. Chung, and J. H. Lee, “Linearity improvement of directly-modulated multi-IF-over-fiber LTE-A mobile fronthaul link using shunt diode predistorter,” in European Conference and Exhibition on Optical Communications 2015 (Optical Society of America, 2015), paper We.4.4.4.

N. Alic, “Cancellation of nonlinear impairments in fiber optic transmission systems,” in Optical Fiber Communications Conf. 2016 (Optical Society of America, 2016), paper Tu2E.1.

3GPP TSGRAN, “User equipment (UE) radio transmission and reception (FDD),” Technical Specification ETSI TS136.101 V9.4.0 (2010).

P. Guo, X. Wang, and Y. Han, “The enhanced genetic algorithms for the optimization design,” in Proc. of IEEE Conference on Biomedical Engineering and Informatics 2010 (IEEE, 2010), pp. 2990–2994.

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Figures (12)

Fig. 1
Fig. 1 Digital Predistorter schematic in a RoF mobile-fronthaul system.
Fig. 2
Fig. 2 Genetic algorithm threshold optimization diagram.
Fig. 3
Fig. 3 Experimental setup for a directly-modulated RoF system.
Fig. 4
Fig. 4 Output signal PSDs without predistortion (blue) and with Volterra (black) and CPWL DPD (red) with 26 coefficients (M=1, N=13 and K=4).
Fig. 5
Fig. 5 EVM experimental results for different coefficient number and memory depths. (a) Band 1 with Volterra model; (b) Band 1 with CPWL model; (c) Band 2 with Volterra model and (d) Band 2 with CPWL model.
Fig. 6
Fig. 6 Output signal constellations with 39 coefficients (N=13, K=4 and M=2). (a) Band 1 without DPD, (b) with Volterra predistorter and (c) with CPWL DPD; (d) Band 2 without DPD, (e) with Volterra predistorter and (f) with CPWL DPD.
Fig. 7
Fig. 7 Threshold allocation with (red) and without (black) optimization for input RF power of 0 dBm, Ibias of 50 mA and a fiber length of 10 km.
Fig. 8
Fig. 8 Threshold amplitudes for several input signal powers with and without optimization process (L = 10 km and Ibias = 50 mA).
Fig. 9
Fig. 9 Output signal PSDs without predistortion and with CPWL and GA-CPWL DPDs with 0 dBm RF input power, 10 km fiber length and 50 mA bias intensity.
Fig. 10
Fig. 10 ACPR experimental measurements for all studied scenarios. (a) 5 MHz and Ibias = 30mA; (b) 15 MHz and Ibias = 30mA; (c) 5 MHz and Ibias = 50mA; (d) 15 MHz and Ibias = 50mA; (e) 5 MHz and Ibias = 70mA and (f) 15 MHz and Ibias = 70mA.
Fig. 11
Fig. 11 EVM experimental results for an input signal power of 4 dBm. (a) 5 MHz without DPD; (b) 5 MHz DPD without optimization; (c) 5 MHz with optimization; (d) 15 MHz without DPD; (e) 15 MHz DPD without optimization and (f) 15 MHz with optimization.
Fig. 12
Fig. 12 EVM performance against input signal power for a length of 20 km and 70 mA bias intensity: (a) 5 MHz and (b) 15 MHz bandwidth signals.

Tables (4)

Tables Icon

Table 1 RoF modeling comparison between Volterra and CPWL Models in terms of NMSE and ACEPR for different Nonlinearity Orders and Memory Depths.

Tables Icon

Table 2 DPD Experimental Results for both Volterra and CPWL Models in terms of NMSE and ACPR for different Nonlinearity Orders and Memory Depths.

Tables Icon

Table 3 Transmitted Signal Power at the PA Output in both Bands without Predistortion and with Volterra and CPWL DPD for different Nonlinearity Orders and Memory Depths.

Tables Icon

Table 4 Experimental Gain Measured for all Studied Scenarios with a Fiber Length of 10 km.

Equations (7)

Equations on this page are rendered with MathJax. Learn more.

u ( n ) p = 1 N m = 0 M a p m x ( n m ) | x ( n m ) | p 1 ,
u ( n ) = m = 0 M a m x ( n m ) + b + k = 1 K c k | m = 0 M a k m x ( n m ) β k | ,
u ( n ) = m = 0 M c m x ( n m ) linear + k = 1 K m = 0 M c k m , 1 x ( n m ) | β k | e j θ ( n m ) 1 st-order basis + k = 1 K m = 0 M c k m , 21 x ( n m ) | β k | e j θ ( n m ) | x ( n ) | 2 nd-order type- 1 + k = 1 K m = 0 M c k m , 22 x ( n m ) | β k | x ( n ) 2 nd-order type- 2 + k = 1 K m = 0 M c k m , 23 x ( n m ) | β k | x ( n m ) 2 nd-order type- 3 + k = 1 K m = 0 M c k m , 24 x ( n ) | β k | x ( n m ) DDR term- 1 + ,  
u ( n ) | C P W L = m = 0 M c m x ( n m ) + k = 1 K m = 0 M c k m , 1 x ( n m ) | β k | e j θ ( n m ) + k = 1 K m = 0 M c k m , 21 x ( n m ) | β k | e j θ ( n m ) | x ( n ) | + k = 1 K m = 0 M c k m , 22 x ( n m ) | β k | x ( n ) .
φ A C P R = min m = 1 , 2 [ 10 log 10 ( a d j _ b a n d ) m Y ( f ) d f ( b a n d ) Y ( f ) d f ] ,
u ( n ) | G A C P W L = m = 0 M c ˜ m x ( n m ) + k = 1 K m = 0 M c ˜ k m , 1 | | x ( n m ) | β ˜ k ( L , I b i a s , P R F ) | e j θ ( n m ) + k = 1 K m = 0 M c ˜ k m , 21 | | x ( n m ) | β ˜ k ( L , I b i a s , P R F ) | e j θ ( n m ) | x ( n ) | + k = 1 K m = 0 M c ˜ k m , 22 | | x ( n m ) | β ˜ k ( L , I b i a s , P R F ) | x ( n ) ,
G norm = G R o F l i n = α G R o F = α P o P i = α η L D 2 2 L o p t 2 G P A L a t t 16 d B Z o u t Z i n ,

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