Abstract

We propose two dynamic bandwidth allocation (DBA) algorithms by considering three dimensions, i.e., time slot, subcarrier, and bit allocation, to minimize the transmitting power of optical network units (ONUs) in orthogonal frequency division multiplexing access passive optical networks (OFDMA-PONs). In the first proposed algorithm, we make use of the three-dimensional DBA algorithm from wireless OFDM, modify it according to the characteristics of the fiber channel, and apply it to upstream access in OFDMA-PONs to reduce the transmitting power of ONUs. In order to further minimize the total transmitting power, we propose the second algorithm by allocating the subcarrier and bit in the same procedure. The complexity of the two proposed algorithms was evaluated by polynomial time. From simulation results, the transmitting power of ONUs under a certain bit error rate is reduced by 30% and 50% using the first and the second proposed algorithms, respectively, compared with the traditional two-dimensional DBA algorithm in OFDMA-PONs.

© 2013 Optical Society of America

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References

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  1. D. Qian, J. Hu, and T. Wang, “10-Gb/s OFDMA-PON for delivery of heterogeneous services,” in Optical Fiber Communication Conf. (OFC), San Diego, CA, 2008.
  2. W. Wei, T. Wang, and C. Qiao, “Resource provisioning for orthogonal frequency division multiple access (OFDMA)-based virtual passive optical networks (VPON),” in Optical Fiber Communication Conf. (OFC), San Diego, CA, 2008.
  3. J. Kani, S. Shimazu, N. Yoshimoto, and H. Hadama, “Energy efficient optical access network technologies,” in Optical Fiber Communication Conf. (OFC), Los Angeles, CA, 2011.
  4. J. Zhang, J. Hu, D. Qian, and T. Wang, “Energy efficient OFDM transceiver design based on traffic tracking and adaptive bandwidth adjustment,” Opt. Express, vol.  19, no. 26, pp. B983–B988, Dec. 2011.
    [CrossRef]
  5. X. Hu, L. Zhang, P. Cao, K. Wang, and Y. Su, “Energy-efficient WDM-OFDM-PON employing shared OFDM modulation modules in optical line terminal,” Opt. Express, vol.  20, no. 7, pp. 8071–8077, Mar. 2012.
    [CrossRef]
  6. Y. Zhao, Y. Qiao, and Y. Ji, “Power efficient and colorless PON upstream system using asymmetric clipping optical OFDM and TDMA technologies,” Opt. Commun., vol.  285, no. 7, pp. 1787–1791, 2012.
    [CrossRef]
  7. K. Kanonakis, E. Giacoumidis, and I. Tomkos, “Physical-layer-aware MAC schemes for dynamic subcarrier assignment in OFDMA-PON networks,” J. Lightwave Technol., vol.  30, no. 12, pp. 1915–1923, June 2012.
    [CrossRef]
  8. K. Kanonakis, N. Cvijetic, I. Tomkos, and T. Wang, “A novel energy and delay efficient OFDMA ‘Meta-MAC’ scheme for heterogeneous PON coexistence,” in Opto-Electronics and Communications Conf., July 2012, pp. 142–143.
  9. C. Wang, W. Wei, and T. Wang, “Multiple channel scheduling algorithms for WDM PONs and OFDMA PONs,” in Optical Fiber Communication Conf. (OFC), 2009, paper OMV6.
  10. J. Zhang, T. Wang, and N. Ansari, “An efficient MAC protocol for asynchronous ONUs in OFDMA PONs,” in Optical Fiber Communication Conf., 2011, paper JWA71.
  11. K. Kanonakis and I. Tomkos, “Improving the efficiency of online upstream scheduling and wavelength assignment in hybrid WDM/TDMA EPON networks,” IEEE J. Sel. Areas Commun., vol.  28, no. 6, pp. 838–848, Aug. 2010.
    [CrossRef]
  12. L. Nadal, M. S. Moreolo, J. M. Fabrega, and G. Junyent, “Low complexity bit rate variable transponders based on optical OFDM with PAPR reduction capabilities,” in 17th European Conf. on Networks and Optical Communications, June 2012, pp. 1–6.
  13. B. S. Krongold, K. Ramchandran, and D. L. Jones, “Computationally efficient optimal power allocation algorithm for multicarrier communication systems,” in Proc. IEEE Int. Conf. Communications, Atlanta, GA, 1998, pp. 1018–1022.
  14. S. K. Lai, R. S. Cheng, K. B. Letaief, and R. D. Murch, “Adaptive trellis coded MQAM and power optimization for OFDM transmission,” in Proc. IEEE Vehicular Technology Conf. (VTC), Houston, TX, May 1999.
  15. C. Wong, R. S. Cheng, K. B. Letaief, and R. D. Murch, “Multiuser OFDM with adaptive subcarrier, bit, and power allocation,” IEEE J. Sel. Areas Commun., vol.  17, no 10, pp. 1747–1758, Oct. 1999.
    [CrossRef]
  16. J. G. Proakis, Digital Communications, 5th ed. New York: McGraw-Hill, 2011.
  17. “NEC: FTTx solution with GEPON” [Online]. Available: http://www.nec.com/en/global/solutions/nsp/fixed/fttx.html .
  18. R. Ruiz and T. Stutzle, “A simple and effective iterated greedy algorithm for the permutation flow shop scheduling problem,” Eur. J. Oper. Res., vol.  177, no. 3, pp. 2033–2049, 2007.
  19. I. Ribas, R. Companys, and X. Martorell, “An iterated greedy algorithm for the flow shop scheduling problem with blocking,” Omega, vol.  39, no. 3, pp. 293–301, 2011.
  20. Texas Instruments, http://www.ti.com/ .

2012 (3)

2011 (2)

J. Zhang, J. Hu, D. Qian, and T. Wang, “Energy efficient OFDM transceiver design based on traffic tracking and adaptive bandwidth adjustment,” Opt. Express, vol.  19, no. 26, pp. B983–B988, Dec. 2011.
[CrossRef]

I. Ribas, R. Companys, and X. Martorell, “An iterated greedy algorithm for the flow shop scheduling problem with blocking,” Omega, vol.  39, no. 3, pp. 293–301, 2011.

2010 (1)

K. Kanonakis and I. Tomkos, “Improving the efficiency of online upstream scheduling and wavelength assignment in hybrid WDM/TDMA EPON networks,” IEEE J. Sel. Areas Commun., vol.  28, no. 6, pp. 838–848, Aug. 2010.
[CrossRef]

2007 (1)

R. Ruiz and T. Stutzle, “A simple and effective iterated greedy algorithm for the permutation flow shop scheduling problem,” Eur. J. Oper. Res., vol.  177, no. 3, pp. 2033–2049, 2007.

1999 (1)

C. Wong, R. S. Cheng, K. B. Letaief, and R. D. Murch, “Multiuser OFDM with adaptive subcarrier, bit, and power allocation,” IEEE J. Sel. Areas Commun., vol.  17, no 10, pp. 1747–1758, Oct. 1999.
[CrossRef]

Ansari, N.

J. Zhang, T. Wang, and N. Ansari, “An efficient MAC protocol for asynchronous ONUs in OFDMA PONs,” in Optical Fiber Communication Conf., 2011, paper JWA71.

Cao, P.

Cheng, R. S.

C. Wong, R. S. Cheng, K. B. Letaief, and R. D. Murch, “Multiuser OFDM with adaptive subcarrier, bit, and power allocation,” IEEE J. Sel. Areas Commun., vol.  17, no 10, pp. 1747–1758, Oct. 1999.
[CrossRef]

S. K. Lai, R. S. Cheng, K. B. Letaief, and R. D. Murch, “Adaptive trellis coded MQAM and power optimization for OFDM transmission,” in Proc. IEEE Vehicular Technology Conf. (VTC), Houston, TX, May 1999.

Companys, R.

I. Ribas, R. Companys, and X. Martorell, “An iterated greedy algorithm for the flow shop scheduling problem with blocking,” Omega, vol.  39, no. 3, pp. 293–301, 2011.

Cvijetic, N.

K. Kanonakis, N. Cvijetic, I. Tomkos, and T. Wang, “A novel energy and delay efficient OFDMA ‘Meta-MAC’ scheme for heterogeneous PON coexistence,” in Opto-Electronics and Communications Conf., July 2012, pp. 142–143.

Fabrega, J. M.

L. Nadal, M. S. Moreolo, J. M. Fabrega, and G. Junyent, “Low complexity bit rate variable transponders based on optical OFDM with PAPR reduction capabilities,” in 17th European Conf. on Networks and Optical Communications, June 2012, pp. 1–6.

Giacoumidis, E.

Hadama, H.

J. Kani, S. Shimazu, N. Yoshimoto, and H. Hadama, “Energy efficient optical access network technologies,” in Optical Fiber Communication Conf. (OFC), Los Angeles, CA, 2011.

Hu, J.

J. Zhang, J. Hu, D. Qian, and T. Wang, “Energy efficient OFDM transceiver design based on traffic tracking and adaptive bandwidth adjustment,” Opt. Express, vol.  19, no. 26, pp. B983–B988, Dec. 2011.
[CrossRef]

D. Qian, J. Hu, and T. Wang, “10-Gb/s OFDMA-PON for delivery of heterogeneous services,” in Optical Fiber Communication Conf. (OFC), San Diego, CA, 2008.

Hu, X.

Ji, Y.

Y. Zhao, Y. Qiao, and Y. Ji, “Power efficient and colorless PON upstream system using asymmetric clipping optical OFDM and TDMA technologies,” Opt. Commun., vol.  285, no. 7, pp. 1787–1791, 2012.
[CrossRef]

Jones, D. L.

B. S. Krongold, K. Ramchandran, and D. L. Jones, “Computationally efficient optimal power allocation algorithm for multicarrier communication systems,” in Proc. IEEE Int. Conf. Communications, Atlanta, GA, 1998, pp. 1018–1022.

Junyent, G.

L. Nadal, M. S. Moreolo, J. M. Fabrega, and G. Junyent, “Low complexity bit rate variable transponders based on optical OFDM with PAPR reduction capabilities,” in 17th European Conf. on Networks and Optical Communications, June 2012, pp. 1–6.

Kani, J.

J. Kani, S. Shimazu, N. Yoshimoto, and H. Hadama, “Energy efficient optical access network technologies,” in Optical Fiber Communication Conf. (OFC), Los Angeles, CA, 2011.

Kanonakis, K.

K. Kanonakis, E. Giacoumidis, and I. Tomkos, “Physical-layer-aware MAC schemes for dynamic subcarrier assignment in OFDMA-PON networks,” J. Lightwave Technol., vol.  30, no. 12, pp. 1915–1923, June 2012.
[CrossRef]

K. Kanonakis and I. Tomkos, “Improving the efficiency of online upstream scheduling and wavelength assignment in hybrid WDM/TDMA EPON networks,” IEEE J. Sel. Areas Commun., vol.  28, no. 6, pp. 838–848, Aug. 2010.
[CrossRef]

K. Kanonakis, N. Cvijetic, I. Tomkos, and T. Wang, “A novel energy and delay efficient OFDMA ‘Meta-MAC’ scheme for heterogeneous PON coexistence,” in Opto-Electronics and Communications Conf., July 2012, pp. 142–143.

Krongold, B. S.

B. S. Krongold, K. Ramchandran, and D. L. Jones, “Computationally efficient optimal power allocation algorithm for multicarrier communication systems,” in Proc. IEEE Int. Conf. Communications, Atlanta, GA, 1998, pp. 1018–1022.

Lai, S. K.

S. K. Lai, R. S. Cheng, K. B. Letaief, and R. D. Murch, “Adaptive trellis coded MQAM and power optimization for OFDM transmission,” in Proc. IEEE Vehicular Technology Conf. (VTC), Houston, TX, May 1999.

Letaief, K. B.

C. Wong, R. S. Cheng, K. B. Letaief, and R. D. Murch, “Multiuser OFDM with adaptive subcarrier, bit, and power allocation,” IEEE J. Sel. Areas Commun., vol.  17, no 10, pp. 1747–1758, Oct. 1999.
[CrossRef]

S. K. Lai, R. S. Cheng, K. B. Letaief, and R. D. Murch, “Adaptive trellis coded MQAM and power optimization for OFDM transmission,” in Proc. IEEE Vehicular Technology Conf. (VTC), Houston, TX, May 1999.

Martorell, X.

I. Ribas, R. Companys, and X. Martorell, “An iterated greedy algorithm for the flow shop scheduling problem with blocking,” Omega, vol.  39, no. 3, pp. 293–301, 2011.

Moreolo, M. S.

L. Nadal, M. S. Moreolo, J. M. Fabrega, and G. Junyent, “Low complexity bit rate variable transponders based on optical OFDM with PAPR reduction capabilities,” in 17th European Conf. on Networks and Optical Communications, June 2012, pp. 1–6.

Murch, R. D.

C. Wong, R. S. Cheng, K. B. Letaief, and R. D. Murch, “Multiuser OFDM with adaptive subcarrier, bit, and power allocation,” IEEE J. Sel. Areas Commun., vol.  17, no 10, pp. 1747–1758, Oct. 1999.
[CrossRef]

S. K. Lai, R. S. Cheng, K. B. Letaief, and R. D. Murch, “Adaptive trellis coded MQAM and power optimization for OFDM transmission,” in Proc. IEEE Vehicular Technology Conf. (VTC), Houston, TX, May 1999.

Nadal, L.

L. Nadal, M. S. Moreolo, J. M. Fabrega, and G. Junyent, “Low complexity bit rate variable transponders based on optical OFDM with PAPR reduction capabilities,” in 17th European Conf. on Networks and Optical Communications, June 2012, pp. 1–6.

Proakis, J. G.

J. G. Proakis, Digital Communications, 5th ed. New York: McGraw-Hill, 2011.

Qian, D.

J. Zhang, J. Hu, D. Qian, and T. Wang, “Energy efficient OFDM transceiver design based on traffic tracking and adaptive bandwidth adjustment,” Opt. Express, vol.  19, no. 26, pp. B983–B988, Dec. 2011.
[CrossRef]

D. Qian, J. Hu, and T. Wang, “10-Gb/s OFDMA-PON for delivery of heterogeneous services,” in Optical Fiber Communication Conf. (OFC), San Diego, CA, 2008.

Qiao, C.

W. Wei, T. Wang, and C. Qiao, “Resource provisioning for orthogonal frequency division multiple access (OFDMA)-based virtual passive optical networks (VPON),” in Optical Fiber Communication Conf. (OFC), San Diego, CA, 2008.

Qiao, Y.

Y. Zhao, Y. Qiao, and Y. Ji, “Power efficient and colorless PON upstream system using asymmetric clipping optical OFDM and TDMA technologies,” Opt. Commun., vol.  285, no. 7, pp. 1787–1791, 2012.
[CrossRef]

Ramchandran, K.

B. S. Krongold, K. Ramchandran, and D. L. Jones, “Computationally efficient optimal power allocation algorithm for multicarrier communication systems,” in Proc. IEEE Int. Conf. Communications, Atlanta, GA, 1998, pp. 1018–1022.

Ribas, I.

I. Ribas, R. Companys, and X. Martorell, “An iterated greedy algorithm for the flow shop scheduling problem with blocking,” Omega, vol.  39, no. 3, pp. 293–301, 2011.

Ruiz, R.

R. Ruiz and T. Stutzle, “A simple and effective iterated greedy algorithm for the permutation flow shop scheduling problem,” Eur. J. Oper. Res., vol.  177, no. 3, pp. 2033–2049, 2007.

Shimazu, S.

J. Kani, S. Shimazu, N. Yoshimoto, and H. Hadama, “Energy efficient optical access network technologies,” in Optical Fiber Communication Conf. (OFC), Los Angeles, CA, 2011.

Stutzle, T.

R. Ruiz and T. Stutzle, “A simple and effective iterated greedy algorithm for the permutation flow shop scheduling problem,” Eur. J. Oper. Res., vol.  177, no. 3, pp. 2033–2049, 2007.

Su, Y.

Tomkos, I.

K. Kanonakis, E. Giacoumidis, and I. Tomkos, “Physical-layer-aware MAC schemes for dynamic subcarrier assignment in OFDMA-PON networks,” J. Lightwave Technol., vol.  30, no. 12, pp. 1915–1923, June 2012.
[CrossRef]

K. Kanonakis and I. Tomkos, “Improving the efficiency of online upstream scheduling and wavelength assignment in hybrid WDM/TDMA EPON networks,” IEEE J. Sel. Areas Commun., vol.  28, no. 6, pp. 838–848, Aug. 2010.
[CrossRef]

K. Kanonakis, N. Cvijetic, I. Tomkos, and T. Wang, “A novel energy and delay efficient OFDMA ‘Meta-MAC’ scheme for heterogeneous PON coexistence,” in Opto-Electronics and Communications Conf., July 2012, pp. 142–143.

Wang, C.

C. Wang, W. Wei, and T. Wang, “Multiple channel scheduling algorithms for WDM PONs and OFDMA PONs,” in Optical Fiber Communication Conf. (OFC), 2009, paper OMV6.

Wang, K.

Wang, T.

J. Zhang, J. Hu, D. Qian, and T. Wang, “Energy efficient OFDM transceiver design based on traffic tracking and adaptive bandwidth adjustment,” Opt. Express, vol.  19, no. 26, pp. B983–B988, Dec. 2011.
[CrossRef]

W. Wei, T. Wang, and C. Qiao, “Resource provisioning for orthogonal frequency division multiple access (OFDMA)-based virtual passive optical networks (VPON),” in Optical Fiber Communication Conf. (OFC), San Diego, CA, 2008.

D. Qian, J. Hu, and T. Wang, “10-Gb/s OFDMA-PON for delivery of heterogeneous services,” in Optical Fiber Communication Conf. (OFC), San Diego, CA, 2008.

C. Wang, W. Wei, and T. Wang, “Multiple channel scheduling algorithms for WDM PONs and OFDMA PONs,” in Optical Fiber Communication Conf. (OFC), 2009, paper OMV6.

J. Zhang, T. Wang, and N. Ansari, “An efficient MAC protocol for asynchronous ONUs in OFDMA PONs,” in Optical Fiber Communication Conf., 2011, paper JWA71.

K. Kanonakis, N. Cvijetic, I. Tomkos, and T. Wang, “A novel energy and delay efficient OFDMA ‘Meta-MAC’ scheme for heterogeneous PON coexistence,” in Opto-Electronics and Communications Conf., July 2012, pp. 142–143.

Wei, W.

C. Wang, W. Wei, and T. Wang, “Multiple channel scheduling algorithms for WDM PONs and OFDMA PONs,” in Optical Fiber Communication Conf. (OFC), 2009, paper OMV6.

W. Wei, T. Wang, and C. Qiao, “Resource provisioning for orthogonal frequency division multiple access (OFDMA)-based virtual passive optical networks (VPON),” in Optical Fiber Communication Conf. (OFC), San Diego, CA, 2008.

Wong, C.

C. Wong, R. S. Cheng, K. B. Letaief, and R. D. Murch, “Multiuser OFDM with adaptive subcarrier, bit, and power allocation,” IEEE J. Sel. Areas Commun., vol.  17, no 10, pp. 1747–1758, Oct. 1999.
[CrossRef]

Yoshimoto, N.

J. Kani, S. Shimazu, N. Yoshimoto, and H. Hadama, “Energy efficient optical access network technologies,” in Optical Fiber Communication Conf. (OFC), Los Angeles, CA, 2011.

Zhang, J.

J. Zhang, J. Hu, D. Qian, and T. Wang, “Energy efficient OFDM transceiver design based on traffic tracking and adaptive bandwidth adjustment,” Opt. Express, vol.  19, no. 26, pp. B983–B988, Dec. 2011.
[CrossRef]

J. Zhang, T. Wang, and N. Ansari, “An efficient MAC protocol for asynchronous ONUs in OFDMA PONs,” in Optical Fiber Communication Conf., 2011, paper JWA71.

Zhang, L.

Zhao, Y.

Y. Zhao, Y. Qiao, and Y. Ji, “Power efficient and colorless PON upstream system using asymmetric clipping optical OFDM and TDMA technologies,” Opt. Commun., vol.  285, no. 7, pp. 1787–1791, 2012.
[CrossRef]

Eur. J. Oper. Res. (1)

R. Ruiz and T. Stutzle, “A simple and effective iterated greedy algorithm for the permutation flow shop scheduling problem,” Eur. J. Oper. Res., vol.  177, no. 3, pp. 2033–2049, 2007.

IEEE J. Sel. Areas Commun. (2)

C. Wong, R. S. Cheng, K. B. Letaief, and R. D. Murch, “Multiuser OFDM with adaptive subcarrier, bit, and power allocation,” IEEE J. Sel. Areas Commun., vol.  17, no 10, pp. 1747–1758, Oct. 1999.
[CrossRef]

K. Kanonakis and I. Tomkos, “Improving the efficiency of online upstream scheduling and wavelength assignment in hybrid WDM/TDMA EPON networks,” IEEE J. Sel. Areas Commun., vol.  28, no. 6, pp. 838–848, Aug. 2010.
[CrossRef]

J. Lightwave Technol. (1)

Omega (1)

I. Ribas, R. Companys, and X. Martorell, “An iterated greedy algorithm for the flow shop scheduling problem with blocking,” Omega, vol.  39, no. 3, pp. 293–301, 2011.

Opt. Commun. (1)

Y. Zhao, Y. Qiao, and Y. Ji, “Power efficient and colorless PON upstream system using asymmetric clipping optical OFDM and TDMA technologies,” Opt. Commun., vol.  285, no. 7, pp. 1787–1791, 2012.
[CrossRef]

Opt. Express (2)

Other (12)

D. Qian, J. Hu, and T. Wang, “10-Gb/s OFDMA-PON for delivery of heterogeneous services,” in Optical Fiber Communication Conf. (OFC), San Diego, CA, 2008.

W. Wei, T. Wang, and C. Qiao, “Resource provisioning for orthogonal frequency division multiple access (OFDMA)-based virtual passive optical networks (VPON),” in Optical Fiber Communication Conf. (OFC), San Diego, CA, 2008.

J. Kani, S. Shimazu, N. Yoshimoto, and H. Hadama, “Energy efficient optical access network technologies,” in Optical Fiber Communication Conf. (OFC), Los Angeles, CA, 2011.

K. Kanonakis, N. Cvijetic, I. Tomkos, and T. Wang, “A novel energy and delay efficient OFDMA ‘Meta-MAC’ scheme for heterogeneous PON coexistence,” in Opto-Electronics and Communications Conf., July 2012, pp. 142–143.

C. Wang, W. Wei, and T. Wang, “Multiple channel scheduling algorithms for WDM PONs and OFDMA PONs,” in Optical Fiber Communication Conf. (OFC), 2009, paper OMV6.

J. Zhang, T. Wang, and N. Ansari, “An efficient MAC protocol for asynchronous ONUs in OFDMA PONs,” in Optical Fiber Communication Conf., 2011, paper JWA71.

Texas Instruments, http://www.ti.com/ .

J. G. Proakis, Digital Communications, 5th ed. New York: McGraw-Hill, 2011.

“NEC: FTTx solution with GEPON” [Online]. Available: http://www.nec.com/en/global/solutions/nsp/fixed/fttx.html .

L. Nadal, M. S. Moreolo, J. M. Fabrega, and G. Junyent, “Low complexity bit rate variable transponders based on optical OFDM with PAPR reduction capabilities,” in 17th European Conf. on Networks and Optical Communications, June 2012, pp. 1–6.

B. S. Krongold, K. Ramchandran, and D. L. Jones, “Computationally efficient optimal power allocation algorithm for multicarrier communication systems,” in Proc. IEEE Int. Conf. Communications, Atlanta, GA, 1998, pp. 1018–1022.

S. K. Lai, R. S. Cheng, K. B. Letaief, and R. D. Murch, “Adaptive trellis coded MQAM and power optimization for OFDM transmission,” in Proc. IEEE Vehicular Technology Conf. (VTC), Houston, TX, May 1999.

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Figures (4)

Fig. 1.
Fig. 1.

Structure of OFDMA-PON system.

Fig. 2.
Fig. 2.

(a) Two-dimensional allocation. (b) Three-dimensional allocation.

Fig. 3.
Fig. 3.

For 4.5Gb/s total bandwidth demand with five ONUs, 128 OFDM subcarriers, and 1.28 GHz bandwidth, subcarrier, and bit allocation results for (a) Algorithm 1 and (b) Algorithm 2.

Fig. 4.
Fig. 4.

Relative transmission power. (a) Overall transmitting power of ONUs versus user’s data rate for different algorithms with five ONUs, 128 OFDM subcarriers, and 1.28 GHz bandwidth. (b) Overall transmitting power of ONUs versus user’s data rate for different algorithms with 32 ONUs, 1024 OFDM subcarriers, and 10.24 GHz bandwidth.

Tables (4)

Tables Icon

Algorithm 1 Subcarrier allocation

Tables Icon

Algorithm 1 Bit allocation

Tables Icon

Algorithm 2 Subcarrier and bit allocation

Tables Icon

Algorithm 2 Update(ck,n,ΔPk)

Equations (8)

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

PT=minck,nDn=1Nk=1KPk,n,
Pk,n=f(ck,n)ak2,
f(c)=N03[Q1(Pe4)]2(2c1),
ΔPk={[f(ck,N2+1)f(ck,N2)][f(ck,N1+1)f(ck,N11)]}/ak2
T=O(N)[O(K)+O(1)]=O(NK)+O(N)=O(NK)
T=O(K)+O(N)[O(K)+O(1)]Subcarrier allocation+O(K){O(Sk)+O(NSk)+O(Rk)[O(Sk)+O(1)]}Bit allocation=O(K)+O(NK)Subcarrier allocation+O(K)[O(Sk)+O(NSk)+O(RkSk)]Bit allocation=O(K)+O(NK)Subcarrier allocation+O(K)[O(Sk)+O(NSk)+O(DmaxSk2)](forRk=SkDmax)Bit allocation=O(K)+O(NK)Subcarrier allocation+O(K)[O(N)+O(N)+O(DmaxN2)]Bit allocation(forSkN)=O(NK)Subcarrier allocation+O(DmaxKN2)Bit allocation=O(DmaxKN2)=O(KN2)(forDmaxis a constant)
Tsub=O(Sk)+O(Dmax)[O(Sk)+O(1)]=O(Sk)+O(DmaxSk)=O(Sk)(forDmaxis a constant).
T=O(K){O(1)+O(Sk)[O(1)+Tsub]+O(Sk)O(1)}Algorithm2Step1+O(SkN)[O(K)+Tsub+O(1)]Algorithm2Step2=O(K)[O(Sk2)+O(Sk)]Algorithm2Step1+O(SkN)[O(K)+O(Sk)]Algorithm2Step2=O(K)O(N2)Algorithm2Step1+O(N)[O(K)+O(N)]Algorithm2Step2(forSk=O(N))=O(KN2)Algorithm2Step1+O(NK)+O(N2)Algorithm2Step2=O(KN2)