Abstract

Designing metropolitan wavelength division multiplexing (WDM) ring networks with minimum deployment cost is a demanding issue in Telecommunication Network planning . We have already presented amplifier placement methods to minimize the number of amplifiers in WDM rings for the case all amplifiers follow a unique gain model. In this paper, we take into account different types of amplifiers with predefined fixed characteristics and costs. We also formulate fiber dispersion limitations on the ring design, and present two efficient methods for placing amplifiers and Dispersion Compensation Modules (DCMs) in WDM rings to minimize the total deployment cost of the system. The first method deals with both linear and nonlinear equations and uses a mixed integer nonlinear programming (MINLP) solver where the second method applies the linear approximation of nonlinear constraints, and uses a mixed integer linear programming (MILP) solver to minimize the total cost of the system. We carry out Simulation experiments to confirm the applicability of the methods and compare the results for various network configurations.

©2006 Optical Society of America

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References

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  1. A. Saleh and J. Simmons, “Architectural principles of optical regional and metropolitan access networks,” J. Lightwave Technol. 17, 2431-2448 (1999).
    [Crossref]
  2. M. Borella, J. Jue, D. Banerjee, B. Ramamurthy, and B. Mukherjee, “Optical components for WDM lightwave networks,” Proceedings of the IEEE 85, 1274-1307 (1997).
    [Crossref]
  3. R. K. Ahuja, T. L. Magnanti, and J. B. Orlin, Network Flows (Prentice Hall, New Jersey, 1993).
  4. R. Ramaswami and K. N. Sivarajan, Optical Networks: A Practical perspective (Morgan Kaufmann, San Francisco, CA, 1998).
  5. B. Sanso and P. Soriano, Telecommunications Network Planning (Kluwer Academic, Norwell, MA, 1999).
    [Crossref]
  6. T. E. Stern and K. Bala, Multiwavelength optical Networks: A Layered approach (Addison Wesley, Reading, MA, 1999).
  7. C.-S. Li, F.-K. Tong, C. Georgiou, and M. Chen, “Gain equalization in metropolitan and wide area optical networks using optical amplifiers,” Proceedings IEEE INFOCOM ’94  1, 130-137 (1994).
  8. B. Ramamurthy, J. Iness, and B. Mukherjee, “Optimizing amplifier placements in a multiwavelength optical LAN/MAN: the equally powered-wavelengths case,” J. Lightwave Technol. 16, 1560-1569 (Sept. 1998).
    [Crossref]
  9. B. Ramamurthy, J. Iness, and B. Mukherjee, “Optimizing amplifier placements in a multiwavelength optical LAN/MAN: the unequally powered wavelengths case,” IEEE/ACM Transactions on Networking 6, 755-767 (1998).
    [Crossref]
  10. J. Iness and B. Mukherjee, “New optical amplifier placement schemes for broadcast networks,” European Transactions on Telecommunications  11, 117-124 (2000).
  11. A. Fumagalli, G. Balestra, and L. Valcarenghi, “Optimal amplifier placement in multi-wavelength optical networks based on simulated annealing,” Proceedings of the SPIE - The International Society for Optical Engineering 3531, 268-279 (1998).
  12. L. Zhong and B. Ramamurthy, “Optimization of amplifier placements in switch-based optical networks,” ICC 2001. IEEE International Conference on Communications 1, 224-228 (2001).
  13. A. Tran, R. Tucker, and N. Boland, “Amplifier placement methods for metropolitan WDM ring networks,” J. Lightwave Technol. 22, 2509-2522 (2004).
    [Crossref]
  14. A. Minagar and M. Premaratne, “Cost Optimal Configuration of Optical Networks,” J. Lightwave Technol. 243295-3302 (2006).
    [Crossref]
  15. P. Saengudomlert, E. Modiano, and R. Gallager, “On-line routing and wavelength assignment for dynamic traffic in WDM ring and torus networks,” IEEE/ACM Transactions on Networking 14, 330-340 (2006).
    [Crossref]
  16. K. Mosharaf, “Optimal Resource Allocation and Fairness Control in All-Optical WDM Networks,” IEEE Journal on Selected Areas in Communications 23, 1496-1507 (2005).
    [Crossref]
  17. B. Mukherjee, “WDM Optical Communication Networks: Progress and Challenges,” IEEE Journal on Selected Areas in Communications 18, 1810-1824 (2000).
    [Crossref]
  18. G. P. Agrawal, Fiber-Optic Communication Systems, 3rd ed. (Wiley-Interscience, New York, 2002).
    [Crossref]
  19. W. Cornwell and I. Andonovic, “Interferometric noise for a single interferer: comparison between theory and experiment,” Electron. Lett. 32, 1501-1502 (1996).
    [Crossref]
  20. R. Fourer, D. M. Gay, and B. W. Kernighan, AMPL: A Modeling Language for Mathematical Programming, 2nd ed. (Duxbury Press, Toronto, 2003).
  21. “MINLP solver on NEOS server,” URL http://neos.mcs.anl.gov/neos/solvers/minco:MINLP/AMPL.html.
  22. “User Manual for MINLP,” URL http://www.maths.dundee.ac.uk/˜ sleyffer/MINLP_manual.ps.Z.
  23. “MINTO solver on NEOS server,” URL http://neos.mcs.anl.gov/neos/solvers/milp:MINTO/AMPL.html.

2006 (2)

A. Minagar and M. Premaratne, “Cost Optimal Configuration of Optical Networks,” J. Lightwave Technol. 243295-3302 (2006).
[Crossref]

P. Saengudomlert, E. Modiano, and R. Gallager, “On-line routing and wavelength assignment for dynamic traffic in WDM ring and torus networks,” IEEE/ACM Transactions on Networking 14, 330-340 (2006).
[Crossref]

2005 (1)

K. Mosharaf, “Optimal Resource Allocation and Fairness Control in All-Optical WDM Networks,” IEEE Journal on Selected Areas in Communications 23, 1496-1507 (2005).
[Crossref]

2004 (1)

2001 (1)

L. Zhong and B. Ramamurthy, “Optimization of amplifier placements in switch-based optical networks,” ICC 2001. IEEE International Conference on Communications 1, 224-228 (2001).

2000 (2)

J. Iness and B. Mukherjee, “New optical amplifier placement schemes for broadcast networks,” European Transactions on Telecommunications  11, 117-124 (2000).

B. Mukherjee, “WDM Optical Communication Networks: Progress and Challenges,” IEEE Journal on Selected Areas in Communications 18, 1810-1824 (2000).
[Crossref]

1999 (1)

1998 (3)

B. Ramamurthy, J. Iness, and B. Mukherjee, “Optimizing amplifier placements in a multiwavelength optical LAN/MAN: the equally powered-wavelengths case,” J. Lightwave Technol. 16, 1560-1569 (Sept. 1998).
[Crossref]

B. Ramamurthy, J. Iness, and B. Mukherjee, “Optimizing amplifier placements in a multiwavelength optical LAN/MAN: the unequally powered wavelengths case,” IEEE/ACM Transactions on Networking 6, 755-767 (1998).
[Crossref]

A. Fumagalli, G. Balestra, and L. Valcarenghi, “Optimal amplifier placement in multi-wavelength optical networks based on simulated annealing,” Proceedings of the SPIE - The International Society for Optical Engineering 3531, 268-279 (1998).

1997 (1)

M. Borella, J. Jue, D. Banerjee, B. Ramamurthy, and B. Mukherjee, “Optical components for WDM lightwave networks,” Proceedings of the IEEE 85, 1274-1307 (1997).
[Crossref]

1996 (1)

W. Cornwell and I. Andonovic, “Interferometric noise for a single interferer: comparison between theory and experiment,” Electron. Lett. 32, 1501-1502 (1996).
[Crossref]

1994 (1)

C.-S. Li, F.-K. Tong, C. Georgiou, and M. Chen, “Gain equalization in metropolitan and wide area optical networks using optical amplifiers,” Proceedings IEEE INFOCOM ’94  1, 130-137 (1994).

Agrawal, G. P.

G. P. Agrawal, Fiber-Optic Communication Systems, 3rd ed. (Wiley-Interscience, New York, 2002).
[Crossref]

Ahuja, R. K.

R. K. Ahuja, T. L. Magnanti, and J. B. Orlin, Network Flows (Prentice Hall, New Jersey, 1993).

Andonovic, I.

W. Cornwell and I. Andonovic, “Interferometric noise for a single interferer: comparison between theory and experiment,” Electron. Lett. 32, 1501-1502 (1996).
[Crossref]

Bala, K.

T. E. Stern and K. Bala, Multiwavelength optical Networks: A Layered approach (Addison Wesley, Reading, MA, 1999).

Balestra, G.

A. Fumagalli, G. Balestra, and L. Valcarenghi, “Optimal amplifier placement in multi-wavelength optical networks based on simulated annealing,” Proceedings of the SPIE - The International Society for Optical Engineering 3531, 268-279 (1998).

Banerjee, D.

M. Borella, J. Jue, D. Banerjee, B. Ramamurthy, and B. Mukherjee, “Optical components for WDM lightwave networks,” Proceedings of the IEEE 85, 1274-1307 (1997).
[Crossref]

Boland, N.

Borella, M.

M. Borella, J. Jue, D. Banerjee, B. Ramamurthy, and B. Mukherjee, “Optical components for WDM lightwave networks,” Proceedings of the IEEE 85, 1274-1307 (1997).
[Crossref]

Chen, M.

C.-S. Li, F.-K. Tong, C. Georgiou, and M. Chen, “Gain equalization in metropolitan and wide area optical networks using optical amplifiers,” Proceedings IEEE INFOCOM ’94  1, 130-137 (1994).

Cornwell, W.

W. Cornwell and I. Andonovic, “Interferometric noise for a single interferer: comparison between theory and experiment,” Electron. Lett. 32, 1501-1502 (1996).
[Crossref]

Fourer, R.

R. Fourer, D. M. Gay, and B. W. Kernighan, AMPL: A Modeling Language for Mathematical Programming, 2nd ed. (Duxbury Press, Toronto, 2003).

Fumagalli, A.

A. Fumagalli, G. Balestra, and L. Valcarenghi, “Optimal amplifier placement in multi-wavelength optical networks based on simulated annealing,” Proceedings of the SPIE - The International Society for Optical Engineering 3531, 268-279 (1998).

Gallager, R.

P. Saengudomlert, E. Modiano, and R. Gallager, “On-line routing and wavelength assignment for dynamic traffic in WDM ring and torus networks,” IEEE/ACM Transactions on Networking 14, 330-340 (2006).
[Crossref]

Gay, D. M.

R. Fourer, D. M. Gay, and B. W. Kernighan, AMPL: A Modeling Language for Mathematical Programming, 2nd ed. (Duxbury Press, Toronto, 2003).

Georgiou, C.

C.-S. Li, F.-K. Tong, C. Georgiou, and M. Chen, “Gain equalization in metropolitan and wide area optical networks using optical amplifiers,” Proceedings IEEE INFOCOM ’94  1, 130-137 (1994).

Iness, J.

J. Iness and B. Mukherjee, “New optical amplifier placement schemes for broadcast networks,” European Transactions on Telecommunications  11, 117-124 (2000).

B. Ramamurthy, J. Iness, and B. Mukherjee, “Optimizing amplifier placements in a multiwavelength optical LAN/MAN: the unequally powered wavelengths case,” IEEE/ACM Transactions on Networking 6, 755-767 (1998).
[Crossref]

B. Ramamurthy, J. Iness, and B. Mukherjee, “Optimizing amplifier placements in a multiwavelength optical LAN/MAN: the equally powered-wavelengths case,” J. Lightwave Technol. 16, 1560-1569 (Sept. 1998).
[Crossref]

Jue, J.

M. Borella, J. Jue, D. Banerjee, B. Ramamurthy, and B. Mukherjee, “Optical components for WDM lightwave networks,” Proceedings of the IEEE 85, 1274-1307 (1997).
[Crossref]

Kernighan, B. W.

R. Fourer, D. M. Gay, and B. W. Kernighan, AMPL: A Modeling Language for Mathematical Programming, 2nd ed. (Duxbury Press, Toronto, 2003).

Li, C.-S.

C.-S. Li, F.-K. Tong, C. Georgiou, and M. Chen, “Gain equalization in metropolitan and wide area optical networks using optical amplifiers,” Proceedings IEEE INFOCOM ’94  1, 130-137 (1994).

Magnanti, T. L.

R. K. Ahuja, T. L. Magnanti, and J. B. Orlin, Network Flows (Prentice Hall, New Jersey, 1993).

Minagar, A.

Modiano, E.

P. Saengudomlert, E. Modiano, and R. Gallager, “On-line routing and wavelength assignment for dynamic traffic in WDM ring and torus networks,” IEEE/ACM Transactions on Networking 14, 330-340 (2006).
[Crossref]

Mosharaf, K.

K. Mosharaf, “Optimal Resource Allocation and Fairness Control in All-Optical WDM Networks,” IEEE Journal on Selected Areas in Communications 23, 1496-1507 (2005).
[Crossref]

Mukherjee, B.

J. Iness and B. Mukherjee, “New optical amplifier placement schemes for broadcast networks,” European Transactions on Telecommunications  11, 117-124 (2000).

B. Mukherjee, “WDM Optical Communication Networks: Progress and Challenges,” IEEE Journal on Selected Areas in Communications 18, 1810-1824 (2000).
[Crossref]

B. Ramamurthy, J. Iness, and B. Mukherjee, “Optimizing amplifier placements in a multiwavelength optical LAN/MAN: the unequally powered wavelengths case,” IEEE/ACM Transactions on Networking 6, 755-767 (1998).
[Crossref]

B. Ramamurthy, J. Iness, and B. Mukherjee, “Optimizing amplifier placements in a multiwavelength optical LAN/MAN: the equally powered-wavelengths case,” J. Lightwave Technol. 16, 1560-1569 (Sept. 1998).
[Crossref]

M. Borella, J. Jue, D. Banerjee, B. Ramamurthy, and B. Mukherjee, “Optical components for WDM lightwave networks,” Proceedings of the IEEE 85, 1274-1307 (1997).
[Crossref]

Orlin, J. B.

R. K. Ahuja, T. L. Magnanti, and J. B. Orlin, Network Flows (Prentice Hall, New Jersey, 1993).

Premaratne, M.

Ramamurthy, B.

L. Zhong and B. Ramamurthy, “Optimization of amplifier placements in switch-based optical networks,” ICC 2001. IEEE International Conference on Communications 1, 224-228 (2001).

B. Ramamurthy, J. Iness, and B. Mukherjee, “Optimizing amplifier placements in a multiwavelength optical LAN/MAN: the unequally powered wavelengths case,” IEEE/ACM Transactions on Networking 6, 755-767 (1998).
[Crossref]

B. Ramamurthy, J. Iness, and B. Mukherjee, “Optimizing amplifier placements in a multiwavelength optical LAN/MAN: the equally powered-wavelengths case,” J. Lightwave Technol. 16, 1560-1569 (Sept. 1998).
[Crossref]

M. Borella, J. Jue, D. Banerjee, B. Ramamurthy, and B. Mukherjee, “Optical components for WDM lightwave networks,” Proceedings of the IEEE 85, 1274-1307 (1997).
[Crossref]

Ramaswami, R.

R. Ramaswami and K. N. Sivarajan, Optical Networks: A Practical perspective (Morgan Kaufmann, San Francisco, CA, 1998).

Saengudomlert, P.

P. Saengudomlert, E. Modiano, and R. Gallager, “On-line routing and wavelength assignment for dynamic traffic in WDM ring and torus networks,” IEEE/ACM Transactions on Networking 14, 330-340 (2006).
[Crossref]

Saleh, A.

Sanso, B.

B. Sanso and P. Soriano, Telecommunications Network Planning (Kluwer Academic, Norwell, MA, 1999).
[Crossref]

Simmons, J.

Sivarajan, K. N.

R. Ramaswami and K. N. Sivarajan, Optical Networks: A Practical perspective (Morgan Kaufmann, San Francisco, CA, 1998).

Soriano, P.

B. Sanso and P. Soriano, Telecommunications Network Planning (Kluwer Academic, Norwell, MA, 1999).
[Crossref]

Stern, T. E.

T. E. Stern and K. Bala, Multiwavelength optical Networks: A Layered approach (Addison Wesley, Reading, MA, 1999).

Tong, F.-K.

C.-S. Li, F.-K. Tong, C. Georgiou, and M. Chen, “Gain equalization in metropolitan and wide area optical networks using optical amplifiers,” Proceedings IEEE INFOCOM ’94  1, 130-137 (1994).

Tran, A.

Tucker, R.

Valcarenghi, L.

A. Fumagalli, G. Balestra, and L. Valcarenghi, “Optimal amplifier placement in multi-wavelength optical networks based on simulated annealing,” Proceedings of the SPIE - The International Society for Optical Engineering 3531, 268-279 (1998).

Zhong, L.

L. Zhong and B. Ramamurthy, “Optimization of amplifier placements in switch-based optical networks,” ICC 2001. IEEE International Conference on Communications 1, 224-228 (2001).

Electron. Lett. (1)

W. Cornwell and I. Andonovic, “Interferometric noise for a single interferer: comparison between theory and experiment,” Electron. Lett. 32, 1501-1502 (1996).
[Crossref]

IEEE International Conference on Communications (1)

L. Zhong and B. Ramamurthy, “Optimization of amplifier placements in switch-based optical networks,” ICC 2001. IEEE International Conference on Communications 1, 224-228 (2001).

IEEE Journal on Selected Areas in Communications (2)

K. Mosharaf, “Optimal Resource Allocation and Fairness Control in All-Optical WDM Networks,” IEEE Journal on Selected Areas in Communications 23, 1496-1507 (2005).
[Crossref]

B. Mukherjee, “WDM Optical Communication Networks: Progress and Challenges,” IEEE Journal on Selected Areas in Communications 18, 1810-1824 (2000).
[Crossref]

IEEE/ACM Transactions on Networking (2)

P. Saengudomlert, E. Modiano, and R. Gallager, “On-line routing and wavelength assignment for dynamic traffic in WDM ring and torus networks,” IEEE/ACM Transactions on Networking 14, 330-340 (2006).
[Crossref]

B. Ramamurthy, J. Iness, and B. Mukherjee, “Optimizing amplifier placements in a multiwavelength optical LAN/MAN: the unequally powered wavelengths case,” IEEE/ACM Transactions on Networking 6, 755-767 (1998).
[Crossref]

J. Lightwave Technol. (4)

Proceedings IEEE INFOCOM (1)

C.-S. Li, F.-K. Tong, C. Georgiou, and M. Chen, “Gain equalization in metropolitan and wide area optical networks using optical amplifiers,” Proceedings IEEE INFOCOM ’94  1, 130-137 (1994).

Proceedings of the IEEE (1)

M. Borella, J. Jue, D. Banerjee, B. Ramamurthy, and B. Mukherjee, “Optical components for WDM lightwave networks,” Proceedings of the IEEE 85, 1274-1307 (1997).
[Crossref]

Proceedings of the SPIE - The International Society for Optical Engineering (1)

A. Fumagalli, G. Balestra, and L. Valcarenghi, “Optimal amplifier placement in multi-wavelength optical networks based on simulated annealing,” Proceedings of the SPIE - The International Society for Optical Engineering 3531, 268-279 (1998).

Other (10)

J. Iness and B. Mukherjee, “New optical amplifier placement schemes for broadcast networks,” European Transactions on Telecommunications  11, 117-124 (2000).

R. K. Ahuja, T. L. Magnanti, and J. B. Orlin, Network Flows (Prentice Hall, New Jersey, 1993).

R. Ramaswami and K. N. Sivarajan, Optical Networks: A Practical perspective (Morgan Kaufmann, San Francisco, CA, 1998).

B. Sanso and P. Soriano, Telecommunications Network Planning (Kluwer Academic, Norwell, MA, 1999).
[Crossref]

T. E. Stern and K. Bala, Multiwavelength optical Networks: A Layered approach (Addison Wesley, Reading, MA, 1999).

G. P. Agrawal, Fiber-Optic Communication Systems, 3rd ed. (Wiley-Interscience, New York, 2002).
[Crossref]

R. Fourer, D. M. Gay, and B. W. Kernighan, AMPL: A Modeling Language for Mathematical Programming, 2nd ed. (Duxbury Press, Toronto, 2003).

“MINLP solver on NEOS server,” URL http://neos.mcs.anl.gov/neos/solvers/minco:MINLP/AMPL.html.

“User Manual for MINLP,” URL http://www.maths.dundee.ac.uk/˜ sleyffer/MINLP_manual.ps.Z.

“MINTO solver on NEOS server,” URL http://neos.mcs.anl.gov/neos/solvers/milp:MINTO/AMPL.html.

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Figures (4)

Fig. 1.
Fig. 1. A typical unidirectional WDM ring network
Fig. 2.
Fig. 2. Amplifier gain G (dB) versus input power P in (dBm) for P sat = 20 dBm, G 0 = 30 dB
Fig. 3.
Fig. 3. Insertion losses and leakage paths at a node in the ring
Fig. 4.
Fig. 4. Amplifier and DCM placement solution for a six-node ring with 10 km node spacing using both Method 1 and Method 2

Tables (7)

Tables Icon

Table 1. Device Parameters

Tables Icon

Table 2. Network Parameters

Tables Icon

Table 4. Set of available amplifiers

Tables Icon

Table 5. Set of available DCMs

Tables Icon

Table 6. Running time, total cost, and solution configuration of Method 1 and Method 2 for different ring topologies

Tables Icon

Table 7. Running time and total cost of Method 2 and the approximation of Method 2 for different ring topologies

Equations (45)

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

G = 1 + P sat P in ln ( G 0 G )
A = 10 log 10 ( 2 N sp h v B 0 10 3 )
B = 10 log 10 ( 2 N sp h v B 1 10 3 )
min imize i = 1 L ( j = 1 N amp n i , j C amp , j + j = 1 N DCM m i , j C DCM , j )
j = 1 N amp n i , j 1 , n i , j 0 , i = 1 , , L
j = 1 N DCM m i , j 1 , m i , j 0 , i = 1 , , L
j = 1 N amp n i , j G amp , j 1 < G i j = 1 N amp n i , j G amp , j i = 1 , , L
P i tot = 10 log 10 ( k = 1 W 10 P i , k 10 + 10 p SCR i ASE β 1 NODE _ SCR i A + B 10 ) α L i
P amp , j min P i tot P amp , j max n i , j = 1 j = 1 , , N amp
Λ i = j = 1 N DCM m i , j γ DCM , j
Ω i = j = 1 N DCM m i , j D DCM , j
P DCM , j min P i tot + G i P DCM , j max m i , j = 1 j = 1 , , N DCM
P i tot + α L i P nonlinear
P i tot + G i P nonlinear
G i , k D max
D i , k + δ L i D min
S ( v ) = ( G 1 ) n sp h v
P i ASE = 10 log 10 [ 10 A 10 ( 10 G i 10 1 ) 10 Λ i 10 + 10 p SCR i ASE + G i Λ i β 1 NODE _ SCR i α L i 10 ]
P DEST i , k = P i , k + G i Λ i α L i β 1 NODE _ DEST i λ k NONDROP NODE _ DEST i
P DEST i , k = D i , k + δ L i + Ω i λ k NONDROP NODE _ DEST i
P i , k + G i Λ i α L i P i ASE Desired _ OSNR λ k DROP NODE _ DEST i
P minr P i , k + G i Λ i α L i β 2 NODE _ DEST i P minr + DR λ k DROP NODE _ DEST i
D minr D i , k + δ L i + Ω i D max r λ k DROP NODE _ DEST i
P DEST i , k = P NODE _ DEST i , k xmit β 3 NODE _ DEST i λ k ADD NODE _ DEST i
P min t = P NODE _ DEST i , k xmit P max t λ k ADD NODE _ DEST i
P DEST i , k = 0 λ k ADD NODE _ DEST i
( P i , k + G i Λ i α L i + IX 1 NODE _ DEST i ) ( P NODE _ DEST i , k xmit β 3 NODE _ DEST i ) 25
λ k ( DROP NODE _ DEST i ADD NODE _ DEST i )
( P NODE _ DEST i , k xmit IX 2 NODE _ DEST i ) ( P i , k + G i Λ i α L i β 2 NODE _ DEST i ) 25
λ k ( DROP NODE _ DEST i ADD NODE _ DEST i )
( i = 1 L ( α L i + Λ i ) + j = 1 N β 1 j ) i = 1 L G i MARGIN
y = 10 log 10 ( k = 1 W + 1 10 x k 10 )
y = k = 1 W + 1 h k x k + h W + 2
x j = [ x 1 j x 2 j x W + 1 j + 1 ] T j = 1 , , M
y j = 10 log 10 ( k = 1 W + 1 10 x k j 10 )
C = j = 1 M h T x j y j 2
C = h T Dh 2 Eh + j = 1 M ( y j ) 2
h = [ j = 1 M ( x j ( x j ) T ) ] 1 [ j = 1 M ( y j x j ) ]
P i tot = k = 1 W ( h k P i , k ) + h W + 1 ( P SRC i ASE β 1 NODE _ SRC i A + B ) + h W + 2 α L i
P i tot = k = 1 15 0.048 P i , k + 0.023 ( P SCR i ASE β 1 NODE _ SCR i A + B ) + 12.025 α L i
P i ASE = 10 log 10 [ 10 A 10 10 G i 10 10 Λ i 10 + 10 P SCR i ASE + G i Λ i β 1 NODE _ SRC i α L i 10 ]
P i ASE = G i Λ i + 10 log 10 [ 10 A 10 + 10 P SRC i ASE β 1 NODE _ SRC i α L i 10 ]
y = 10 log 10 ( 10 x 1 10 + F )
P i ASE = G i Λ i + h 1 ( P SRC i ASE β 1 NODE _ SRC i α L i ) + h 2
P i ASE = G i Λ i + 0.541 ( P SRC i ASE β 1 NODE _ SRC i α L i ) + 19.156

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