# Network Planning of the CATV communication networks - PowerPoint

Document Sample

```					Network Planning of the CATV
communication networks
Arthur, K. W. Peng, OPLAB
d6725005@im.ntu.edu.tw
April 22, 2005
Agenda
Introduction
Problem Description and Formulation
Formulation Analysis and Reformulation
Numerical Experiments
Conclusion
Q&A
CATV Communication Network
Technology
TRUNK
NETWORK
Satellite dish
Trunk
Amplifier

Bridger
Amplifier                                     Tap

Splitter     Distribution
Direction       Netw ork
Couplers

Line Extender

Television

The Network Structure of CATV Networks
Network Planning ---
製圖
幹線系統設計
餽線系統設計
反向系統設計

頭端幹線系統

Figure 2-10

相對信號位準與損失的系統點

Similar to the design of downlink.
Noise Funneling
   Limit the number of branch and amplifier.
前向---反向放大器
and repetitive.
   CATV CAD: Gen Enterprise Ltd.
   Symplex Suite of software: SpanPro Inc.
   Program System：Lode Data Corporation
   Cable Tools: Goldcom Inc.
Feature
   Auto-tracking the signal quality.
   Helping the design to calculate the network
requirement, cost, etc.
   The design is still depend on the experience of the
network designer.
CATV Network Planning Tools
•Stand-alone version   •Web-based version
Mathematical Formulation and
Network Optimization
Basic ideas: formulate the network and using
network optimization technique to find the optimal
solution.

CNR                 Fl     Mv
X-MOD
l     Ov
CNR
Bv               X-MOD
CSO
Fv                CTB
User

Gv

Fv

Mv
Av
Performance Requirements

Performance requirements in
downstream
   CNR (Carrier to Noise Ratio) ≧43dB
   X-MOD (Cross Modulation ) ≦-46dB
   CSO (Composite Second Order) ≦-53dB
   CTB (Composite Triple Beat) ≦-53dB
Performance Requirements
(cont’d)

Performance requirements in upstream
Problem Formulation
Problem description
   Given :
   downstream performance objectives
   upstream performance objectives
   specifications of network components
   cost structure of network components
   number and position of endusers
   terrain which networks will pass through and the
associated cost
   Determine:
 routing
 allocation of network components
 operational parameters (e.g., gain of each amplifier)
Problem Formulation
Features
   Nonlinear problems
   Hard to solve directly by standard methods
   Some techniques needed
 Problem Decomposition
 Steiner Tree Problem

   Network Optimization
 Geometric Programming
   Posynomial form
Problem Decomposition and
Reformulation
Part I: Steiner Tree Problems
min  yl Cl
lL

(13) v y l  1                       v  V
lLin

(14) y l  0 or 1                     l  L
(15)    pl x p  yl | W |           l  L
wW pPw

(16)  x p  1                    w  W
pPw

(17) x p  0 or 1                 p  Pw , w  W
Problem Decomposition and
Reformulation (cont’d)

User3

User1

User2

Steiner vertices   regular vertices
Problem Decomposition and
Reformulation (cont’d)
Heuristic approximation algorithms
   Minimum Cost Paths Heuristic (MPH)
G  (V , E , d )        S V      S  {v1 , v2 , v3 ,...,vk }
PATH (W , s ) : shortest path from a connected component W
to a vertex s in G
 ( PATH (W , s )) : the cost of Path(W,s)
step 1 : V1  {v1}
step 2 : for each i  2 ,3,...,k do
find a vertex vi in S-Vi-1 such that
PATH(Vi-1 ,vi ))  min{ ( PATH(Vi-1 ,v j )) | v j  S-Vi-1}
Vi  add PATH(Vi-1 ,vi ) to Vi-1
Problem Decomposition and
Reformulation (cont’d)
Problem Decomposition and
Reformulation (cont’d)
Part II

min  [d 1 ( Al )1 ]   {z v [d 2 ( Fv ) 1  d 3 (Gv )1  d 4 ( M v )1
lL                vV


 1          1           1
 d 5 ( Bv )  d 6 (Ov ) ]  z v [d 7 ( Fv )  d 8 (Gv )  d 9 ( M v ) ]
1            1


 z v [d 10 ( Av )1 ]}
L : the set of links in the given candidate topology
V : the set of nodes in the given candidate topology
s.t.
Problem Decomposition and
Reformulation (cont’d)
H      Hpc                  pc

(1) Si  Gpi Api  Apj pj  10                     w  W
i 1                 j 1
H pc                                                        Csys
z   pn    Fpn                  
(2)  (                                           59
)  10       10
w  W
n 1          n 1           n 1
S  Gpi Api  Apjpj * 10 10
i 1            j 1                                   M sys
H pc                                   n    n 1                                *0.5

(3)  z ( M pi )
pi
0.5
  Gpi Api  Apjpj  10            10
i 1                                 i 1   j 1
 Bsys
H pc                                 n      n 1                               *0.5

(4)  z ( Bpi )
pi
0.5
  Gpi Api  Apjpj  10            10
i 1                                i 1    j 1
Osys
H pc                                n      n 1
 10
(5)  z (Opi )   Gpi Api  Apjpj  10 w  W

pi
1
i 1                               i 1    j 1
Problem Decomposition and
Reformulation (cont’d)

H pc        H pc
(6)  Gpi Api  Apj  1          w W v V p
i  H pv     j  H pv

          1     
    
 0.5
Csys

(7) s  10  Ft  (  zv  zv )  10 10 w  W
5.9
vV p   vVP

V p : the node set of path p
VP : the node set of path set P
Decision Variables :

Gv : gain of upstream amplifier

s : input signal strength to upstream amplifier

Ft : noise figure of upstream amplifier
Problem Decomposition and
Reformulation (cont’d)

H pc

  0.5                M sys
*0.5
(8)  zpi ( M t )  s  Gpi  10    10
w  W
i 1

Decision Variable :

M t : cross modulation of upstream amplifier
Solution Approaches
Posynomial problem
min g 0 (t )                                                                      (IP)
s.t. : t1  0 , t 2  0 , ... , t m  0                                           (1)
g1 ( t )  1 , g 2 ( t )  1 , ... , g p ( t )  1                         (2)
g k (t )   c t                                     , k  0, 1, ..., p,
ai 1 ai 2          aim
i 2    t 2      ...t   m
iJ [ k ]

   aij : arbitrary real numbers
    ci : positive
    gk(t) : posynomials
Solution Approaches (cont’d)
Dual problem
p
n     ci
max v ( )  [(                ) i ]  k ( ) k ( )   (IP)
i 1   i          k 1

s.t. :  1  0,  2  0, ... n  0                        Positivity condition
 i  1                                         Normality condition
jJ [ 0 ]
n                                                 Orthogonality condition
 aij i  0                j  1,2,..., p
i 1

k ( )    i ,                 k  1,2,..., p
iJ [ k ]
Solution Approaches (cont’d)
Penalty method                          n
min    ln v ( )  J 1 (   i  1)  J 2 (  aij i ) 2 j  1,2,...,m
2
iJ [ 0 ]             i 1

where J 1 and J 2 are large positive numbers.

Steepest descent method
Rounding procedure
Computational Experiments
Solution modules
Module 1
Determining the Interconnection and
Routing of CATV Networks

Module 2
Determining Locations to Place
Amplifiers

Module 3
Determining Configurations and
Parameters of CATV Components

Module 4
Determining Configurations and
Parameters of CATV Reverse Modules
Computational Experiments
91                                        100

90
81

71                                        80

61                                        70

51                                        60

41                                        50

31                                        40

21                                        30

11                                        20

1
2   3   4   5   6   7   8   9   10
Computational Experiments
The constructed steiner tree
91                                        100

90
81

71                                        80

61                                        70

51                                        60

41                                        50

31                                        40

21                                        30

11                                        20

1
2   3   4   5   6   7   8   9   10
Computational Experiments
Deciding the locations and parameters
of amplifiers
91                                                       100
zg=0.053235                          90
81
zg=0.064211        80
71

61                                                       70

51                                                       60

41                                                       50

31                                                       40
zg=0.064212
21                                                       30

11           zg=0.117608                                 20

1
2   3     4    5      6      7      8     9    10
Conclusion
It is feasible to use mathematical
programming methods in CATV network
planning
The solution provided by this approach can
be used to evaluate the QoS in many
situation.
As a core module, we can add more features:
 New network components
 New Services
Future Research Directions
Network Planning and Management
   CATV network planning and optimization
 Layering
 QoS
 Fault tolerance/Reliability
   CATV network performance
 Capacity management