W-CDMA Network Design

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W-CDMA Network Design
Qibin Cai1 Joakim Kalvenes2 Jeffery
Kennington1 Eli Olinick1 Dinesh Rajan1 Southern
Methodist University 1 School of Engineering
2Edwin L. Cox School of Business Supported in
part by Office of Naval Research Award
N00014-96-1-0315
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Wireless Network Design Inputs

• Hot spots concentration points of
  users/subscribers (demand)
• Potential locations for radio towers (cells)
• Potential locations for mobile telephone
  switching offices (MTSO)
• Locations of access point(s) to Public Switched
  Telephone Network (PSTN)
• Costs for linking
• towers to MTSOs,
• MTSOs to each other or to PSTN

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Wireless Network Design Problem

• Determine
• Which radio towers to build (base station
  location)
• How to assign subscribers to towers (service
  assignment)
• Which MTSOs to use
• Topology of MTSO/PSTN backbone network
• Maximize profit revenue per subscriber served
  minus infrastructure costs

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Wireless Network Design Tool
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Optimization Model for Wireless Network Design
Sets

• L is the set of candidate tower locations.
• M is the set of subscriber locations.
• Cm is the set of tower locations that can service
  subscribers in location m.
• Pl is the set of subscriber locations that can
  be serviced by tower l.
• K is the set of candidate MTSO locations
• Location 0 is the PSTN gateway
• K0 K ? 0.

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Optimization Model for Wireless Network Design
Constants

• dm is the demand (channel equivalents) in
  subscriber location m.
• r is the annual revenue generated per channel.
• al is the cost of building and operating a tower
  at location .
• bk is the cost of building an MTSO at location k.
• clk the cost of providing a link from tower l to
  MTSO k.
• hjk the cost of providing a link from MTSO j to
  MTSO/PSTN k.
• ? is the maximum number of towers that an MTSO
  can support.

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Optimization Model for Wireless Network Design
Constants

• SIRmin is the minimum allowable
  signal-to-interference ratio.
• s 1 1/SIRmin.
• gml is the attenuation factor from location m to
  tower l.
• Ptarget is the desired strength for signals
  received at the towers.
• To reach tower l with sufficient strength, a
  handset at location m transmits with power level
  Ptarget / gml.

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Optimization Model for Wireless Network Design
Power Control Example
Received signal strength must be at least the
target value Ptar
Signal is attenuated by a factor of g13
Subscriber at Location 1 Assigned to Tower 3
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Optimization Model for Wireless Network Design
Decision Variables Used in the Model

• Binary variable yl1 iff a tower is constructed
  at location l.
• The integer variable xml denotes the number of
  customers (channel equivalents) at subscriber
  location m served by the tower at location l.
• Binary variable zk1 iff an MTSO or PSTN is
  established at location k.
• Binary variable slk1 iff tower l is connected to
  MTSO k.
• Binary variable wjk 1 iff a link is established
  between MTSOs j and k.
• ujk units of flow on the link between MTSOs j
  and k.

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Optimization Model for Wireless Network Design
Signal-to-Interference Ratio (SIR)
Tower 3
Tower 4
Subscriber at Location 1 assigned to Tower 3
Two subscribers at Location 2 assigned to Tower 4
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Optimization Model for Wireless Network Design
Quality of Service (QoS) Constraints

• For known attenuation factors, gml, the total
  received power at tower location l, PlTOT , is
  given by
• For a session assigned to tower l
• the signal strength is Ptarget
• the interference is given by PlTOT Ptarget
• QoS constraint on minimum signal-to-interference
  ratio for each session (channel) assigned to
  tower l

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Optimization Model for Wireless Network Design
Quality of Service (QoS) Constraints
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Optimization Model for Wireless Network Design
Integer Programming Model

• The objective of the model is to maximize profit
• subject to the following constraints

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Optimization Model for Wireless Network Design
Connection Constraints
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Optimization Model for Wireless Network Design
Flow Constraints for Backbone Construction
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Computational Experiments

• Computing resources used
• Compaq AlphaServer DS20E with dual EV6.7 (21264A)
  667 MHz processors and 4,096 MB of RAM
• Latest releases of CPLEX and AMPL
• Computational time
• Increases substantially as L increases from 40
  to 160
• Very sensitive to value of ?
• Lower Bound Procedure
• Solve IP with ?l 0 for all l
• Stop branch-and-bound process when the optimality
  gap (w.r.t LP) is 5
• Estimated Upper Bound Procedure
• Relax integrality constraints on x, y, and s
  variables.
• Solve MIP to optimality with ?l 0 for all l

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Data for Computational Experiments

• Restrict
• Two Series of Test Problems
• Candidate towers placed randomly in 13.5 km by
  8.5 km service area
• 1,000 to 2,000 subscriber locations dm u1,10
• L drawn from 40, 80, 120, 160
• K 5, placed randomly in central 1.5 km by 1.0
  km rectangle
• Simulated data for North Dallas area
• M 2,000 with dm u1,10
• L 120
• K 5

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Sample Results for Data Set 1
Upper Bound Procedure Upper Bound Procedure Upper Bound Procedure Upper Bound Procedure Best Feasible Solution from Lower Bound Procedure Best Feasible Solution from Lower Bound Procedure Best Feasible Solution from Lower Bound Procedure Best Feasible Solution from Lower Bound Procedure Best Feasible Solution from Lower Bound Procedure
Problem L M Towers Demand Profit CPU Towers Demand Profit CPU Gap
R110 40 1,000 35.6 92.60 18.33 00002 37 92.80 18.22 00020 0.60
R160 80 1,000 42.0 92.20 17.55 00843 39 87.50 16.74 00140 4.62
R210 120 1,000 50.0 94.20 17.66 04318 51 91.50 16.97 00848 3.91
R410 160 1,000 53.1 93.10 16.81 05702 53 90.30 16.21 01507 3.57
R260 40 2,000 37.0 65.30 26.72 00014 38 65.30 26.6 00117 0.45
R310 80 2,000 62.4 87.60 34.93 01004 65 86.80 34.33 00351 1.72
R360 120 2,000 N/A N/A N/A 20000 75 93.40 36.42 01452 5.00
R460 160 2,000 N/A N/A N/A 20000 88 93.70 35.24 05640 5.00

• Solution times for Lower Bound Procedure varied
  from 30 seconds to 1 hour of CPU time.
• Average value of 2.0 Cm 8.4.

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Data Set 2 North Dallas Area

• M 2,000, dm u1,10, L 120, and K 5

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Results for North Dallas
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Sample Results with Heuristics
Heuristic 1 Cm 1 Heuristic 1 Cm 1 Heuristic 1 Cm 1 Heuristic 1 Cm 1   Heuristic 2 Cm 2 Heuristic 2 Cm 2 Heuristic 2 Cm 2 Heuristic 2 Cm 2 Heuristic 2 Cm 2
Problem L M Towers Demand Profit CPU Gap Towers Demand Profit CPU Gap
R110 40 1,000 40 93.50 18.09 00001 1.31 37 92.80 18.22 00014 0.60
R160 80 1,000 67 92.40 15.05 00001 14.25 47 90.40 16.53 00033 5.81
R210 120 1,000 94 93.00 13.03 00001 26.22 67 93.90 15.88 00114 10.08
R410 160 1,000 94 83.90 10.53 00001 37.36 76 92.10 14.26 00054 15.17
R260 40 2,000 40 65.30 26.38 00003 1.27 38 65.30 26.6 00045 0.45
R310 80 2,000 79 89.80 33.90 00002 2.95 65 86.50 34.21 00152 2.06
R360 120 2,000 113 96.50 34.39 00002 10.30 85 94.30 35.98 00336 6.15
R460 160 2,000 141 96.40 31.51 00001 15.06 100 93.30 33.99 00623 8.37
Geo. Mean Geo. Mean 3.55
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The Power-Revenue Trade-Off
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Downlink Modeling
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Conclusions and Directions for Future Work

• IP model for W-CDMA problem
• Too many variables to be solved to optimality
  with commercial solvers
• Developed cuts and a two-step procedure to find
  high-quality solutions with guaranteed optimality
  gap.
• Largest problems took up to 1 hour of CPU time
• Heuristic 2 reduces computation times by an order
  of magnitude and still finds fairly good
  solutions
• Results for North Dallas problems on par with
  randomly generated data sets.
• Model can be integrated into a planning tool
  quick resolves with new tower locations added to
  original data
• Extensions
• Construct a two-connected backbone with at least
  two gateways
• Consider sectoring
• Tighten the ?l parameters