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Base Station Location and Service Assignment in W-CDMA Networks

Explore efficient base station placement and subscriber assignment in CDMA networks to maximize profit and system capacity while meeting service quality constraints. Enhance your understanding of CDMA technology for optimal network design.

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Base Station Location and Service Assignment in W-CDMA Networks

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  1. Base Station Location and Service Assignment in W-CDMA Networks Joakim Kalvenes1 Jeffery Kennington2 Eli Olinick2 Southern Methodist University 1Edwin L. Cox School of Business 2School of Engineering

  2. Wireless Network Design: Inputs • Potential locations for radio towers (cells) • “Hot spots”: concentration points of users/subscribers (demand) • 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, and MTSOs to PSTN

  3. Wireless Network Design: Problem • Determine which radio towers to build (base station location) • Determine how to assign subscribers to towers (service assignment) • Determine which MTSOs to use • Maximize profit: revenue per subscriber served minus infrastructure costs

  4. Wireless Network Design Tool

  5. Code Division Multiple Access (CDMA)Technology • The basis for 3G cellular systems • Channel (frequency) allocation is not an explicit issue since the full spectrum is available in each cell • New calls cause incremental noise (interference) • New calls admitted as long as the signal-to-noise ratio stays with in system limit • Power transmitted by handset depends on distance to assigned radio tower • Tower location and assignment of customer locations to towers must be determined simultaneously

  6. Tower 3 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

  7. 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

  8. Some Related CDMA Literature: Base Station Location & Service Assignment • Galota, Glasser, Reith, and Vollmer (2001) • Profit maximization • Polynomial-time approximation scheme • Amaldi, Capone, and Malucelli (2001a, 2001b) • Minimize cost to serve all users • Randomized add-drop heuristic • Tabu search to improve solutions • Mathar and Schmeink (2001) • Maximize system capacity for a fixed budget • Simplified interference model

  9. Our New Model for CDMA Base Station Location and Service Assignment • Integer linear program (ILP) • Maximizes profit • Enforces hard constraints on signal-to-interference ratio • Incorporates FCC licensing rules for US providers

  10. Constants and Sets Used in the Model • L isthe set of candidate tower locations. • M isthe set of subscriber locations. • gmℓis the attenuation factor from location m to tower ℓ. • is the set of tower locations that can service customers in location . • is the set of customer locations that can be serviced by tower ℓ.

  11. More Constants and Sets Used in the Model • dmis the demand (channel equivalents) in location • r is the annual revenue generated per channel. • is the FCC mandated minimum service requirement. • is the cost of building and operating a tower at location . • SIRminis the minimum allowable signal-to-interference ratio. • s = 1 + 1/SIRmin.

  12. Decision Variables Used in the Model • yℓ =1 if a tower is constructed at location ℓ; and zero, otherwise. • The integer variable xmℓ denotes the number of customers (channel equivalents) at that are served by the tower at location • The indicator variable qm =1 if and only if location m can be served by at least one of the selected towers.

  13. Integer Programming Model The objective of the model is to maximize profit: subject to the following constraints:

  14. Integer Programming Model

  15. 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:

  16. Quality of Service (QoS) Constraints

  17. Enhancing the Basic ILP Model • Global Valid Inequalities • Optimality Cuts • Post-Processing Procedure • Branching Rule

  18. Global Valid Inequalities

  19. Global Valid Inequalities

  20. Optimality Cuts • If customers at site m are served, then profit is maximized by assigning them to the available tower that has the largest attenuation factor (i.e., the nearest available tower). • We can add the following cuts to formulation

  21. Optimality Cuts: Derivation

  22. Optimality Cuts: Derivation

  23. Post Processing • Values of the attenuation factors (gij) have a large range • Coefficients in QoS constraints (6) may differ in magnitude by as much as 109. • Causes scaling problems so that solutions returned by CPLEX are not always feasible • Post-processing procedure ensures feasibility within a reasonable tolerance

  24. Phase II: Eliminating Infeasibilities

  25. Computational Experiments • Branching on tower-location decisions (y's) before customer assignment (x's) reduces branch-and-bound time. • Number of (8) cuts depends on |Cm|; may actually increase solution time if too large. • Computing resources used • Compaq AlphaServer DS20E with dual EV6.7 (21264A) 667 MHz processors and 4,096 MB of RAM • CPLEX version 6.6.0 • AMPL release 9.10.27

  26. Parameters for Dense Data Set Based on data generation used by Amaldi et al. [2001a,b]

  27. Results for Dense Test Data Set PP gives number of problems (out of 20) requiring post processing.

  28. Parameters for Sparse Data Set 300 problem instances: 100 sets of subscriber locations each with 3 distributions for demand at each location.

  29. Results for Sparse Data Set * Only 10 instances were attempted. ** Only 69 of 100 instances were solved within the limits of 8 hours of CPU time and 1.8 Gb RAM.

  30. Conclusions • Branching rule and cuts enable CPLEX to solve realistically sized problem instances of our model • Dense network structure • Previous work uses randomized local search • Our solutions provably within 5% of optimal on average • Sparse network structure • Solved a set of 300 test problems with |L| = 40 and |M| = 250 • Average optimality gap = 1.2% and average CPU time = 13 minutes • Extensions (suggested by a well-known cellular provider) • Maximize capacity of existing 2G system to provide CDMA • Capacity expansion of an existing 3G system subject to budget constraint

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