W-CDMA Network Design

1. 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

2. 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

3. 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

4. Wireless Network Design Tool

5. Optimization Model for Wireless Network Design: Sets • L isthe set of candidate tower locations. • M isthe set of subscriber locations. • Cm is the set of tower locations that can service subscribers in location m. • Plis 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}.

6. Optimization Model for Wireless Network Design: Constants • dmis the demand (channel equivalents) in subscriber location m. • r is the annual revenue generated per channel. • alis 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.

7. Optimization Model for Wireless Network Design: Constants • SIRminis the minimum allowable signal-to-interference ratio. • s = 1 + 1/SIRmin. • gmℓis 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.

8. Tower 3 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

9. Optimization Model for Wireless Network Design: Decision Variables Used in the Model • Binary variable yℓ=1 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 zk=1 iff an MTSO or PSTN is established at location k. • Binary variable slk=1 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.

10. 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

11. 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:

12. Optimization Model for Wireless Network Design: Quality of Service (QoS) Constraints

13. Optimization Model for Wireless Network Design: Integer Programming Model The objective of the model is to maximize profit: subject to the following constraints:

14. Optimization Model for Wireless Network Design: Connection Constraints

15. Optimization Model for Wireless Network Design: Flow Constraints for Backbone Construction

16. 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

17. 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~ u[1,10] • |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~ u[1,10] • |L| = 120 • |K| = 5

18. Sample Results for Data Set 1 • Solution times for Lower Bound Procedure varied from 30 seconds to 1 hour of CPU time. • Average value of 2.0 ≤ |Cm| ≤ 8.4.

19. Data Set 2: North Dallas Area |M| = 2,000, dm~ u[1,10], |L| = 120, and |K| = 5

20. Results for North Dallas

21. Sample Results with Heuristics

22. The Power-Revenue Trade-Off

23. Downlink Modeling

24. 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