Lecture 5-7: Cell Planning of Cellular Networks

1. Lecture 5-7:Cell Planning of Cellular Networks June 22 + July 6, 2008 896960 Introduction to Algorithmic Wireless Communications David Amzallag david.amzallag@bt.com www.cs.technion.ac.il/~amzallag/awc

2. What is a cell planning? • Planning a network of base stations (configurations) to provide the required coverage of the service area with respect to current and future traffic requirements, available capacities, interference, and the desired QoS • What is a typical outcome? • Coverage vs. capacity planning • Cell planning towards the fourth generation (4G)

3. Fourth generation cellular networks 100 Mbit/sec – 1Gbit/sec 15 Mbit/sec • High data rate (also in compare to HSDPA and LTE, in the downlink) • System capacity is expected to be 10 times larger than current 3G systems • Drastic reduction in costs (1/10 to 1/100 per bit) • Cell planning with capacity limitations • “Base station on sprinkler” → high frequency → higher interference → small cells → larger number of base stations • OFDMA as the multiple access technique • Smart antennas and adaptive antennas • New approaches for optimization problems are required (e.g., radio access network design, satisfying mobile stations by more than one base station [IEEE 802.16e], automatic cell planning, self-configuring networks)

4. How to model the interference? • is the fraction of the capacity of a base station to a client • is the contribution of base station to client

5. How to compute ? • In general, • Since for relative small values of Two models of interference

6. A tale of two cell planning problems • A set of clients, each has a given demand • A set of possible base station configurations, each has a given capacityinstallationcost and a subsetof clients admissible to be covered by it • An interference matrix The budgeted cell planning problem (BCPP) asks for a subset of base stations whose cost does not exceed a given budget and the total number of (fully) satisfied clients is maximized. The minimum-cost cell planning problem (CPP) asks for a subset of base stations of minimum cost that satisfy at least of the demands of all the clients, All-or-Nothing coverage type constraint

7. Current cell planning solutions • Extensive study in the last years; Only special cases of the problem were investigated (almost all are minimum-cost type objectives) • Not supporting external impact matrix or interference • No capacity handling • In most cases, only meta-heuristics are used; No approximation algorithms • Not supporting budget constraint • Not supporting (fast) “special cases”

8. The budgeted cell planning problem

9. On the approximabaility of BCPP 2006 2007 1999 2004 Budgeted unique coverage [DFHS] All-or-nothing demand maximization [ABRS] Budgeted maximum coverage [KMN] Maximizing submodular functions [Sviridenko] approximable within Budgeted facility location In general, not approximable within [tight] For r-restricted version approximable within [tight] Budgeted cell planning Submodularity:

10. On the approximabaility of BCPP Here comes the bad news, as expected A Subset Sum instance The corresponding BCPP instance Conclusion. It is NP-hard to find a feasible solution to the budgeted cell planning problem

11. The k4k-budgeted cell planning problem • Adopting the k4k property: Every set of k base stations can fully satisfy at least k clients, for every integer k • Still NP-hard • Good news: No longer NP-hard to approximate • General idea behind our - approximation algorithm: • A best-of-two-candidates algorithm • How many clients are satisfying by more than one base station? • Covering clients by a single base station

12. How many clients are satisfied by more than one base station? When the corresponding graph is acyclic Base station Mobile client Leaves are the clients satisfiedby a single BS

13. How many clients are satisfied by more than one base station? When the corresponding graph contains cycles Edge weights are Client of demand of 7 Base station i’ gives client j’ 3 units Cycle canceling algorithm on BS with capacity of 10 Conclusion. (here is the set of clients that are satisfied by more than one base station)

14. Satisfying clients by a single base station The client assignment problem (CAP) • How many clients can be covered by a set of opened base stations? How many more can be covered if another base station is to be opened next? Formally, for a given set of BSs, let be the number of clients that can be covered, each by exactly one BS. • CAP’s resume: • The function is not submodular • CAP is NP-hard • Special case of the well-studied GAP (approximable within [FGMS, 2006])

15. Satisfying clients by a single base station The client assignment problem (CAP) • Algorithm 1. Pick a minimum-demand client Find the first BS in a given order that can cover If it exists – then assign to this BS; Otherwise, leave client uncovered • Properties: • Algorithm 1 is a ½-approximation algorithm to CAP • For every set of BSs and every base station • For every set of BSs and every base stations [Algorithm 1]

16. Satisfying clients by a single base station The budgeted maximum assignment problem (BMAP) • Find a subset of BSs whose cost does not exceed a given budget that maximizes • BMAP’s resume: • A generalization (capacitated) of the budgeted maximum coverage problem ([KMN, 1999]) • A greedy -approximation algorithm (maximizing ) [Algorithm 2]

17. A -approximation algorithm for the k4k-BCPP ← the output of BMAP algorithm on the same instance ← the maximum number of base stations that can be opened using budget ifthen Output and a set of clients that can be covered using the k4k-oracle else Output and the clients covered by CAP algorithm for these base stations [Algorithm 3]

18. Analysis Number of clients covered by Algorithm 3 Value of optimal solution for the BMAP instance property Cycle canceling

19. The minimum-cost cell planning problem

20. The minimum-cost cell planning problem • Special case: without interference • An - approximation algorithm • An - approximation algorithm (here ); a generalization for the hard capacitated set cover problem (Chuzhoy & Naor, FOCS 2002) • On greedy algorithms for the minimum-cost CPP • Good practical results in two sets of simulations

21. Integer programming formulation

22. A relaxation of the non-interference case • Observation:

23. An approximation algorithm • Calculate as an optimal solution of the LP relaxation. • For all do • with probability • for all do • Return and

24. Analysis • The expected value of the cost of the solution produced by the algorithm is at most where is the value of the optimal solution to the LP relaxation. • For every client the probability that is not covered is at most • Conclusion: The algorithm is an approximation algorithm for the minimum-cost cell planning problem.

25. Planning “greenfield” networks

26. Solution cost LP cost Extended Tutschku Greedy algorithm Randomized rounding 2.987 1.683 1.886 Number of base stations 32 15 21 Cell planning in Helsinki