1. [1][1][1][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.comwww.cs.technion.ac.il/~amzallag/awc

2. [2][2][2][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. [3][3][3][3] Fourth generation cellular networks – 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) 100 Mbit/sec – 1Gbit/sec 15 Mbit/sec

4. [4][4][4][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. [5][5][5][5] How to compute ? – In general, – Since for relative small values of – Two models of interference

6. [6][6][6][6] A tale of two cell planning problems clientsdemand – A set of clients, each has a given demand base station configurations capacityinstallation cost – A set of possible base station configurations, each has a given capacity installation cost and a subset of clients admissible to be covered by it interference matrix – An interference matrix minimum-cost cell planning problem 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, budgeted cell planning problem 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.  All-or-Nothing coverage type constraint

7. [7][7][7][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. [8][8][8][8] The budgeted cell planning problem

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

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

11. [11] The k 4 k -budgeted cell planning problem k 4 k property – Adopting the k 4 k property: Every set of k base stations can fully satisfy at least k clients, for every integer k NP- – Still NP-hard NP – Good news: No longer NP-hard to approximate – General idea behind our - approximation algorithm: – A best-of-two-candidates algorithm more – How many clients are satisfying by more than one base station? – Covering clients by a single base station

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

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

14. [14] Satisfying clients by a single base station – 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 – CAP’s resume: not – The function is not submodular NP – CAP is NP-hard – Special case of the well-studied GAP (approximable within [FGMS, 2006]) The client assignment problem (CAP)

15. [15] Satisfying clients by a single base station – Algorithm 1 – 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] The client assignment problem (CAP)

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

17. [17] A -approximation algorithm for the k 4 k -BCPP ← the output of BMAP algorithm on the same instance ← the maximum number of base stations that can be opened using budget ifthen if then Output and a set of clients that can be covered using the k 4 k -oracle else else Output and the clients covered by CAP algorithm for these base stations [Algorithm 3]

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

19. [19] The minimum-cost cell planning problem

20. [20] The minimum-cost cell planning problem – Special case: without interference – An - approximation algorithm hard capacitated set cover problem – 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. [21] Integer programming formulation

22. [22] A relaxation of the non-interference case – Observation – Observation:

23. [23] An approximation algorithm 1.Calculate as an optimal solution of the LP relaxation. 2. 3.For all do 4. with probability 5. for all do 6. 7.Return and

24. [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 – Conclusion: The algorithm is an approximation algorithm for the minimum- cost cell planning problem.

25. [25] Planning “greenfield” networks

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