[1][1][1][1] Lecture 5-7: Cell Planning of Cellular Networks June 22 + July 6, Introduction to Algorithmic Wireless Communications David Amzallag

[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] 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 e], automatic cell planning, self-configuring networks) 100 Mbit/sec – 1Gbit/sec 15 Mbit/sec

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

[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] 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] The budgeted cell planning problem

[9][9][9][9] On the approximabaility of BCPP 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] 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] 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] 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] 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] 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] 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] 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] 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] 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 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] Integer programming formulation

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

[23] An approximation algorithm 1.Calculate as an optimal solution of the LP relaxation For all do 4. with probability 5. for all do 6. 7.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 – Conclusion: The algorithm is an approximation algorithm for the minimum- cost cell planning problem.

[25] Planning “greenfield” networks

[26] Cell planning in Helsinki Randomized rounding Greedy algorithm Extended Tutschku Solution cost LP cost Number of base stations