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Cell Planning of 4G Cellular NetworksCell Planning of 4G Cellular Networks

David AmzallagDavid Amzallag

Computer Science Department, TechnionComputer Science Department, Technion

Joint work with Roee Engelberg (Technion), Seffi Naor (Microsoft Joint work with Roee Engelberg (Technion), Seffi Naor (Microsoft

Research) and Danny Raz (Technion)Research) and Danny Raz (Technion)

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What is a cell planning?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)

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Introducing the 4G cellular networksIntroducing the 4G cellular networks

– High data rate (also in compare to HSDPA, in the downlink) + applications

– 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

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How to model the interference?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

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How to compute ? How to compute ?

– In general,

– Since for relative small values of

–

Two models of interference

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A tale of two cell planning problemsA tale of two cell planning problems

– A set of clientsclients, each has a given demanddemand

– A set of possible base station configurationsbase station configurations, each has a given capacitycapacity installationinstallation costcost and a subset of clients admissible to be covered by it

– An interference matrixinterference matrix

The minimum-cost cell planning problemminimum-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,

The budgeted cell planning problembudgeted 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

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Current cell planning solutionsCurrent 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”

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On the approximabaility of BCPPOn the approximabaility of BCPP

1999 20062004

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:

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On the approximabaility of BCPPOn the approximabaility of BCPPHere comes the bad news, as expectedHere comes the bad news, as expected

A Subset Sum instance

The corresponding BCPP instance

Conclusion. It is NPNP-hard to find a feasible solution to the budgeted cell planning problem

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The The kk44kk-budgeted cell planning problem-budgeted cell planning problem

– Adopting the kk44kk property property: Every set of k base stations can fully satisfy at least k clients, for every integer k

– Still NP-NP-hard

– Good news: No longer NPNP-hard to approximate

– General idea behind our - approximation algorithm:

– A best-of-two-candidates algorithm

– How many clients are satisfying by moremore than one base station?

– Covering clients by a single base station

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LeavesLeaves are the clients

satisfied by a singlesingle BS

How many clients are satisfied by How many clients are satisfied by moremore than one base than one base station?station?When the corresponding graph is acyclicWhen the corresponding graph is acyclic

Base station

Mobile client

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How many clients are satisfied by How many clients are satisfied by moremore than one base than one base station?station?

3

)(15

5

)(8

)(12

)(9)(10

)(7

)(11

)(10

10

2

7

3

4

7

5

)(15

3

)(8

)(12

)(9)(10

)(7

)(11

)(10

12

9

1

6

5

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 cyclesWhen the corresponding graph contains cycles

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Satisfying clients by a Satisfying clients by a singlesingle base station 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 resumeCAP’s resume:

– The function is notnot submodular

– CAP is NPNP-hard

– Special case of the well-studied GAP (approximable within [FGMS, 2006])

The client assignment problem (CAP)The client assignment problem (CAP)

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Satisfying clients by a Satisfying clients by a singlesingle base station base station

– Algorithm 1Algorithm 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: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)The client assignment problem (CAP)

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Satisfying clients by a Satisfying clients by a singlesingle base station base station

– Find a subset of BSs whose cost does not exceed a given budget that maximizes

– BMAP’s resumeBMAP’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 The budgeted maximum assignment problem (BMAP)(BMAP)

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A -approximation algorithm for the A -approximation algorithm for the kk44kk-BCPP-BCPP

← the output of BMAP algorithm on the same instance

← the maximum number of base stations that can be opened using budget

ifif thenthen

Output and a set of clients that can be covered using the k4k-oracle

elseelse

Output and the clients covered by CAP algorithm for these base stations

[Algorithm 3]

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AnalysisAnalysis

Number of clients covered by Algorithm 3 Value of optimal solution for the BMAP instance

property

Cycle canceling

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Open problemsOpen problems

– Minimum-cost cell planning problem Minimum-cost cell planning problem (CPP)(CPP)

– Special case: without interference

– An - approximation algorithm

– An - approximation algorithm (here )

– Good practical results in two sets of simulations

– What about the general case?

– Minimum-cost site-planning problem