Lecture 5-7: Cell Planning of Cellular Networks - PowerPoint PPT Presentation

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

• 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)

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)

• is the fraction of the capacity of a base

station to a client

• is the contribution of base station to client

• In general,
• Since for relative small values of

Two models of interference

• 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

• 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”

The budgeted cell planning problem

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:

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

• 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

When the corresponding graph is acyclic

Base station

Mobile client

Leaves are the clients satisfiedby a single BS

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)

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])

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]

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]

← 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]

Number of clients covered by Algorithm 3

Value of optimal solution for the BMAP instance

property

Cycle canceling

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

• Observation:

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

• 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.

Planning “greenfield” networks

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