Antenna Placement in Wireless Networks Shiva P Kasiviswanathan - - PowerPoint PPT Presentation

antenna placement in wireless networks
SMART_READER_LITE
LIVE PREVIEW

Antenna Placement in Wireless Networks Shiva P Kasiviswanathan - - PowerPoint PPT Presentation

Antenna Placement in Wireless Networks Shiva P Kasiviswanathan Pennsylvania State University University Park Antenna Placement in Wireless Networks p. 1/9 Layout of the Presentation Problem Definition and Motivation Antenna Placement in


slide-1
SLIDE 1

Antenna Placement in Wireless Networks

Shiva P Kasiviswanathan Pennsylvania State University University Park

Antenna Placement in Wireless Networks – p. 1/9

slide-2
SLIDE 2

Layout of the Presentation

Problem Definition and Motivation

Antenna Placement in Wireless Networks – p. 2/9

slide-3
SLIDE 3

Layout of the Presentation

Problem Definition and Motivation Survey of techniques involved.

Antenna Placement in Wireless Networks – p. 2/9

slide-4
SLIDE 4

Layout of the Presentation

Problem Definition and Motivation Survey of techniques involved. Our approach for the problem.

Antenna Placement in Wireless Networks – p. 2/9

slide-5
SLIDE 5

Layout of the Presentation

Problem Definition and Motivation Survey of techniques involved. Our approach for the problem. Results on hardness and approximation results.

Antenna Placement in Wireless Networks – p. 2/9

slide-6
SLIDE 6

Layout of the Presentation

Problem Definition and Motivation Survey of techniques involved. Our approach for the problem. Results on hardness and approximation results. Brief Overview of the proofs.

Antenna Placement in Wireless Networks – p. 2/9

slide-7
SLIDE 7

Layout of the Presentation

Problem Definition and Motivation Survey of techniques involved. Our approach for the problem. Results on hardness and approximation results. Brief Overview of the proofs. Outline of future work.

Antenna Placement in Wireless Networks – p. 2/9

slide-8
SLIDE 8

Problem Definition

Input: Locations of users and base station in plane.

Antenna Placement in Wireless Networks – p. 3/9

slide-9
SLIDE 9

Problem Definition

Input: Locations of users and base station in plane. Characteristics of Antenna (B = 1, θ, R).

Antenna Placement in Wireless Networks – p. 3/9

slide-10
SLIDE 10

Problem Definition

Input: Locations of users and base station in plane. Characteristics of Antenna (B = 1, θ, R). User i has bandwidth requirement of bi.

Antenna Placement in Wireless Networks – p. 3/9

slide-11
SLIDE 11

Problem Definition

Input: Locations of users and base station in plane. Characteristics of Antenna (B = 1, θ, R). User i has bandwidth requirement of bi. Output: Orientation of Antenna j, and

Antenna Placement in Wireless Networks – p. 3/9

slide-12
SLIDE 12

Problem Definition

Input: Locations of users and base station in plane. Characteristics of Antenna (B = 1, θ, R). User i has bandwidth requirement of bi. Output: Orientation of Antenna j, and List of users assigned to antenna j say B(j) such that

  • i∈B(j)

bi ≤ 1

Antenna Placement in Wireless Networks – p. 3/9

slide-13
SLIDE 13

Problem Definition

Input: Locations of users and base station in plane. Characteristics of Antenna (B = 1, θ, R). User i has bandwidth requirement of bi. Output: Orientation of Antenna j, and List of users assigned to antenna j say B(j) such that

  • i∈B(j)

bi ≤ 1

Objective: Minimize some criteria.

Antenna Placement in Wireless Networks – p. 3/9

slide-14
SLIDE 14

Minimizing number of Antennas

NP hard: Reduction from Bin Packing.

Antenna Placement in Wireless Networks – p. 4/9

slide-15
SLIDE 15

Minimizing number of Antennas

NP hard: Reduction from Bin Packing.

(3

2 − ǫ) hardness of approximation from Partition problem.

Antenna Placement in Wireless Networks – p. 4/9

slide-16
SLIDE 16

Minimizing number of Antennas

NP hard: Reduction from Bin Packing.

(3

2 − ǫ) hardness of approximation from Partition problem.

So best we can hope is 3

2 approximation.

Antenna Placement in Wireless Networks – p. 4/9

slide-17
SLIDE 17

Minimizing number of Antennas

NP hard: Reduction from Bin Packing.

(3

2 − ǫ) hardness of approximation from Partition problem.

So best we can hope is 3

2 approximation.

Greedy gives factor 2 approximation.

Antenna Placement in Wireless Networks – p. 4/9

slide-18
SLIDE 18

GREEDY Algorithm

1) In phase i (1 ≤ i ≤ n) a) Start with antenna 1 having its right extreme point passing through i. b) Greedily pack in anticlockwise direction users starting from i, pack till maximal k s.t.,k

j=i bj ≤ 1

c) Start another antenna at (k + 1) and repeat previous step. d) Let Si be the number of antennas needed at this phase. 2) Output min{S1, S2, . . . , Sn}.

Antenna Placement in Wireless Networks – p. 5/9

slide-19
SLIDE 19

Working of Algorithm

0.5 0.3 0.3 0.3 0.4 0.5

Antenna Placement in Wireless Networks – p. 6/9

slide-20
SLIDE 20

Working of Algorithm

0.5 0.3 0.3 0.3 0.4 0.5 Special Zone

Antenna Placement in Wireless Networks – p. 6/9

slide-21
SLIDE 21

Idea behind Factor 2

Two lower bounds, Angular LB and Weight LB

Antenna Placement in Wireless Networks – p. 7/9

slide-22
SLIDE 22

Idea behind Factor 2

Two lower bounds, Angular LB and Weight LB If two points separated more than θ they need different antennas.

Antenna Placement in Wireless Networks – p. 7/9

slide-23
SLIDE 23

Idea behind Factor 2

Two lower bounds, Angular LB and Weight LB If two points separated more than θ they need different antennas. If

bi is W, then ⌈W⌉ antennas needed.

Antenna Placement in Wireless Networks – p. 7/9

slide-24
SLIDE 24

Idea behind Factor 2

Two lower bounds, Angular LB and Weight LB If two points separated more than θ they need different antennas. If

bi is W, then ⌈W⌉ antennas needed.

We consider the zone:

Antenna Placement in Wireless Networks – p. 7/9

slide-25
SLIDE 25

Idea behind Factor 2

Two lower bounds, Angular LB and Weight LB If two points separated more than θ they need different antennas. If

bi is W, then ⌈W⌉ antennas needed.

We consider the zone:

Antenna Placement in Wireless Networks – p. 7/9

slide-26
SLIDE 26

Idea behind Factor 2 Contd...

If p antennas needed outside the zone we show p ≤ LB

Antenna Placement in Wireless Networks – p. 8/9

slide-27
SLIDE 27

Idea behind Factor 2 Contd...

If p antennas needed outside the zone we show p ≤ LB Total weight in the zone is at most W

2 .

Antenna Placement in Wireless Networks – p. 8/9

slide-28
SLIDE 28

Idea behind Factor 2 Contd...

If p antennas needed outside the zone we show p ≤ LB Total weight in the zone is at most W

2 .

Zone require atmost W

2 (≤ p) antennas.

Antenna Placement in Wireless Networks – p. 8/9

slide-29
SLIDE 29

Idea behind Factor 2 Contd...

If p antennas needed outside the zone we show p ≤ LB Total weight in the zone is at most W

2 .

Zone require atmost W

2 (≤ p) antennas.

So we need in total p + W/2(≤ 2p) antennas.

Antenna Placement in Wireless Networks – p. 8/9

slide-30
SLIDE 30

Future Work...

If antennas are fixed can we minimize banwidth.

Antenna Placement in Wireless Networks – p. 9/9

slide-31
SLIDE 31

Future Work...

If antennas are fixed can we minimize banwidth. Yes, there is a (2, 1) bicriteria approximation.

Antenna Placement in Wireless Networks – p. 9/9

slide-32
SLIDE 32

Future Work...

If antennas are fixed can we minimize banwidth. Yes, there is a (2, 1) bicriteria approximation. Max-Min Fairness is another good metric.

Antenna Placement in Wireless Networks – p. 9/9

slide-33
SLIDE 33

Future Work...

If antennas are fixed can we minimize banwidth. Yes, there is a (2, 1) bicriteria approximation. Max-Min Fairness is another good metric. Mobility of users ignored and can be incorporated.

Antenna Placement in Wireless Networks – p. 9/9