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 Wireless Networks – p. 2/9

Layout of the Presentation Problem Definition and Motivation Survey of techniques involved. Antenna Placement in Wireless Networks – p. 2/9

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

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

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

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

Problem Definition Input: Locations of users and base station in plane. Antenna Placement in Wireless Networks – p. 3/9

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

Problem Definition Input: Locations of users and base station in plane. Characteristics of Antenna ( B = 1 , θ, R ) . User i has bandwidth requirement of b i . Antenna Placement in Wireless Networks – p. 3/9

Problem Definition Input: Locations of users and base station in plane. Characteristics of Antenna ( B = 1 , θ, R ) . User i has bandwidth requirement of b i . Output: Orientation of Antenna j , and Antenna Placement in Wireless Networks – p. 3/9

Problem Definition Input: Locations of users and base station in plane. Characteristics of Antenna ( B = 1 , θ, R ) . User i has bandwidth requirement of b i . Output: Orientation of Antenna j , and List of users assigned to antenna j say B ( j ) such that � b i ≤ 1 i ∈ B ( j ) Antenna Placement in Wireless Networks – p. 3/9

Problem Definition Input: Locations of users and base station in plane. Characteristics of Antenna ( B = 1 , θ, R ) . User i has bandwidth requirement of b i . Output: Orientation of Antenna j , and List of users assigned to antenna j say B ( j ) such that � b i ≤ 1 i ∈ B ( j ) Objective: Minimize some criteria. Antenna Placement in Wireless Networks – p. 3/9

Minimizing number of Antennas NP hard: Reduction from Bin Packing. Antenna Placement in Wireless Networks – p. 4/9

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

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

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

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 b j ≤ 1 c) Start another antenna at ( k + 1) and repeat previous step. d) Let S i be the number of antennas needed at this phase. 2) Output min { S 1 , S 2 , . . . , S n } . Antenna Placement in Wireless Networks – p. 5/9

Working of Algorithm 0.3 0.3 0.5 0.3 0.4 0.5 Antenna Placement in Wireless Networks – p. 6/9

Working of Algorithm 0.3 0.3 0.5 Special Zone 0.3 0.4 0.5 Antenna Placement in Wireless Networks – p. 6/9

Idea behind Factor 2 Two lower bounds, Angular LB and Weight LB Antenna Placement in Wireless Networks – p. 7/9

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

Idea behind Factor 2 Two lower bounds, Angular LB and Weight LB If two points separated more than θ they need different antennas. If � b i is W , then ⌈ W ⌉ antennas needed. Antenna Placement in Wireless Networks – p. 7/9

Idea behind Factor 2 Two lower bounds, Angular LB and Weight LB If two points separated more than θ they need different antennas. If � b i is W , then ⌈ W ⌉ antennas needed. We consider the zone: Antenna Placement in Wireless Networks – p. 7/9

Idea behind Factor 2 Two lower bounds, Angular LB and Weight LB If two points separated more than θ they need different antennas. If � b i is W , then ⌈ W ⌉ antennas needed. We consider the zone: Antenna Placement in Wireless Networks – p. 7/9

Idea behind Factor 2 Contd... If p antennas needed outside the zone we show p ≤ LB Antenna Placement in Wireless Networks – p. 8/9

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

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

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( ≤ 2 p ) antennas. Antenna Placement in Wireless Networks – p. 8/9

Future Work... If antennas are fixed can we minimize banwidth. Antenna Placement in Wireless Networks – p. 9/9

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

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

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