DARP: Distance-Aware Relay Placement in WiMAX Mesh Networks
Weiyi Zhang*, Shi Bai*, Guoliang Xue§, Jian Tang†, Chonggang Wang‡
* Department of Computer Science, North Dakota State University, Fargo§ Department of Computer Science and Engineering, Arizona State University, Tempe
† Department of Electrical Engineering and Computer Science, Syracuse University, Syracuse‡ NEC Laboratories America, Princeton, USA
IEEE INFOCOM 2011
Outline
• Introduction
• Motivation & Problem
• Observation & Goals
• System Model
• Solution for DARP: Distance-Aware Relay station Placement– LORC-MIS // lower tier
– LORC-HS // lower tier
– MUST // upper tier
• Simulation
• Conclusion
Introduction
• The emerging WiMAX technology is the 4G standard for– high-speed (up to 75Mbps)
– long-range communications
BSSS
SS
SS
Introduction
• IEEE 802.16j enhances IEEE 802.16e by the concept of mesh networks– Base Station (BS)
– Relay Station (RS)
– Subscriber Station (SS)
BS
RS
SSRS
SS
SS
• WiMAX 802.16j Relay Station– eliminate coverage hole
– Range extension
Introduction
InternetCoverageExtension
Coverage Hole
Mobile Access
BuildingPenetration
SS
RS
BS
RS
RS
RS
SS
• n Subscriber Stations (SS)– different user data rate requests
• Problem:– finding where to place a minimum number of relay nodes
– to satisfy the certain performance requests
Motivation
SS BSSS
SS
SS
SS
Observation – distance aware
• Signal to noise ratio (SNR) at receiver– SNRr = Pr / N0
– Pr : power level at the receiver
– N0 : noise power is normally a constant
SS user data rate requests: 35 Mbps
Observation – distance aware
• Two-ray ground path loss model– Pr = Pt Gt Gr Ht
2 Hr2 d -
– Pt : Transmission power (constant)
– Gt / Gr : gains of transmitter/receiver antenna (constant)
– Ht /Hr : heights of transmitter/receiver antenna (constant)
– d : Euclidean distance between transmitter and receiver : attenuation factor (constant : 2~4)
SS SS
higher data rate request lower data rate request
Goals
• Given a WiMAX mesh network– One BS
– A set of SSs, S = {s1, s2, …, Sn}
– A set of distance requirements for the SSs, D = {d1, d2, …, dn}
SS
BS
SS
Goals
• Solve the distance-aware relay placement (DARP) problem by a minimum number of RSs– Providing feasible coverage for each SS
• covered by at least one RS or BS
– Each placed RS has enough data rate to relay traffic for each SS or another RS
SSSS
BS
25 Mbps
RS
25 Mbps
System Model
• A WiMAX mesh network– n SSs, S = {s1, s2, …, Sn}
• Distance requirements D = {d1, d2, …, dn}
• No routing and traffic relay capabilities
– BS, is aware of the location and distance requirement of each SS
SS
BS
SS
Solution for DARP problem
• Two-tiered relay model
SS
SS
BS
RS
lower tier
upper tier
LORC-MISLORC-HS
MUST
LORC-MIS
• LORC-MIS– LOwer-tier Relay Coverage –
Maximal Independent Set based approximation solution
SS
SS
lower tier
LORC-MIS
• First consider the SS with the smallest distance requirement– Highest user data rate requirement
12
34
5C4
C5
C3
C1 C2
d2
d1
d3
d4d5
LORC-MIS
• Construct a regular hexagon with 7 possible positions
S2 d2
A2H
23d 23d
F2H C
2H
B2H
E2H D
2H
3d
d
LORC-MIS
• Choose the point which covers most SSs
A2H
F2H
E2H
D2H
C2H
B2H
A5H B
5H
C5H
D5HE
5H
F5H
S2
S5
S1
S4 S3
• LORC-HS– LOwer-tier Relay Coverage –
Hitting Set based approximation solution
LORC-HS
SS
SS
lower tier
LORC-HS
• Find the Minimum hitting set– to cover all SSs // {p0, p2}
– admits PTAS [18]
s2s1
s3
p3p1
p0
p7p6
p2
p4 p5s0
S0={p0, p1}S1={p0, p1 , p2 , p3 , p4 , p5 , p7}S2={p2, p3 , p4 , p5 , p6}S3={p2, p4 , p5 , p6 , p7}
[18] N. Mustafa and S. Ray, PTAS for geometric hitting set problems via local search, SCG’09, pp. 17-22.
MUST
• Minimum Upper-tier Steiner Tree
upper tier
BS
RS
MUST
• The “MUST” ensures data rate for each individual SS or RS
RS3
RS1
RS2
BS
A B
C
15
15
1516
18
18
MUST
• Construct a complete graph
• Assign edge weight w– Number of RSs
RS1 RS2
BS
d1=10
w=3
d2=5
10
20 21
16
5
w=4
w=3
min
( , )( , ) 1
i j
i j
e x xw x x
d
min min 5ii Sd d
MUST
• Minimum spanning tree
min
( , )( , ) 1
i j
i j
e x xw x x
d
min min 5ii Sd d
RS1 RS2
BS
d1=5
w=3
d2=5
20
16
w=3
MUST
• Place RSs on edges
RS1 RS2
BS
d1=5
w=3
d2=5
20
16
w=3
5
4
5
5
5
4 4 4
Simulation Setup
• SSs are uniformly distributed in a square playing ground– 20002000
– 30003000
• Distance requirements randomly distributed in [100,150]
• BS is deployed at the center of the field
• All figures illustrate the average of 10 test runs for various scenarios
Simulation
Simulation – lower-tier relay coverage
Simulation – upper-tier relay connectivity
Simulation
Simulation
Conclusion
• This paper studies the Distance-Aware Relay Placement (DARP) problem– Multi-hop relay placement
– Relay coverage
– Relay connectivity
TheENDThanks for your attention !