Throughput-Optimal Configuration of Fixed Multi-Hop Wireless Networks

1
Throughput-Optimal Configuration of Fixed
Multi-Hop Wireless Networks

• C. Rosenberg

This work was done in collaboration with A.
Karnik, A. Iyer, and S. Muthaiah.
2
Context Scheduled Wireless Mesh Networks

• Mesh routers (e.g., subscriber stations, access
  points, etc.) form a multi-hop wireless network.
• Network is managed.
• No mobility.
• Wireless ?
• Understanding modelling physical layer is key
  (fading, interference, etc.).
• Access scheme is key.
• WLAN traffic is aggregated at the router and the
  traffic flows are (mostly) to or from the gateway.

WLAN
Primarily interested in engineering fixed and
managed wireless mesh networks (WMN).
3
Modeling Wireless Communications

• Designing wireless networks is quite challenging,
  owing to the complexity underlying wireless
  communications.
• A particular source of complexity interference.
• Wireless medium characteristics
• Signal power radiated into space
• Signal power attenuates over distance
• Signal decoded by treating sum of unwanted
  signals as noise decoding is probabilistic.
• Unlike the wireline case, the physical layer
  cannot be abstracted by few simple parameters.

4
Managing Access to the Medium

• Owing to the interference wireless links cause
  one another, it is necessary to arbitrate access
  to the wireless medium.
• Medium access could be based on scheduling or
  random access.

Scheduled Random Access
Explicit conflict-free schedules Randomized channel access
Possible to assign a capacity to each link No notion of link capacity
Centralized, complex Distributed, robust
Superior performance Much inferior performance
802.16 supports centralized scheduling 802.11 is based on CSMA/CA

• Conflict-free scheduled networks the focus of
  this work.
• Results for networks based on IEEE 802.16
• Bounds on performance of IEEE 802.11-networks

5
Focus of Our Work

• Interplay between physical layer, network
  mechanisms, and performance.

6
Aim of Our Work

• We seek answers to the following two questions
• Q1 Capacity Given a set of nodes with arbitrary
  locations, and a set of data flows specified as
  source-destination pairs, what is the maximum
  achievable throughput, under certain constraints
  on the radio parameters (in particular,
  regulatory constraints on transmit power)?
• Q2 Optimal Configuration Further, how should
  the network be configured to achieve this
  maximum? By configuration, we mean the complete
  choice of the set of links, flow routes, link
  schedules, and transmit power and modulation
  scheme for each link.
• Maximum throughput
• max-min flow rate maximize the minimum
  end-to-end flow throughput achievable in the
  network
• Classical notion of capacity a la Gupta-Kumar
• Cumulative interferences from multiple links are
  considered, SINR (signal-to-interference-and-noise
  ratio) model.
• Link rate is a step function of the transmit
  power.
• Our model allows for multiple modulations and
  multiple power levels

7
An Important Preamble

• When we compared simplistic physical channel
  models used in the literature, with one based on
  SINR, we found
• Models such as the capture threshold model (used
  in ns-2), or the protocol model, predict
  different qualitative behavior while studying
  performance of MAC protocols.
• The capture threshold model, the protocol model
  and a model based on fixed ranges for
  communication and interference, also predict
  throughput performance which is in contrast with
  the predictions of the SINR based model for
  scheduled networks.
• In particular, for a grid mesh network, the
  maximum throughput at very low power, has
  different orders of growth in the number of
  nodes, for different models.

8
Prior Work

• Asymptotic Approach Capacity Scaling
• Characterize capacity in an order sense,
  Gupta-Kumar 1
• Decode and forward architecture is order optimal,
  Xie-Kumar 2
• More work in scaling laws under different models,
  Mhatre-Rosenberg 3
• Mainly addresses capacity (Q1) in an order sense
  proofs construct optimal configuration (Q2) again
  in an order sense
• Algorithmic Approach Joint Optimization
• Dynamic Routing and Power Control, Neely et. al.
  4
• Minimize power subject to link data-rate
  constraints, Cruz and Santhanam 5
• Algorithms/policies implicitly construct optimal
  configuration (Q2) does not address capacity (Q1)

9
Motivation

• Despite works on capacity scaling and joint
  optimization
• No feel for actual numbers for capacity.
• No insights into overall trends of capacity with
  transmit power, modulation schemes, etc.
• No structural insights.
• Our aim is to address Q1 and Q2 for arbitrary
  networks.
• Important from two perspectives
• Structural Properties
• Does optimal configuration have any structural
  implications?
• Is power used to improve range or data-rate?
• Is min-hop routing optimal? When? and so on
• Engineering of networks upcoming standards like
  IEEE 802.16 provide
• Multi-rate capability via adaptive modulation and
  coding
• Message-passing mechanisms
• Framework for coordinated network operation
• A complete answer to Q1 and Q2
• not only provides capacity,
• but also optimal design in terms of the
  sophisticated features of upcoming standards,
• Engineering guidelines.

10
Assumptions and Problem Setup

• Traffic requirements are static or quasi-static
• Appropriate for large backbone/back-haul type of
  networks
• Channel gains are almost time-invariant
• Realistic in urban/suburban areas with roof-top
  antennas 6
• Radio parameters and physical layer
• Allowable power vectors
• Feasible modulation and coding schemes
• In wireless communication, a successful
  transmission is specified in terms of an
  acceptable (bit) error rate (BER).
• A modulation scheme z provides a specific
  transmission rate c(z)
• To transmit data from i to j using z while
  maintaining a specified BER, the Signal to Noise
  Interference Ratio (SINR) at the receiver must be
  greater than some threshold ß(z).

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Assumptions and Model (contd.)

• Hence the SINR requirement for transmission on
  link l from i to j is specified as
• Pl is the transmitting power of i, N0 is the
  average thermal noise power.
• The sum in the denominator is over the links
  transmitting simultaneously with l.
• Gll and Gll resp. denote the channel gains on
  link l, and the channel gain from the transmitter
  of link l to j.
• Thus for transmission success not all wireless
  links can be active simultaneously
• Link conflict relationships
• Given a setting of power and a modulation scheme,
  each link has a conflict set
• Conflict set consists of subsets each subset
  member consists of links which together disturb
  the given link

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Assumptions and Model (contd.)

• Conflict Set
• Each v represents a conflict set member for link
  l
• Realistic scheduling constraints as compared to
  protocol model or k-hop interference model
• Conflict graphs only model pairwise or binary
  conflict relationships
• Conflict set idea is more general
• Conflict sets specify multiple conflict graphs
• If v is a unit vector, conflict relationships
  can be expressed as a conflict graph
• Independent Sets
• An independent set I is a set of links which can
  be activated simultaneously, without conflicts
• Denote the set of independent sets by

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Assumptions and Model (contd.)

• Link Scheduling
• Set of independent sets
• Set of conflict-free schedules
• Link capacities under a conflict-free schedule
• Data flows and routing
• Flow traffic split along routes such that

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Formal Problem Statement

• First set of constraints link capacity
  constraints
• LHS Traffic imposed on link
• RHS Link capacity under conflict-free schedule
  a
• Third set to maximize the minimum
• Optimal solution exists under certain conditions

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A Note on Problem Formulation

• Our formulation is very powerful and allows for
  numerous scenarios
• Can be reduced to optimal routing problem if the
  powers and modulations are chosen from discrete
  sets
• introduce an artificial link for every feasible
  combination of power and modulation
• Can be generalized to achieve weighted max-min
  throughput
• flow f has weight wf depending on its priority,
  willingness-to-pay, etc.
• can yield throughputs proportional to per node
  traffic demands
• Conflict set structure can be seen as specifying
  multiple contention graphs
• can include any interference model as special
  case

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Scaling Transmit Power Improves Capacity

• Here ll(z, P) denotes the optimal solution for
  fixed PHY parameters
• If transmit power of each node is scaled up by
  same factor, then optimum throughput cannot
  decrease
• Why?
• SINR improves
• New links could become feasible
• In contrast with protocols like COMPOW common
  minimum power 7
• Also, proved by Behzad and Rubin 8

17
Addressing Computational Complexity

• Hardness result
• The problem of determining the max-min throughput
  of a network, given any conflict structure
  specified in terms of the conflict sets, is
  NP-hard
• Independent set problem can be reduced to our
  problem
• Smart enumerative technique
• Under the assumptions
• Channel gain is isotropic path loss
• Minimum node separation of dmin
• Bounded network area of LxL
• Maximum number of links that can be scheduled
  simultaneously is upper bounded by B depending
  only on dmin, L, the path loss exponent and
  minimum SINR requirement
• Enumerate all subsets of links, of size B or
  less, and check if they are independent
• We develop a computational tool
• input node/gateway locations, available power
  levels and modulation schemes at each node, flows
• output routing, scheduling and PHY parameters on
  each link

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Set-up for Computational Results

• For grids and arbitrary networks.
• For grids
• nodes placed on a unit grid with gateway in the
  bottom left corner (except when stated
  otherwise) NxN grid has 1 gateway and n N2- 1
  nodes
• grid side8m, far-field crossover distance01m,
  noise power-100dBm
• The flows are all assumed identical and going
  towards the gateway (unidirectional) or from and
  to the gateway (bi-directional)
• All nodes use same transmission power and same
  modulation (except when stated otherwise)
• Base modulation has rate 1 with SINR threshold 10
  dB
• Higher modulations rate 4, threshold 20 dB, and
  rate 8, threshold 25 dB
• Channel experiences only isotropic path loss (can
  be generalized), path loss exponent 4 (except
  when stated otherwise)

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5x5 Grid Network 1 Power, 1 Modulation

• The optimum throughput is non decreasing with
  power (bottom right)
• Let Pmin be the minimum power for which the grid
  is connected (-13.8 dBm)
• The maximum throughput is low
• The optimal routing is min hop (bottom left)
• Let PSH be the minimum power for which single hop
  is possible (16.2 dBm)
• Routing and scheduling are very simple
• Maximum throughput is R(m)/n where R(m) is the
  link rate when modulation m is used.
• For intermediate powers, routing can be quite
  complex (bottom center uses -1.85 dBm)

20
5x5 Grid Impact of Modulation Schemes

• Normalized throughput (left) and size of largest
  independent set used in optimal configuration
  (right) as a function of transmit power for
  different (single) modulation schemes.
• A higher rate modulation reduces spatial reuse,
  but may lead to high throughput gains
• A lower rate modulation provides connectivity at
  lower transmit powers
• Pmin -13.8 dBm, -3.8dBm, 1.2 dBm and PSH 16.2
  dBm, 26.2dBm, 31.2 dBm (for modulation 1,2,3
  resp.)

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Multiple Power and Modulation Levels

• Top right Normalized throughput vs. transmit
  power for the 5x5 grid of previous slide
• With modulation 1
• With modulation 2
• With both modulations 1 2
• Using both modulations provides
• Connectivity at lower powers
• High throughput at higher powers
• Bottom right Normalized throughput vs. transmit
  power for a 4x4 grid network
• With 1 or 2 power levels and modulation 2
• We compare 1 power level P with 2 power levels P
  and P - 5dBm.
• Using 2 power levels provides better flexibility
  at the physical layer

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Interference-avoiding Routing

• Two flows red and blue source and destination
  apparent from RHS figure
• Optimal routing (left) throughput 2/7 solid
  links carry 85 of the traffic
• Minimum hop routing (right) throughput 1/7
• Illustration of interference-avoiding routing

23
No Obvious Trade-offs

• Mesh network 15 nodes, 1 gateway on 4x4 grid
• Optimal routing with 2 power levels and 1
  modulation scheme (left) and 2 power levels and
  2 modulation schemes (right)

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Hexagonal Topology and Many Flows

• IEEE 802.16-like mesh network
• 36 subscriber stations and 1 base station
  (center)
• Many-to-one (upload) traffic (30 of traffic) and
  one-to-many (download) traffic (70 of traffic)
• Transmit power of -13 dBm uplink throughput
  0.00144 downlink 0.00433
• Routes unlike the tree-based structures
  considered in literature

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Single Gateway Placement

• Motivation
• Gateway placement is necessary.

Grid Topology
Throughput Curves
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Single Gateway Placement

• Gateway placement is necessary in arbitrary
  networks and no placement is optimal for all Ps.

Optimal Throughput Curves
Arbitrary Network Topology
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Beyond Omni-Directional Antennas

• Limitations of omni-directional (om-d) antennas.
• high power is required for high throughput.
• Interference reduces spatial reuse.
• Advantages of smart antennas
• Low interference.
• Less power to reach the same distance as compared
  to om-d antennas.
• Designed to transmit or receive power in a
  particular direction
• Characterized by
• Directivity concentration of radiated power in a
  particular direction
• Beamwidth (?). maximum spread of the gain
  defined at 3dB points
• Radiation pattern depiction of the relative
  field strength
• Gain (?)

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5x5 Grid with Smart Antennas
Variation of Spatial-Reuse with power
Variation of ? with transmit power (in dBm)

• Using smart antennas reduces the transmitter
  power requirements considerably.
• Better spatial reuse is enabled by the use of
  smart antennas.
• Network throughput at low powers is considerably
  enhanced.
• However the maximum achievable network
  throughput remains identical to omni-
  directional antennas since the bottleneck is the
  gateway.

29
5x5 Grid with Smart Antennas
Omni-directional antenna with transmit power
-7.75 dBm
Smart antennas with beam-width 52o and transmit
power -22.48 dBm
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Extensions and Future Work

• Two main assumptions
• Static channel gains
• Traffic is static
• For uncertain channel gains
• Possible to use robust design consider
  independent sets which always remain independent
• For stochastically time-varying channel gains
• If channel process iid across slots, can use
  average statistics to yield sufficient conditions
  on outage
• Static traffic
• Makes sense for a managed network
• Further studies
• Lifetime
• Other objective functions
• Multiple gateway placement
• Computational tool

31
References
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32
Our References

• A. Karnik, A. Iyer and C. Rosenberg
  Throughput-optimal Configuration of Fixed
  Wireless Networks, accepted in IEEE/ACM
  Transaction in Networking, July 07.
• S. N. Muthaiah and C. Rosenberg Single Gateway
  Placement in Wireless Mesh Networks submitted to
  ICC08.
• S. N. Muthaiah, A. Iyer, A. Karnik and C.
  Rosenberg Design of High Throughput Scheduled
  Mesh Networks A Case For Directional Antennas,
  in proceedings of IEEE Globecom 2007, Washington,
  November 2007.
• A. Iyer, C. Rosenberg and A. Karnik, What is the
  Right Model for Wireless Channel Interference? in
  the proceedings of The Third International
  Conference on Quality of Service in Heterogeneous
  Wired/Wireless Networks (QShine 2006), Waterloo,
  Canada, August 2006. Invited paper.