Wireless Network Capacity

1
Wireless Network Capacity

• Jamar Parris
• Xi Liu

2
Areas Covered

• Fixed Nodes
• Mobility of Nodes

3
Focus

• All wireless networks
• Causes issues
• Medium access issues
• No centralized control complicates matters
• Physical layer issues
• Transmission power must be high enough to reach
  receiver whilst causing minimal interference to
  others.

4
Useful Information

• Packets sent in multi-hop fashion
• Packets can be buffered at intermediate nodes
• Several nodes can transmit simultaneously
  provided no interference from others
• Two types of networks considered
• Arbitrary Networks
• Random Networks

5
Arbitrary Networks

• Node locations, destinations, traffic demands,
  range are all arbitrary.
• 2 models used to describe successful transmission
  from hop to hop
• Protocol Model
• Physical Model
• Adds a signal to interference ratio
• Adds a ambient power level

6
Arbitrary Networks

• Assume 1 bit meter is when one bit is transported
  the distance of 1 meter
• Multiple credit not given for same bit carried to
  several destinations e.g. multicast
• Sum of products of bits and distances over which
  they are carried indicates transport capacity

7
Arbitrary Networks Results

• Transport capacity under Protocol Model is
• This depends on
• Nodes being optimally placed
• Traffic pattern optimally chosen
• Transmission range being optimally chosen.

8
Transport Throughput Capacity

• If the capacity were to be equally divided, each
  node would get
• Now if source and destination pair were 1m away
• Throughput and Transport Capacity would be equal
• It should be noted that transport capacity
  increases when the signal power decays more
  rapidly with distance

9
Random Networks

• Each node randomly chooses destination
• Destination chosen independently as the node
  closest to a randomly located point
• All transmissions use the same range
• Nodes are randomly located either on the surface
  of a sphere or in a plane

10
Random Networks

• Sphere
• Every node in a cell is within range of every
  other node in its own cell or adjacent cells
• If two cells are not interfering neighbors than
  their transmissions cannot collide.
• Number of interfering neighbors are bounded so
  that each cell has chance to transmit.
• Each cell contains at least one node to make
  relaying feasible.

11
Sphere
12
Random Networks

• Also uses Protocol Physical Model
• Uses Different Criteria for successful
  transmission
• Under Protocol Model - Results
• Results same for both the sphere and plane
• Throughput Capacity is
• Throughput constriction is caused by the need for
  all nodes to share the channel with other nodes
• Under Physical model, throughput capacity is

13
Relay Nodes

• Idea is to add additional nodes who only relay
  packets and are not themselves sources
• This allows for an increase in throughput
• However, number of relay nodes to have an
  significant increase in capacity can be large.
• For example, with 100 nodes, to make capacity
  equal to five times its value when there are no
  relay nodes, you need 4476 relays.

14
Trade-Offs

• Throughput versus range
• Increasing range of each node would reduce hops
  traversed. However, since nodes close to receiver
  need to be idle to avoid collision, throughput
  would actually decrease.
• Actually reducing range to as small as possible
  is whats needed.
• However, range can only get so small before the
  network loses connectivity

15
Inferences of the paper

• Maybe you should group nodes into cells and then
  designate one node to carry the burden of
  relaying multi-hop packets.
• Maybe connect base stations by wired links to
  improve capacity.
• If we assign a base station in each cell to
  communicate with other distant base stations
  wirelessly, base stations inherit same capacity
  limitation.

16
Inferences of Paper

• According to tests, subdividing the channel W
  into W1, W2, etc. did not change anything.
• As number of nodes increase throughput will also
  decrease.

17
Issues with this paper

• Interference is not factored in
• Access to wireless channel not coordinated
• Mobility not included
• Link failures not included
• Hence adapted and distributed traffic routing not
  included.
• Claims that the above will only reduce capacity.
• Not all of these is necessarily true

18
Mobility of Nodes

• Follows the same model, only nodes are mobile as
  opposed to fixed
• Network Topology changes over time
• Incurs delay, good for applications that can
  tolerate delays of minutes to even hours.
• E-Mail
• Database Synchronization

19
Mobility of Nodes

• Transmit only when nodes are close to each other.
• Reduces number of hops each packet must take,
  increasing throughput.
• Each node has an infinite stream of packets to
  send to its destination.
• The S-D association does not change over time,
  only the nodes themselves move.

20
Two Scenarios Used

• Mobile Nodes without Relaying
• Mobile Nodes with Relaying

21
Mobile Nodes without Relaying

• The problem with fixed nodes is that throughput
  reaches zero because number of relay nodes packet
  must go through increases
• In this scenario, we expect that any two nodes
  can be expected to be close to each other from
  time to time.
• Improve capacity by not relaying at all and only
  let sources transmit directly to destinations.

22
Results

• If the range is large (i.e. transmissions over
  long distances are allowed). many S-D pairs are
  within range.
• Interference however will limit the number of
  concurrent transmissions over long distances
• Makes throughput interference limited
• Also, if range is small, only a small fraction of
  S-D pairs will be close enough to transmit a
  packet.
• Makes throughput distance limited.
• Throughput per session decreases as n gets larger
  if only direct transmissions are allowed.

23
Mobile Nodes With Relaying

• Problems with no relaying
• Find a way to communicate only locally to
  overcome interference limitation
• Find a way to ensure that there are enough
  sender-receiver pairs to transmit to overcome
  distance limitation
• Proposed Solution
• Direct communication not enough, so introduce
  relaying.

24
Basic Idea

• Spread the traffic stream between the source and
  destination to a large number of intermediate
  relay nodes
• Each packet goes through one relay that buffers
  the packet until final destination delivery is
  possible
• For each S-D, every other node except S D can
  serve as relay nodes
• Goal is packets of every source node will be
  distributed across all nodes in the network

25
Basic Idea

• This ensures that every other node in the network
  will have packets buffered destined to every
  other node not including itself
• Hence, a sender-receiver pair always has a packet
  to send unlike in the case without relaying
• How many times must a packet be relayed in order
  to spread traffic uniformly?

26
Number of Hops per packet

• It turns out only one
• The probability of an arbitrary node to be
  scheduled to receive a packet from source S in
  equal for all nodes and independent of S
• Each packet therefore has to make only two hops
• Source to relay
• Relay to destination
• Total achievable throughput is

27
2 Phases

• Phase 1
• Scheduling of packet transmissions from source to
  relays or from source to final destination in one
  hop if possible
• Phase 2
• Scheduling of transmissions from relay to final
  destination or from source to destination if
  possible.
• When a receiver is identified, sender checks to
  see if it has any packets for which receiver is
  the destination, if it is, it transmits.
• In either phase, direct transmission is allowed
  since it is possible for a sender receiver pair
  to be a source destination pair as well.

28
Phase 1 Phase 2
29
Centralized vs. Distributed Implementation

• This model allowed for central coordinated
  scheduling, relaying and routing.
• Authors believe algorithm can be implemented in a
  distributed manner as well
• In this case
• At each instant, node can randomly and
  independently determine if they want to be a
  sender or potential receiver
• Each sender seeks out a receiver close to it and
  attempts to send data to it

30
Distributed Implementation

• Same phases as in centralized
• Multiple senders may attempt to send to same
  receiver
• Authors analysis showed that probability of
  success is reasonable even with many users

31
Problem

• Since capacity in both phases are identical,
  delay experienced from source to destination can
  be infinite even for a finite number of nodes if
  capacity in phase 1 fully used.
• Author Fix?
• Allow both source to relay and relay to
  destination transmissions to occur concurrently
  but give priority to relay to destination
  transmissions.

32
Sender Centric versus Receiver Centric

• So far, sender selects the closest receiver to
  send to
• What if receiver selects the closest sender from
  which to receive?
• At first, it may seem that results should be the
  same, but in fact this is not the case
• Problems occur if several receivers select the
  same sender

33
Two possible outcomes

• If the sender can only select one receiver to
  send to, sender-receiver pairs need to be
  eliminated,
• If sender can generate multiple signals for
  several receivers, we need to account for the
  fact the desired signal is only a fraction of
  unit power.
• Authors found no elegant want to integrate these
  complications into the proof

34
Receiver centric approach preferable

• If there is a single receiver
• This is due to the fact that the selected sender
  always has the strongest signal
• In the receiver centric approach, interference is
  smaller.
• Signal to interference ratio is larger in
  receiver centric approach
• Throughput is also slightly higher than in the
  sender centric approach

35
Throughput Comparison
Sender Centric
Receiver Centric
36
Downlink Uplink Throughput

• Downlink from source to all relays
• Uplink from relays to destination
• Due to multi-user diversity, throughput of
  downlink is high due to fact that at any one time
  a relay node is likely to be close to source
• The same also applies for uplink
• This is in essence a statistical multiplexing
  effect due to a large number of network users

37
Implications Conclusions

• Make use of delay tolerance of applications to
  improve throughput in a mobile wireless network
• Impossible to support a high throughput per
  source-destination pair using direct
  communication, they are too far apart most of the
  time
• This idea must be combined with a two hop
  strategy to achieve high throughput
• Drastic improvement in throughput over fixed
  nodes in previous paper

38
Problems with this model

• Nodes have entirely random mobility patterns.
• What if mobility is constrained?
• Delay increases as the system gets larger but at
  the same time so does throughput
• No constraint on delay imposed
• This implies that with a constraint on delay
  imposed the maximum achievable throughput must
  decrease.
• Must balance throughput and delay

39
Capacity of Ad Hoc Network

• Examine the capacity at a detailed level
• Single Cell Capacity
• Capacity of a Chain of Nodes
• Capacity of a Regular Lattice Network
• Capacity of Random Network
• Some conditions that per-node capacity scales
• Local traffic pattern

40
Capacity of A Single Cell

• All nodes can hear each other
• Four-way handshake
• 2Mbps
• Expect to see 1.8Mbps for 1500B data packet if
  control overhead is counted
• 1.7Mbps if IFS is counted

41
Capacity of A Chain of Nodes - Analysis
42
Capacity of A Chain of Nodes - Analysis
1
2
3
5
6
4
Radio Range of Node
Interference Range of Node 4
43
Capacity of A Chain of Nodes - Analysis
Total Max. Channel Utilization 1/4
1
2
3
5
6
4
Radio Range of Node
Interference Range of Node 4
44
Capacity of A Chain of Nodes Simulation

• Node 1 sends as fast as its MAC allows
• With Longer Chains, Utilization levels go
  substantially low.
• For a 1500 Byte packet size, it is as low as 15
  (1/7) of 1.7Mbps
• It is possible to achieve ¼ under 802.11 MAC
• 802.11 failed to find an optimal schedule
• Backoff waste

500 B
1500 B
64 B
45

Discrepancy
Backoff wastage large backoff at node 1 (5.4)



46
Capacity of A Regular Lattice Network

• Two communication patterns

Scenario 1
Scenario 2
47
Capacity of A Regular Lattice Network

• Scenario 1

Internode Distance 200 m
Interference radius 550 m
Every third row can operate Without interference
to give a Maximum throughput of 1/4 Thus flow
in such a lattice network is expected
(theoretically) to reach 1/12
48
Capacity of A Regular Lattice Network

• Expected
• (1/12) 1.7 0.14 Mbps
• Observed
• 0.1 Mbps
• Discrepancy
• Same as in chain

49
Capacity of A Regular Lattice Network
Traffic flow direction

• Scenario 2

1) Optimal Scheduling possible with predetermined
routes. 2) Overall throughput can be maximized
(in theory) with one vertical flow in one time
unit and horizontal flows in another 3) Per-flow
throughput is expected to be (1/24)
50
Capacity of A Regular Lattice Network
Slightly less than half of the per-flow
throughput without cross traffic Possible
Problem Head of queue block
51
Capacity of Random Network

• Expect to see similar total capacity to lattice
  network
• No dramatically loss
• 1) Hole in area
• 2) Center is more susceptible to congestion

52
Traffic Pattern

• Random traffic pattern
• The capacity available to each node is
  O(1/sqrt(n))
• Scalable traffic pattern
• Exactly local traffic fixed distance
• Power law distance distribution if the distance
  distribution decays more rapidly than the square
  of distance
• The basic idea is that the average path length in
  scalable traffic pattern should be kept constant

53
Impact of Interference on Multi-hop Wireless
Network Performance

• Framework to answer questions about the capacity
  of specific topologies with specific traffic
  pattern
• Assumptions
• No mobility
• Fluid model
• Centralized scheduler
• The basic idea is to model as a standard network
  flow problem with wireless constraints

54
Network Flow Model

• Connectivity graph
• Each vertex represents a wireless node
• Directed edge from A to B if B is within range of
  A
• Linear programming that solves the MAXFLOW problem

55
Conflict Graph (Contention Graph)

• Each edge in the connectivity graph (link)
  represented by a vertex in conflict graph
• An undirected edge between two vertices (links)
  if one link will interfere with the other
• If there are an edge between two links, then the
  two links cannot transmit together

56
Clique Constraints

• Cliques in conflict graph
• At most one link in a clique can be active at any
  instance
• Augment MAXFLOW LP to get upper bound

57
Properties of Clique Constraints

• Finding all cliques takes exponential time
• Even if all cliques are found, no optimality is
  guaranteed
• More cliques added, more tight the bound
• Tradeoff between computation and performance

58
Independent Set Constraints

• All links belong to an independent set can be
  active together
• No two independent sets can active at the same
  time
• Augment MAXFLOW LP to get lower bound

59
Properties of Independent Set Constraint

• Lower bound is always feasible
• LP can output a schedule
• Finding all independent sets takes exponential
  time
• The lower bound is optimal is all independent
  sets are found
• Lower bound will increase if we add more
  independent sets
• If upper and lower bound converge, the optimality
  is guaranteed

60
Some Generalizations

• Multiple radio on orthogonal channels
• Multiple, non-interfering links between nodes
• Directional antenna
• Appropriate edges in connectivity graph
• Conflict graph can also accommodate
• Multiple sender/receiver
• Multi-commodity flow problem for LP

61
Routing

• Shortest path is not enough
• Channel quality should be considered
• May introduce congestion
• Interference-aware routing
• Prefer routes that use up minimum amount of
  spectrum resource
• Advantageous sometimes even with 802.11 MAC

62
Limitations

• Computation cost
• 2-5 minutes for 100 nodes
• No guarantee to get optimal schedule in
  polynomial time
• Change in conflict graph
• Slow vs. fast change
• Fairness is bad

63
Capacity of Multi-Channel Wireless Networks

• Multiple channels share a fixed bandwidth
• Consider multiple channels and multiple
  interfaces in networks
• of channel c, of interface m per node
• What if we use less interfaces than channels
• m lt c
• Intuitively, capacity degradation may occur

64
Results

• The capacity is dependent on the ratio c/m, and
  not on the exact value of either c or m

For Arbitrary network There is always a
capacity loss
65
Results

• No degradation when c/m O(log n)
• If c O(log n), then m 1 suffices

For Random network
66
Capacity of Power Constrained Ad-hoc Network

• Consider model with low spectral efficiency
• Arbitrary large bandwidth
• Power constrained
• Two applications
• UWB
• Sensor network
• The result is that throughput increases with node
  enter the network

67
Intuition

• SINR Signal / (Noise Interference)
• Noise noise density bandwidth
• In bandwidth-constrained scenario, SINR is
  dominated by interference
• In low spectral efficiency, SINR is mainly
  affected by ambient noise

68
Question

• What are the fundamental limitations of wireless
  network?

69
Summary Factors Influencing Capacity

• Node placement
• Traffic pattern
• Static / Mobile
• Available Bandwidth
• Multi-Channel
• Infrastructure support
• Directional / Omnidirectional antenna

70
Thanks!

• Question?
• Suggestion?

71
Reference

• P. Gupta and P. R. Kumar, " The capacity of
  wireless networks,'' IEEE Transactions on
  Information Theory , vol. IT-46, no. 2, pp.
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