Cooperative Networking

1
Scaling of Wireless ad-hoc networks

• Cooperative Networking
• Presented by Sepideh Dolatshahi
• Feb 27 2008

2
Outline

• Insight, Measure and Definitions
• A brief History
• Dense vs. Extended Networks
• Problem Description, model

3
Insight

• Capacity and Connectivity two measures for the
  performance of mobile ad hoc networks
• Capacity and rate
• Shannon's noisy-channel coding theorem reliable
  communication is possible over noisy channels
  provided that the rate of communication is below
  a certain threshold called the channel
  capacity(using appropriate encoding and decoding
  systems)
• For any information rate R lt C and coding error e
  gt 0, for large enough N, there exists a code of
  length N and rate R and a decoding algorithm,
  such that the maximal probability of block error
  is e

4
Defn Capacity

• p(y x) inherent fixed property of channel
• X the space of messages transmitted during a
  unit time
• Y the space of messages received during a unit
  time
• Capacity The max mutual information
• Mutual Information measures the amount of
  information that can be obtained about R.V. X by
  observing Y.

5
Defn Throughput

• The total throughput of the system T(n) n
  R(n)

6
A brief history

• The seminal paper by Gupta/Gumar initiated the
  study of scaling laws in large ad-hoc wireless
  networks 2000
• With classical multihop architectures O(
  )
• Aeron and Saligrama n2/3

7
Dense vs. Extended networks

• Interference-limitedness vs. coverage-limitedness
  two operating regimes of cellular networks

8
Problem Description, model

• N nodes uniformly and independently distributed
  in square of unit area in dense scaling area n
  in extended scaling
• Destinations paired up one-to-one in an arbitrary
  fashion
• A common average transmit power of P joules per
  symbol
• Channel

9
Main results for dense networks

• Information theoretic upper bound on the
  achievable scaling law for throughput
• The main result of this paper
• Let a 2 , For every e gt 0 , ? Ke gt 0
  independent of n such that with high probability,
  an aggregate throughput of
• can be achieved for all possible pairings
  between source and destination.

10
The key Lemma

• A network with n nodes subject to interference
  from external sources,
• a gt 2
• The signal received by node i
• is the collection of
  uncorrelated zero mean stationary and ergodic
  random processes with power

11
The key Lemma(cntd)

• Assumptions
• there exists a scheme such that for each n , with
  probability at least 1-e-nc1 achieves an
  aggregate throughput
• The per node average power budget required to
  realize this scheme is upper-bounded by P/n as
  opposed to P.
• Result
• One can construct another scheme for this
  network that achieves a higher aggregate
  throughput

12
A rough description of how the new scheme can be
constructed

• Base idea Clustering and Long-range MIMO
  transmissions
• We introduce three phases

13
Phase 1 of 3 Setting up transmit cooperation
14
Phase 1 of 3 Setting up transmit cooperation
(cntd)

• M nodes in each cluster ? traffic demand of
  exchanging M(M-1) M2 bits handled by setting up
  M subphases an assigning M node-destination pair
  for each subphase
• Assuming an aggregate throughput of Mb
• Each subphase M1-b time slots gt M2-b time
  slots

15
Phase 2 of 3 MIMO transmissions
16
Phase 2 of 3 MIMO transmissions (cntd)

• Offers significant increases in data throughput
  and link range without additional bandwidth or
  transmit power. It achieves this by higher
  spectral efficiency (more bits per second per
  hertz of bandwidth) and link reliability or
  diversity (reduced fading).

17
Phase 2 of 3 MIMO transmissions (cntd)

• Successive long-distance MIMO transmissions
  between source-destination pairs One at a time
• M bits of s are simultaneously transmitted by the
  M nodes in the cluster to the M nodes in cluster
  containing d.
• N source-destination pairs gt n time slots

18
Phase 3 of 3 Cooperate to decode
19
Phase 3 of 3 Cooperate to decode (cntd)

• Nodes quantize each received bit into Q bits
  called observation
• Same explanations as the 1st phase
• QM2 bits handled by setting up M subphases an
  assigning M node-destination pair for each
  subphase
• Assuming an aggregate throughput of Mb
• Each subphase QM1-b time slots gt QM2-b time
  slots

20
Note

• Clusters can work in parallel in phases 1,3
  because according to assumptions of the lemma
• For a gt 2 the aggregate interference at a
  particular cluster caused by other active nodes
  is bounded
• He interference by different nodes in one cluster
  are zero-mean and uncorrelated

21
Aggregate throughput
22
Maximizing throughput

• Maximizing throughput by choosing M n1/(2-b)
  yields

23
Back to the main results for dense networks

• Start the simple scheme of direct transmission
  between s-d pairs(TDMA) gt
  gt b0
• Apply the key lemma once
• Applying that h times yields
• Given any e gt 0
• choose h s.th.

24
Back to the main results for dense networks

• Schematically

25
Main results for extended networks

• Compared to dense networks the distance between
  nodes is increased by a factor of square root of
  n

26
Main results for extended networks (cntd)

• Thus the received powers are all decreased by a
  factor na /2
• Equivalent to a dense network with the average
  power constraint for each node decreased to P/ na
  /2 instead of P
• A simple bursty modification of our hierarchical
  scheme run our hierarchical scheme a fraction
  1/n a /2-1 of time gt Aggregate throughput

27
Main results for extended networks (cntd)

• Consider an extended network on a by
  square. There are two cases
• 2 alt3 For every e gt 0 , with high
  probability, an aggregate throughput of
• a 3