Multiple Access in General

1
(No Transcript)
2
Multiple Access in General

• Contention Based
• Scheduled
• (TDMA, FDMA, Orthogonal CDMA)
• Hybrids of All Sorts
• (including CSMA-CA aka 802.11)
• Many S-D Pairs
• Scheduled Access Unavoidable
• No node can transmit and receive in the same slot
  on the same channel

Single Receiver Networks
X
X
X
X
X
X
X
X
X
X
X
Mutli-Hop Ad Hoc Networks
3
Outline

• Scheduled Access in the context of Cross-Layer
  Design
• Scheduled Access in the context of Power Control
• Scheduled Access in the context of Network Coding
• The Combinatorial Curse vs. An Alternative
  Formation
• (speculative)

4
1. Cross-Layer Design (One View)

• Layered structure of networks
• Coupling between layers in wireless networks
• Cross-layer design to improve performance

5
Focus on Scheduling

• Classical View
• No conflicts requirement
• (Rigid Connectivity Model)
• Sets Si for fraction of time ?i to max
  throughput
• (or meet demand in min frame length)
• NP-complete
• Alternative View
• For given set SK are there transmission power
  levels Pi such that

6
Back to joint scheduling and power control

• Scheduling rules
• A node can only be associated with one active
  link at a time
• A node can NOT transmit and receive, or transmit
  to gt1 node,
• or receive from gt1 node at the same time
• SINR requirement

• The link with a lowest link metric has the top
  priority

7
Joint scheduling and power control

• Link metric for scheduling

High priority to links with large queue and less
blocking of other links (In the sprit of
cross-layer design)
8
Joint scheduling and power control

• Proposed joint scheduling and power control
  algorithm
• Links are considered in the order of link
  metric as candidates for
• activation in a given slot
• Each time a new link is tried, the well-known
  iterative power control
• algorithm is run to find the optimum power
  vector
• Limit the number of iterations to a fixed
  number N
• If the SINR requirement can be satisfied,
  accept this link and remove
• blocked links If not, reject this link. Links
  are tried one by one until all
• the links have been tried
• Some marginal protection a (agt1, replacing ß by
  ßa,) significantly
• reduces the number of iterations to satisfy
  SINR requirement, at the
• risk of reducing the number of simultaneous
  transmissions

9
Joint scheduling and routing

• How are the candidate links (i,j) determined in
  the first place?
• Joint scheduling and routing algorithm
• Bandwidth requirement can not be satisfied by
  scheduling only
• (For example unbalanced topology)
• Queues do not build up uniformly among all nodes
• Routes are updated periodically to react to the
  scheduling
• Bellman-Ford algorithm with routing distance
• Prefer routes with less delay,
• less energy consumption

10
All Kinds of Extensions

• Distributed algorithm and its simulation.
  Trade-off between performance and complexity
• Trade-off between performance and energy
  consumption
• Use of CDMA instead of the FDMA/TDMA multiple
  access method
• Adaptation of rate along with power control to
  make flexible use of the resources
• Addition of multiuser detection

11
2. Focus back on scheduling

• Given N transmitters and N receivers what
  matchings are feasible?

Criterion of feasibility
N
N
If , either one or no matchings are
feasible
Surprising result
If , all matchings are
feasible
Additionally
12
Scheduling/Power Control (cont.)

• If ? lt ? lt 1 ?
• Then ? ?K and ?SK s.t. ? lt ?K lt ?SK lt
  1
• such that
• If ? lt ? lt ?K, any K of the N transmitters can
  be matched to any K of the N receivers
• If ?K lt ? lt ?SK, any transmitters in a
  specific set SK of K transmitters can be matched
  to a corresponding set of K receivers
• Bounds on the values of ?, ?K, ?SK can be
  obtained

13
3. Network coding

• Possibly a revolutionary development
• Fundamental reversal of classical thinking
• Abandon the principle of packet integrity
  preservation
• Exploit correlations create correlations to
  exploit them

14
Network coding- Contd

• Bottom Line Rates predicted by capacities of the
  links of a min-cut are feasible (need not be
  through routing)
• Through linear codes
• (1999 R. Yeung et al, subsequently Medard,
  Koetter and others)
• Our work Extend the concept in wireless
  networks in conjunction with
  scheduling

15
Wired vs. wireless network coding

• Network coding has been originally developed for
  wired networks
• Nodes transmit and receive different information
  on different links at the same time
• Information packets flow continuously in the
  network without any interference
• Objective Extend network coding to wireless
  networks with extra constraints
• Nodes make omnidirectional transmissions of one
  packet per time slot
• Packets traverse the network in a
  store-and-forward manner (with delay effects)
• No node may transmit and receive a packet
  simultaneously
• Hence, we need to schedule transmitters and
  receivers separately in TDMA fashion
• There are possibly destructive interference
  effects among concurrent transmissions
• Medium access control (e.g. scheduling) is
  necessary to coordinate transmissions

16
Properties of wireless network coding

• Medium access control (MAC) and network coding
  (or routing as a special case) are interdependent
  in ad hoc wireless networks
• Joint specification of MAC and network coding is
  necessary for an ad hoc wireless network to
  operate
• Multiple performance criteria throughput,
  delay, energy efficiency
• Omnidirectional transmissions introduce node
  costs (e.g. energy expenditure) instead of link
  costs (as in wired networks) and impose
  node-based network coding
• We need time-varying network codes to support
  wireless network operation
• Nodes either encode and transmit packets or
  receive and decode packets or remain idle (e.g.
  to avoid packet collisions) over disjoint time
  intervals

17
Example of wireless network coding

• Source s wishes to transmit packets of 1 bit to
  destinations y z
• Assume classical collision channel model
• Channel outcomes success, idle, or collision
• Limited transmission/reception ranges with sharp
  boundaries

Encoding w performs b1 b2 Decoding 1. z
performs b1 (b1 b2) to recover b2


2. y performs b2
(b1 b2) to recover b1
18
Network coding vs. routing

• Network realizations for
• optimal routing solution

• Performance measures
• r average number of packets (bits)
  delivered to each destination per unit time
• eavg average transmission energy consumed to
  deliver a packet to any destination
• davg average delay per packet (in terms of
  time slots)

• Performance objectives can possibly conflict
  depending on topology and traffic

19
Joint Scheduling and Network Coding Solution

• Step 1 Predetermine conflict-free wireless
  network realizations , and
• assign minimum power Pi (m) to
  each node i for any realization Nm.
• Step 1 determines the flows zi, j(m) on
  link (i, j) for network realization Nm.

Step 2 Assign time fractions ?m to each
network realization Nm , and
determine flows xi, j(m) (d) addressed to each
destination d through network coding
in order to either
(i) maximize throughput r , or
(ii) minimize average cost
for given r, where
, or (iii)
minimize .
20
Step 1 Construction of Network Realizations

• A simple heuristic to construct wireless network
  realizations
• Assume classical collision channel model and
  sharp circular transmission/reception ranges.

transmitter
receiver
21
Complete Set of Network Realizations

• Activate each node (except source node) as a
  transmitter and receiver at least one time over
  all network realizations.
• For the SINR-based physical model, we can use a
  similar scheduling heuristic
• based on power control to determine
  conflict-free network realizations.

22
Step 2 Time Allocation to Network Realizations

• Next Problem Find time fraction ?m allocated to
  each network realization Nm.
• Construct a hypothetical wired network graph N g
  from the given wireless
• network realizations with time
  allocation as follows

N1
N2
N g
N3
s
s
s
s
? 2
? 1
u
t
u
t
u
t
u
t
? 2
? 1
w
w
w
? 2
? 1
w
y
z
y
z
y
z
? 3
? 3
y
z
Link Capacity

• The capacity of any link on the graph N g is
  equal to the time-average number of
• successful transmissions on that link over all
  wireless network realizations .

23
Wireless Formulation of Cuts and Flows
ci (s, y) the sum of capacities of links
crossed by the cut Ci that
separates source s from
destination y

• Define

• Omnidirectional transmissions require that
• the contribution of a node to any cut is limited
  
• to the value of at most one per unit time.

c1 (s, y) ?1 ?2 , c2 (s, y) 2 ?2 ,
c3 (s, y) ?1 ?2 , c4 (s, y) 2
?1 , c5 (s, y) ?1 ?3 , c6 (s, y) ?2
?3 , c7 (s, y) 2 ?2 , c8 (s, y)
?2 ?2 ?3 ,

• Choose in order to maximize r
  min d ?D min i ci (s, d)
• or minimize average cost
  for given r, or minimize .

• ?1 ?2 ?3 1/3 maximizes r to 2/3
  (achievable only by network coding).

24
Comparison of network coding and routing

• Consider a tandem network with classical
  collision channels
• There are total of n nodes randomly distributed
  on the network
• 5 source nodes are randomly chosen out of n nodes
• Each source node independently chooses its
  multicast group of size m

• Network coding improves routing, if a relay node
  combines traffic incoming from both
• neighbors

• Improvement is not possible for the cases with
  single source or directional
• transmissions

25
Challenges

• Joint Design of Network Codes with MAC AND
  Routing
• Criteria
• Throughput (Capacity)
• Delay (Scheduling or Contention)
• Energy
• Cyclic Graphs

26
4. A Speculative Formation of Scheduling

• S-D Pairs
• Let Pij(?) be the transmission powers at
  sources i for destinations j during ?
  percentage of time.
• Find the optimal values of the Pij(?) so as to
  maximize a performance criterion subject to rate
  (or other) constraints

• Imbedding the scheduling problem in a continuous
  variable optimization domain
• Optimal values for some of the Pijs may be zero
  for different ?s
• Result Schedule (without searching a discrete
  set!)

Key
27
Conclusions

• Scheduling is a Central Component of Wireless
  Network Design
• In its own right as a MAC Alternative
• In conjunction with
• Power Assignment
• Routing
• Network Coding
• As part of Cross-Layer Design
• Possibility of Escaping the Combinatorial Curse