Lecture no' 4

1
Lecture no. 4

• September 25, 2003

2
Performance of wireless systems review

• Up to this point we saw that the performance of
  the wireless channels is limited by two main
  problems
• channel impairments fading
• Interference from users using the same channels
• We also have seen that a good of measure of
  quality for a wireless link is the SIR
  (signal-to-interference ratio)
• Interference is mitigated by orthogonalizing the
  users (completely separate them)
• in time TDMA (time division multiple access)
• in frequency FDMA (frequency division multiple
  access)
• using orthogonal codes CDMA (code division
  multiple access)
• We have also seen that the disadvantage of using
  orthogonal signaling is that the number of
  possible users is limited by the available
  bandwidth.

3
Performance of wireless systems review
frequency

• Simplest example FDMA

user 1
user 2
Each user assigned a different frequency channel
to transmit
user 3
user 4
user 5
time
For cellular systems, every provider has a
spectrum of frequencies auctioned. Important
note There are different bands allocated for
transmission on the uplink (from mobile to BS)
and for the downlink transmission! The total
number of users that can be supported given that
spectrum is
4
Cellular capacity and frequency reuse

• Limited coverage of a cell need to implement a
  multiple cell system
• Because of interference cannot reuse the same
  channels to close to each other -gt frequency
  reuse
• Homework problem no. 6

BS1
BS2
r
r
Neglect shadow fading
d
Same value but less likely to occur compared to
downlink worst case
5
NJ Turnpike scenario - uplink

• Consider more neighboring cells

BS3
BS5
BS1
BS4
BS2
r
r
r
r
d
SIR computed here (at BS) for uplink
6
NJ Turnpike scenario - downlink

• Consider more neighboring cells

BS3
BS5
BS1
BS4
BS2
r
r
r
r
d
SIR computed here (at mobile) for downlink
Downlink SIR better, but uplink SIR much more
unlikely to occur
7
Capacity and outage

• SIR measure of the link quality users
  satisfaction
• From the network provider point of view support
  more users for given bandwidth interested in
  high capacity
• Capacity can be expressed as cellular efficiency

channels/cell
Computed for worst interference conditions
Opposite assumptions - worst case analysis -gt
pessimistic results - shadow fading neglected -gt
optimistic results
If shadow fading considered large fluctuations
for the received signal - one approach
include a fade margin on top of the required
SIR - guarantees that all terminals obtain an
adequate SIR - too restrictive -gt too low
capacity
8
Outage capacity

• In practice we will allow some percentage of the
  calls to experience bad quality channels -gt
  received SIR lt target SIR
• If terminals are moving channel conditions will
  change, the overall performance will improve
• Data packets lost retransmitted ARQ schemes
• Voice packets lost dropped voice can
  tolerate some losses lt 1
• Every time a user cannot meet its target SIR we
  call this an outage.
• Outage probability
• Notation conventions link gains denoted as Gij
  (other classical notation in the literature hij)

M1
BS1

downlink
BS2
M2

9
Outage probability
M1
BS1

uplink
M2
BS2

Compute outage probability for the
uplink -consider the SIR for an arbitrary user
j, assigned to an arbitrary BS 0
M of cells P transmitted powers X
activity variable Gij lognormal r.v.
10
Outage probability

• of terms in the sum Binomial distributed
  (channel assignment independent distributed in
  all cells)

Mc of active users/cell, i.e., users
requesting connection in a given cell -
Poisson distributed with expected value ?Ac
Activity factor
11
Compute outage probability

• If equal powers for all transmitters

Cell 0
Dk
Cell k
Dk reuse distance Dk distance between the
interfering mobile (worst case) to the
BS Approximation Dk ? D for all neighboring
cell in the first tier
neglect the interference coming for
cells in second tier, third, etc
GI composite fading, at high loads closely
approx by a lognormal distribution
12
Compute outage probability - cont

• The approximation works reasonably well for lower
  loads differences mainly in the tail of the
  distribution
• For capacity analysis good approx
• The outage probability at distance r

13
Outage capacity final result

• If r is a r.v. with some density p(r)
• Outage probability constraint gives condition on
  the reuse distance
• Up to now, the users QoS has been measured only
  in terms of SIR
• Another important measure blocking probability
  probability that a call request is denied as a
  consequence of unavailable channels at the base
  station
• This leads to another type of analysis traffic
  based capacity analysis

14
Traffic based capacity analysis

• Assumption allocation of channels in different
  cells is done independently
• Compute the assignment failure rate
• Making the notation

trunking gain
15
Queueing theory analysis

• Number of channels available for traffic -gt
  number of servers
• Duration of a call -gt service time for a queue
  server
• Exponential distributed (mean duration 1/?)
• New call arrivals Poisson distributed with mean
  ?
• If no server is free, a new call can be queued
  (and waits for a channel to be free) or it can be
  blocked
• Representation of a cell as an equivalent
  queueing system

1
2
M/M/?/B queue
3
B length of buffer
?
16
Queueing theory results

• If the calls are not queued at the BS (B0)
• Probability that the cell is blocked
  probability that all servers are busy
• If B ? 0, need to consider yet another QoS
  measure for users call connection delay (how
  long a user has to wait in the queue until a
  channel becomes available)

17
M/M/?/B queue

• Blocking probability
• 
  (1)
• p0 probability of an empty queue and no one in
  service
• Average connection delay
• (2)

Probability of queueing
18
Admission control

• The call connection delay and the blocking
  probabilities depend on the system capacity (?),
  traffic characteristics (?,?) and are also
  influenced by the choice of B (buffer length)
• The management of the resources at the network
  level, which may include selection of B and
  servers allocation is done by the admission
  control.
• The previous case discussed is the simplest one,
  in which all users are treated equally.
• If heterogeneous services (voice, data, video,
  etc)
• Different QoS requirements for different classes
  of traffic
• Need to be treated differently by the admission
  control
• Example 2 types of traffic (arrival rates ?1 and
  ?2)
• Simplest admission control first come, first
  serve complete sharing policy
• Does not differentiate among different classes of
  service

19
Threshold policy

• Another approach threshold policy
  differentiate between different classes of
  traffic
• Suppose that the two classes have different
  blocking probability constraints
• Different buffer dimensions and resource
  partitioning might help

1
2
K1
1
2
K2
20
Threshold policy - cont

• First class better service class given
  priority
• Delay constraints W1, and blocking prob.
  constraints Pb1
• Second class blocking prob. constraints Pb2, no
  delay constraints
• Solution
• From (1) and (2) select K1 and B1 such that
  constraints are met
• For class 2 -gt select K2 ?-K1, then determine
  B2 for Pb2 constraint, from (1)
• Although the threshold policy improves the
  performance, it is not optimal, since it is based
  on static allocation of resources (determined a
  priori, based on statistical information, no
  measurements used for dynamically adjusting the
  performance)
• Optimal policy one class of admission control
  based on a semi-Markov decision process
  formulation (SMDP)

21
Optimal admission control policy

• SMDP process for which the next state of the
  system depends only on the current state and the
  action chosen
• Admission control policy allocate the resources
  dynamically, as a function of the current state
  of the system
• The SMDP formulation requires
• State space definition characterizes the
  physical layer resources
• An action space definition given the current
  state, what action to take (characterizes the
  admission control)
• Cost associated with the current decision
• Depends on the current state and the chosen
  action
• The cost can be selected such that the optimal
  admission policy minimizes the overall blocking
  probability in the system
• The optimal policy given in the form of a
  look-up table
• If in state i, take action a(i)
• The optimization is complex, but it can be done
  in advance and then the admission control can use
  the look-up table to coordinate channel assignment

22
Cross-layer design aspects

• Channel assignment by the admission control
  influences the level of interference in the
  system -gt influences the performance of the
  physical layer -gt changes the admissible state
  space -gt influences the design of the admission
  policy
• An example of admission control design using an
  SMDP formulation will be discussed for CDMA
  systems later on.