October 23, 2003

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Lecture 7

• October 23, 2003

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Last lecture

• Distributed power control
• Standard interference function
• Sufficient condition but not necessary
• If the standard interference function condition
  is true distributed, iterative power control
  algorithm is convergent towards the minimum power
  solution convergence rate geometric
• Some distributed power control algorithms may not
  meet the standard interference function condition
• Example USOPC
• How to prove convergence for USOPC ?

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Convergence of USOPC

• A general power control algorithm can be proved
  to be convergent if it can be expressed as
• For an achievable target SIR, the error vector
  
• goes to zero iff (if and only if)
• It can be shown that USOPC can be written in the
  above form, with M and N appropriately selected
  (see i) for more details)

4
Constrained power control

• Wireless networks tight energy constraints,
  especially at the mobile terminal maximum
  transmitted power limit
• Constrained DPC DCPC
• Standard Interference function
• If I(p) is a standard interference function,
  then, is also a
  standard interference function

5
Distributed SIR balancing algorithm

• Practical problem transmitter powers are all
  increasing
• Choose ? to normalize the powers only the ratio
  of power matters (no noise case)
• May not be possible to implement it in a
  completely distributed way

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Combined rate and power control

• Different modulations use different rates,
  require different SIR for same BER target
• Combined rate and power control problem select
  rate and power such that BER is met
• Rate is achievable, if the corresponding target
  SIR is achievable
• A rate vector is instantaneously achievable if
  there exist a positive power vector
  , such that
• to maximize the rate assume all users transmit
  with max power
• A rate vector
  is achievable in an average sense, if

- component wise
instantaneously achievable rate vectors
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Rate allocation example

• Assumptions
• each link require a minimum transmission rate
• non real time traffic
• Requirement maximize the total throughput (sum
  of rates)
• For two users

subject to
Feasibility condition
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Rate allocation example - cont

• Relationship rate SIR Shannon capacity for
  band-limited channels
• Using () in () gt achievable rate regions can
  be derived
• convex curves maximum rate is achieved for
  simultaneous transmission
• concave curves maximum average rate obtained by
  time multiplexing the transmissions

Average rate scheduling
r2
r1
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Some conclusions for rate scheduling example

• If noise negligible interference main constraint
• Better use orthogonal scheduling TDMA, FDMA,
  etc
• If noise matters (limited energy for
  transmission) non-orthogonal schemes may have
  advantages
• One example of non-orthogonal multiplexing is
  CDMA (Code Division Multiple Access)

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CDMA

• Basic CDMA principle all users transmit
  simultaneously using the same frequency band and
  are characterized by different signature
  sequences codes si, i1,2,, K (K number of
  users)
• Signature codes can be selected to be orthogonal
  users are completely separated from each other
• Disadvantages
• number of users that can be supported in the
  system is limited by the number of orthogonal
  codes
• If length of code is N, max K N
• Orthogonality cannot be maintained for
  asynchronous transmission
• Codes can also be selected non-orthogonal but
  with small cross-correlations
• Random codes all entries are -1 or 1 with equal
  probability (coin flips)
• Pseudo-random codes (IS-95 cellular CDMA)
  m-sequences
• very long sequences cyclically repeated
  (generated by linear shift registers) appear as
  random
• different statistical properties than random
  codes

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Simple single user CDMA system

- bit waveform
spreading gain
0
Tb
Tc
- signature sequence waveform
-signature sequence code
- Multiply them together what happens to the
spectrum?
is this good or bad?
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Properties of spread spectrum

• At a first glance bad uses more bandwidth for
  the same transmission rate
• Very important advantages
• Resistant to frequency selective fading
• A deep fade affects only partially the signal on
  that particular frequency signal can still be
  recovered
• Without spreading the signal is completely lost
• Exploits multipath rake receiver
• Low probability of intercept
• Low signal level noise like
• Hard to eavesdrop
• Creates reduced interference to other users
• Resistance to jamming and interference
• Narrow band jamming and interference affects only
  partially the signal
• The last two properties are particularly
  attractive for unlicensed bands
• Because of its resistance to interference can
  have frequency reuse 1 - big capacity advantage

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Multiple users

• Every user has a different signature sequence
• The received signal
• To detect signal 1 matched filter receiver

MAI multi-access interference
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Performance and optimality

• Performance depends on
• Powers implement power control
• Cross-correlations
• For random sequences
• Matched filter optimal for Gaussian noise
• Assumption central limit theorem interference
  is Gaussian

interference power
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Probability of error
BPSK/QPSK
If K is large neglect the noise contribution
All received powers equal
SIR key measure for performance determines
capacity soft capacity
Note a K user asynchronous system ? (2K-1)
synchronous system (virtual users) for
asynchronous systems
What is wrong with this analysis? -
Interference is not AWGN noise ! - matched
filter suboptimal - error
probability approximation
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Factors that influence the capacity

• Receiver design
• Better receivers to account for the
  interferences structure
• Power control and imperfections in power control
  loops
• Derivation based on equal received powers
  assumption
• Some other factors not yet accounted for in the
  previous SIR formula
• Joint power control and rate allocations for
  MF receivers
• - for non-normalized spreading sequences, and
  system bandwidth W

single cell assumption traffic burstiness
neglected influence of MAC layer

• -spreading gain of
• user i
• different transmission rates
• using different spreading gain

interference from neighboring cells
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Power control feasibility and optimal powers

• Minimum power solution impose SIRi ?i for all
  users i 1..K
• Minimum power solution
• Power control feasibility condition

- optimizes the physical layer performance -
Based on network and MAC layer inf of active
users K
K random variable, influenced by - traffic
activity - MAC performance
- gives the available physical layer resources -
basis for admission control and MAC design
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MAC design for integrated media

• Example voice and data
• QoS measures SIR, access delay, outage
  probability
• SIR higher for data - very reliable
  transmission required
• voice can tolerate occasional errors lower SIR
  requirement
• Delay voice delay intolerant
• data is delay tolerant but a certain average
  access delay requirement may be imposed (related
  to average throughput requirement)
• Outage probability voice cannot retransmit lost
  packets can tolerate about 1 losses outage
  probability constraint 1
• System requirement efficient use of resources
• Pack users as tightly as possible
• Traffic characteristics voice periods of
  inactivity
• Main idea
• schedule more data when the voice activity is low
• hybrid CDMA/ TDMA schedule traffic in time
  slots
• Delay for voice guaranteed by MAC by giving
  priority to voice
• Delay for data combination with admission
  control

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MAC layer design steps

• Measure current level of interference
• Predict future levels (in the next slot)
• determine residual capacity available for data
  (e.g. using the power control feasibility
  condition)
• Implement access method for data users
  transmission in the next slot, such that the
  number of successful users meet closely the
  residual capacity value
• to low inefficient resource utilization
• to high outage
• Design criteria for MAC
• maximize capacity
• minimize outage probability
• account for average delay requirements for data
• fairness issues
• low complexity and distributed implementation

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Simple MAC design example

• Data users always backlogged
• Number of active voice users cumulative discrete
  Markov chain
• can determine conditional probabilities, and
  compute prediction errors
• Total resources power control feasibility
  condition
• At slot n, v(n) is measured, d(n) is determined,
  d(n) residual capacity for data
• is predicted, based on the
  statistics of the voice traffic
  
• Access control schedules users to
  transmit in the next time slot

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Simple MAC example - continuation

• Various types of data access may be implemented
• Some examples
• Perfect scheduling requires the base station to
  tell every data user when to transmit
  requires lot of signaling
• Random access based on broadcast feedback and
  access probability p
• Base station adjusts value of access probability
  p and broadcasts this value for data users every
  time slot
• Every user flips a coin with p. If successful,
  transmit.
• - Outage is caused by
• Imperfect prediction of the residual capacity
• Imperfect scheduling in random access methods
• An average delay for data can be guaranteed by
  the admission control by limiting the number of
  users (voice and data) in the system

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Potential cross-layer design interactions

• MAC determines the number of active users in the
  system -gt influences the optimal power selection
  at the physical layer, and consequently the
  physical layer capacity -gt MAC performance
• Errors in prediction and scheduling at MAC -gt
  errors in target power assignment -gt imperfect
  power control
• Imperfect power control -gt target SIRs not met
  voice packets are lost, data has to rely on
  retransmissions -gt delay requirements at MAC
  layer cannot be met anymore
• For matched filters, no direct feedback from
  MAC/Admission control on filter adaptation is
  required situation will change for the case of
  multi-user receivers

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References

• i Jantti, R. Seong-Lyun Kim , Second-order
  power control with asymptotically fast
  convergence , IEEE Journal on Jantti, R.
  Seong-Lyun Kim Selected Areas in
  Communications,, Volume 18, Issue 3 , March
  2000, Page(s) 447 -457
• ii C. Comaniciu, N.B. Mandayam, "Delta
  Modulation based Prediction for Access Control in
  Integrated Voice/Data CDMA Systems", IEEE Journal
  on Selected Areas in Communication (JSAC), vol
  18, No 1, January 2000, pp. 112 - 122.