Channel Statistics of a CDMA System with Closed Loop Power Control

1
Channel Statistics of a CDMA System with Closed
Loop Power Control

• Team
• Vishal Monga, Sundar Subramanian, Sandhya
  Govindaraju, Ritu Kar
• May 3, 2003

2
Introduction

• A CDMA Cellular System

• Synchronization of signals in the uplink not
• guaranteed (codes not truly orthogonal)
  Sudjai et. al
• Power leakage from interfering users

3
Power Control in Cellular Systems

• Why power control?
• Near-far effect
• Mechanism to compensate for channel fading
• Interference reduction, prolong battery life
• Types of Power Control
• Open Loop Base station transmits power based on
  received signal strength (RSS) no feedback
• Closed Loop Base station sends feedback to
  mobile on what power levels to transmit
• Power Control Tradeoffs Rappaport, 1998
• Achieve acceptable SIR vs. minimize transmit
  power
• Update rate vs. Overhead (effect of coherence
  time?)
• Ideal power control would eliminate fading!

4
Power Control contd

• Perfect Power Control is impossible
• Continuous updates needed
• Feedback channel is not error free !
• Power Control Strategies
• Fixed-Step or Adaptive
• Aims to converge to an equal power
  configuration
• Closed Loop Power Control Algorithms
• Upper bound on performance in Spread Spectrum
  Systems Hanley, 1995
• SIR optimal algorithms Li Gajic, 2002 Liu
  Wong, 2002
• Optimal Dynamic Power control Veeravalli et. al,
  2000

5
Channel Statistics with Power Control

• A simple example
• Effect is more pronounced in case of multiple
  users

Ideal power control ? multiple access
interference (MAI) approximated Gaussian for
large of users Yao, 1977, Pursley,
1977 Imperfect power control ? non-Gaussian
channel Actual channel statistics needed for
analysis viz. capacity calculation
6
Objective

• Goal Given a power control algorithm channel
  model (fading characteristics), estimate
• Received signal statistics
• Signal to Interference Ratio (SIR)/Interference
  statistics
• Capacity (number of users/cell) using actual
  SIR compare with Gaussian assumption for
  interference
• Channel model/fading characteristics
• Rician fading assumed
• Include Rayleigh as a special case
• Develop a framework for analysis that can be
  easily extended

7
Selected Power Control Model

• Fixed-step power control algorithm Chang, 1993

Step size

• Desired level of 0 dBW (1 W) at the receiver
• Update rate a function of channel coherence
  time/doppler
• Quantizer makes a hard decision
• Return channel errors possible ?

8
Markov model for feedback errors

• Model fading as finite state Markov (FSM)
  process
• Each SNR state sk denotes a particular BER
  channel
• Markov approximation models the fading
  statistics such
• as level crossings/average fades Wang et.al.
  1995

• Transition Probabilities pij P(sj j/ si
  i)
• Ratio of expected number of level crossings of
  the state SNR
• boundary to average number of blocks/sec
  Moayeri, 1995

9
Markov model for feedback errors

• Invariant distribution p
• p(k) is the probability that the channel fade
  (rician/rayleigh)
• lies between sk and sk1
• Probability of return channel error
• Find Pr (bit error) in return channel based on
  current SNR
• state predicted by the process

• Number of SNR states?
• chosen 10 initially Gilbert, 1960
• can be varied (increased) for finer sampling of
  channel state
• Overestimating errors artificially ruins power
  control
• Choose fading statistics appropriately helps
  make
• conservative estimates

10
Simulation Parameters

• Channel Model
• Rician parameter K varied from inf (Rayleigh) to
  6 dB
• Channel coherence time (or doppler)
• Number of SNR states for simulating feedback
  error
• Power Control Model
• Update rate (should depend on channel coherence
  time)
• Step-size for power updates, varied from -13 to
  7 dB
• System parameters
• IS-95 W 1.25 MHz, R 8 Kbps
• Number of mobile users and their location
• Location controlled by random start up conditions

11
Power Control Performance (Rician)
No Feedback Errors
Feedback errors simulated via FSM model
K -3 dB
12
Power Control Performance (Rayleigh)
No Feedback Errors
Feedback errors simulated via FSM model
13
Power Control Performance (Rician)
No Feedback Errors
Feedback errors simulated via FSM model
14
Power Control Performance (Rayleigh)
No Feedback Errors
Feedback errors simulated via FSM model
15
Received Signal Statistics (Rician)
No Feedback Errors
Feedback errors simulated via FSM model
16
Received Signal Statistics (Rayleigh)
No Feedback Errors
Feedback errors simulated via FSM model
17
Capacity in CDMA cellular systems

• MAI generally modeled as Gaussian
• Valid when the channel is non-fading i.e. perfect
  power control is achieved
• Capacity (N) in number of users/cell Viterbi
  et.al, 1991

Eb/No chosen for a given BER with some reliability
W total spread bandwidth (1.25 MHz for IS-95) R
information bit rate, ? background (thermal)
noise S Signal power (equal for all users) a
Voice activity factor 3/8 Gilhousen, 1991
18
Capacity in CDMA cellular systems

• Capacity estimates from actual (simulated) SIR
• Local-mean Eb/No given by Ariyavisitakul,
  1993
• -- short term SIR normalized by local mean
• short term ? SIR statistics over a sliding window
  in time
• ? ( unity) -- depends on PN sequence Weber,
  1981
• Given a bound on average BER for acceptable
  performance Viterbi et.al, 1991 compute

• required local-mean bit
  energy to noise

19
Capacity in CDMA cellular systems

• Determine Probability of system outage
• For ß reliability, upper bounded by (1-ß)
  
• System capacity determined by the maximum
  allowable user density N that allows
• We choose ß 99 as in Viterbi et.al, 1991

20
SIR Statistics and Capacity (IS-95)

• Recall for ß ( 99) reliability,
• capacity is given by the largest N
• that allows
• Capacity assuming Gaussian
• interference
• N 84 users/cell
• Simulated Capacity
• Rician N 63 users/cell
• Rayleigh N 58 users/cell

Rician
IS-95, S/I99 -15dB
Rayleigh
21
Inferences

• Capacity
• The Gaussian approximation overestimates
  capacity!
• 20-25 overshoot for Rician, 33 Rayleigh
• Rayleigh a bit too conservative?
• Power Control
• Converges in an average sense
• SIR based control is preferable but requires a
  wealth
• of information on interactions among
  individual users
• Ariyavisitakul, 1994
• Number of Users
• Power control becomes difficult with more users
  
• controlled by different base stations
• Interference and SIR statistics difficult to
  analyze

22
Contributions

• Simulated and analyzed
• Received signal statistics (not Gaussian!)
• Signal to Interference Ratio (SIR)/Interference
  statistic
• Incorporated a Finite State Markov (FSMC) model
  for simulating feedback errors
• Capacity in CDMA systems
• Established in a fading environment capacity is
  overestimated by Gaussian interference
  approximation
• In non-fading however, the approximation holds
  firm
• Developed a framework for analysis
• Extends readily to a different choice of channel
  model and/or power control algorithm

23
Conclusion Future Work

• Conclusion
• SIR statistics determine capacity to a very
  large extent in CDMA systems
• A Gaussian approximation is inaccurate when power
  control is imperfect (fading remains)
• Future Work
• Incorporate more sophisticated power control
• Test other environments viz. WCDMA, CDMA2000
• Evaluate impact of power control on other system
  design issues?
• Develop analytical bounds on capacity and other
  system quality metrics (in imperfect power
  control)