Interference Modelling in Spatially Distributed Shadowed Wireless Systems

1
Interference Modelling in Spatially Distributed
Shadowed Wireless Systems

• Neelesh B. Mehta
• ECE Department, IISc

Project 602 duration April 2008 to March 2010
2
Outline

• Summary of research output
• Inter-cell interference modeling
• Our two approaches
• Results
• Conclusions

3
Summary of Output Conference Publications

• Sarabjot Singh and Neelesh B. Mehta, An
  Alternate Model for Uplink Interference in CDMA
  Systems with Power Control, National Conference
  on Communications (NCC), Guwahati, India, Jan.
  2009.
• Neelesh B. Mehta, Sarabjot Singh, and Andreas F.
  Molisch, An Accurate Model For Interference From
  Spatially Distributed Shadowed Users in CDMA
  Uplinks, IEEE Global Telecommunications Conf.
  (Globecom), Honolulu, USA, Nov.\ 2009

4
Summary of Output Journal Publications

• Sarabjot Singh, Neelesh B. Mehta, Andreas F.
  Molisch, and Abhijit Mukhopadhyay,
  Moment-Matched Lognormal Modeling of Uplink
  Interference with Power Control and Cell
  Selection, IEEE Trans. on Wireless
  Communications, March 2010.
• Neelesh B. Mehta, Sarabjot Singh, Abhijit
  Mukhopadhyay, and Andreas F. Molisch, Accurately
  Modeling the Interference From Spatially
  Distributed Shadowed Users in CDMA Uplinks, To
  be submitted to IEEE Trans. on Communications,
  2010.

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Uplink Interference
Inter-cell interference
BS
Reference cell
Neighboring cell

• Mobile stations tx. to base station
• Multiple interferers contribute to UL
  interference
• Interference is random
• Important to model it correctly

6
Wireless Propagation Characteristics

• Path loss (d)
• Shadowing (s)
• Lognormal distribution
• Fading (f)
• Rayleigh, Ricean, Nakagami-m

s
f
P
Rx. power
Tx. power
Path loss
Shadowing
Fading
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Lognormal Probability Distribution
Lognormal Prob. Distribution
pX(x)
x

• A skewed distribution
• Several and varied applications in wireless
  propagation, finance, health care, reliability
  theory, optics, etc.

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Conventional Model Gaussian Approximation

• Problem Closed-form tractable expressions for
  probability distribution of sum are not known
• Conventional solution Model as a Gaussian RV
• Chan, Hanly01 Tse,Viswanath05
• Two justifications given
• Central limit theorem
• Less randomness in the presence of power control
  and cell site selection

9
Our Approach Approximate As A Lognormal
Model inter-cell interference as a lognormal
random variable

• Related literature supports this approach
• Works much better given number of summands
• Mehta et al'07, Fenton-Wilkinson60,
  Schleher77, Schwartz-Yeh82, Beaulieu-Xie04
• Permanence' of lognormal sums
• W. A. Janos 70, R. Barakat76

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Unique Feature of Our Problem Several Sources of
Randomness

• User locations are random within a cell
• Use Poisson point process model
• Number of users is also random
• Interferers transmit power is random
• Power control
• Cell site selection

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Our Two Methods to Fix Lognormal Parameters
Lognormal
Goal Determine the two parameters µ and s

• Developed two methods
• Moment-matching method
• MGF-matching method

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Moment Matching Key Results

• Match the first two moments of total uplink
  interference
• Advantage Closed-form expressions possible

13
CCDF Matching To See Tail Behaviour
Ave. of users/cell 10 First tier interference
Complementary CDF
Total interference

• Lognormal tracks the actual CCDF very well
• Better than conventional Gaussian

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CDF Matching To See Head Behaviour
Ave. number of users/cell 10
CDF
Total interference

• Lognormal significantly better than Gaussian
• Gaussian CDF high for small value of interference
• Off by 2 orders of magnitude

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With Cell Selection (Handoff Set Size 2)

• Moment matching based lognormal approximation is
  better than Gaussian even with cell site
  selection
• Shown for first-tier interference

16
Further Improvement Using MGF Matching

• Key idea Match moment generating function
  instead of moments
• Advantage Gives the parametric flexibility to
  match both portions of distribution well
• Technical enabler Can evaluate MGF relatively
  easily when users are distributed as per a
  Poisson spatial process
• Benefit from the extensive theory on Poisson
  processes

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Improved Lognormal Approximation Method

• MGF of the total uplink interference from users
  in cell k

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6. Results CDF and CCDF Matching Accuracy
30 users/cell on average
CCDF
CDF
First-tier interference

• Lognormal approximation is significantly better
  than Gaussian
• MGF-based lognormal approximation is better than
  moment-based lognormal approximation

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Conclusion

• Goal Model inter-cell interference in uplink of
  CDMA systems
• Showed Lognormal is better than the conventional
  Gaussian
• New methods To determine parameters of
  approximating lognormal
• First method Based on moment-matching
• Second improved method MGF-based moment matching

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Extensions

• Two model generalizations
• Extend the femto cells
• Multiple femto cells within a macrocell
• Hybrid macrocell/microcell cellular layouts
• Two other improvements
• Include peak power constraints
• Better cell area approximation techniques

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Inter-Cell Interference in CDMA Uplinks

• Spreading codes diminish interference but do not
  annul it
• Sum of signals from many users served by other
  BSs
• Undergoes shadowing/fading

It is a random variable. How do we characterize
it?
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System Model With Power Control
Interfering cell
Reference cell

• Fading-averaged inter-cell interference
• Path loss and shadowing model

• Interference power (with power control) at BS 0
  from users served by BS k, located at x1(k), . .
  . , xNk(k)

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User Location and Number Modelling

• Model as a Poisson Spatial Process
• Characterized by an intensity parameter (?)
• Analytically tractable model
• Probability that Nk users occur within a cell of
  area A equals

Analysis approximation
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Sum of Fixed Number of Lognormals CDF

• Percentile (CDF) plot comparison

S-Y method
Moment matching
CDF
Simulations
Mehta et al
Mehta, Wu, Molisch, Zhang, IEEE Trans.
Wireless 2007
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Sum of Fixed Number of Lognormals CCDF
Complementary CDF
Fenton-Wilkinson
Log scale
S-Y
Simulation
Mehta et al

• Various approaches exist to accurately
  characterize the approximating lognormal

Mehta, Wu, Molisch, Zhang, IEEE Trans.
Wireless 2007
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CCDF Matching (Denser User Population)
Ave. of users/cell 30 First tier interference
Complementary CDF
Total interference

• Lognormal approximation is still significantly
  better
• In sync with literature on sums of fixed number
  of lognormals

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Sources of Inter-Cell Interference
2
2
2

• First tier interference
• Second tier interference

1
2
2
1
1
2
2
1
1
1
2
2
2
2
2

• Must model inter-cell interference accurately
• Cell planning and base station deployment
• Signal outage probability evaluation
• Performance of link adaptation

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CDF Matching (Denser User Population)
Ave. number of users/cell 30
CDF
Total interference

• Lognormal better than Gaussian even for denser
  populations!
• However, inaccuracy does increase

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With Cell Site Selection Power Control
Reference cell
Neighboring interfering cell

• Serving base station chosen by a user need not be
  the geographically closest one
• Due to shadowing
• Depends on soft handoff set size
• The number of neighboring base stations a user
  tracks

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First Tier Interference (Handoff Set Size 3)
CDF
CCDF

• Lognormal approximation is still better!

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Second Tier Interference (Handoff Set Size 2)
CDF
CCDF

• Second-tier cells are further away

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Zero Tier Interference (Handoff Set Size 2)
CDF
CCDF

• Even users located within reference cell can
  cause inter-cell interference
• Gaussian does well in this case!