Mitigation of Radio Frequency Interference from the Computer Platform to Improve Wireless Data Communication

1
Mitigation of Radio Frequency Interferencefrom
the Computer Platform to ImproveWireless Data
Communication
Preliminary Results
Prof. Brian L. Evans Prof. Brian L. Evans
Graduate Students Kapil Gulati and Marcel Nassar
Undergraduate Students Navid Aghasadeghi and Arvind Sujeeth
Last Updated May 31, 2007
2
Outline

1. Problem Definition
2. Noise Modeling
3. Estimation of Noise Model Parameters
4. Filtering and Detection
5. Conclusion
6. Future Work

3

• I. Problem Definition
• Within computing platforms, wireless transceivers
  experience radio frequency interference (RFI)
  from computer subsystems, esp. from clocks
  (harmonics) and busses
• Objectives
• Develop offline methods to improve communication
  performance in the presence of computer platform
  RFI
• Develop adaptive online algorithms for these
  methods
• Approach
• Statistical modeling of RFI
• Filtering/detection based on estimation of model
  parameters

Well be using noise and interference
interchangeably
4
Common Spectral Occupancy
Standard Carrier (GHz) Wireless Networking Example Interfering Computer Subsystems
Bluetooth 2.4 Personal Area Network Gigabit Ethernet, PCI Express Bus, Memory, LCD
IEEE 802. 11 b/g/n 2.4 Wireless LAN (Wi-Fi) Gigabit Ethernet, PCI Express Bus, Memory, LCD
IEEE 802.16e 2.52.69 3.33.8 5.7255.85 Mobile Broadband(Wi-Max) PCI Express Bus, Memory, LCD
IEEE 802.11a 5.2 Wireless LAN (Wi-Fi) PCI Express Bus, Memory, LCD
5

• II. Noise Modeling
• RFI is a combination of independent radiation
  events, and predominantly has non-Gaussian
  statistics
• Statistical-Physical Models (Middleton Class A,
  B, C)
• Independent of physical conditions (universal)
• Sum of independent Gaussian and Poisson
  interference
• Models nonlinear phenomena governing
  electromagnetic interference
• Alpha-Stable Processes
• Models statistical properties of impulsive
  noise
• Approximation to Middleton Class B noise

6
Middleton Class A, B, C Models
Class A Narrowband interference (coherent
reception) Uniquely represented
by two parameters Class B Broadband
interference (incoherent reception)
Uniquely represented by six
parameters Class C Sum of class A and class B
(approx. as class B)
7
Middleton Class A Model
Envelope statistics
Probability densityfunction (pdf)
Envelope for Gaussian signal has Rayleigh
distribution
Parameters Description Range
Overlap Index. Product of average number of emissions per second and mean duration of typical emission A ? 10-2, 1
Gaussian Factor. Ratio of second-order moment of Gaussian component to that of non-Gaussian component G ? 10-6, 1
8
Middleton Class A Statistics
As A ? ?, Class A pdf converges to Gaussian
Example for A 0.15 and G 0.1
Power Spectral Density
9
Symmetric Alpha Stable Model Characteristic
Function
Parameters
Characteristic exponent indicative of the
thickness of the tail of impulsiveness of the
noise
Localization parameter (analogous to mean)
Dispersion parameter (analogous to variance)
No closed-form expression for pdf except for a
1 (Cauchy), a 2 (Gaussian), a 1/2 (Levy) and
a 0 (not very useful) Approximate pdf using
inverse transform of power series expansion of
characteristic function
10
Symmetric Alpha Stable Statistics
Example exponent a 1.5, mean d 0 and
variance g 10
10-4
Probability Density Function
Power Spectral Density
11
III. Estimation of Noise Model Parameters

• For the Middleton Class A Model
• Expectation maximization (EM) Zabin Poor,
  1991
• Based on envelope statistics (Middleton)
• Based on moments (Middleton)
• For the Symmetric Alpha Stable Model
• Based on extreme order statistics Tsihrintzis
  Nikias, 1996
• For the Middleton Class B Model
• No closed-form estimator exists
• Approximate methods based on envelope statistics
  or moments

12
Estimation of Middleton Class A Model Parameters

• Expectation maximization
• E Calculate log-likelihood function w/ current
  parameter values
• M Find parameter set that maximizes
  log-likelihood function
• EM estimator for Class A parameters Zabin
  Poor, 1991
• Expresses envelope statistics as sum of weighted
  pdfs
• Maximization step is iterative
• Given A, maximize K (with K A G). Root
  2nd-order polynomial.
• Given K, maximize A. Root 4th-order poly. (after
  approximation).

13
Results of EM Estimator for Class A Parameters
Iterations for Parameter A to Converge

• PDFs with 11 summation terms
• 50 simulation runs per setting

• Convergence criterion
• Example learning curve

14
Estimation of Symmetric Alpha Stable Parameters

• Based on extreme order statistics Tsihrintzis
  Nikias, 1996
• PDFs of max and min of sequence of independently
  and identically distributed (IID) data samples
  follow
• PDF of maximum
• PDF of minimum
• Extreme order statistics of Symmetric Alpha
  Stable pdf approach Frechets distribution as N
  goes to infinity
• Parameter estimators then based on simple order
  statistics
• Advantage Fast / computationally efficient
  (non-iterative)
• Disadvantage Requires large set of data samples
  (N 20,000)

15
Results for Symmetric Alpha Stable Parameter
Estimator
Data length (N) was 10,000 samples Results
averaged over 100 simulation runs Example on this
slide (which is continued on next slide) uses g
5 and d 10
Mean squared error in estimate of characteristic
exponent a
16
Results for Symmetric Alpha Stable Parameter
Estimator
g 5
d 10
Mean squared error in estimate of dispersion
(variance) g
Mean squared error in estimate of localization
(mean) d
17
Results on Measured RFI Data

• Data set of 80,000 samples collected using 20
  GSPS scope
• Measured data represents "broadband" noise
• Symmetric Alpha Stable Process expected to work
  well since PDF of measured data is symmetric
• Middleton Class A will model PDF beyond a certain
  point
• Middleton Class B envelope PDF has same form as
  Middleton Class A envelope PDF beyond an envelope
  value (inflection point)
• we expect the envelope PDF to match closely to
  Middleton Class A envelope PDF beyond the
  inflection point.

18
Results on Measured RFI Data

• Modeling PDF as Symmetric Alpha Stable process

Estimated Parameters Estimated Parameters
Localization (d) -0.0393
Dispersion (?) 0.5833
Characteristic Exponent (a) 1.5525
fX(x) - PDF
x noise amplitude
19
Results on Measured RFI Data

• Modeling envelope PDF using Middleton Class A
  model

Expected Envelope PDFs match beyond a certain
envelope Envelope computed via non-linear lowpass
filtering obtained via Teager operator, zn
(xn)2 xn-1xn1
fZ(z) Envelope PDF
Estimated Parameters Estimated Parameters
Overlap Index (AA) 0.5403
Gaussian Factor (G) 0.0096
z noise envelope
20
IV. Filtering and Detection

• Wiener filtering (linear)
• Requires knowledge of signal and noise statistics
• Provides benchmark for non-linear methods
• Other filtering
• Adaptive noise cancellation
• Nonlinear filtering
• Detection in Middleton Class A and B noise
• Coherent detection Spaulding Middleton, 1977
• Incoherent detection Spaulding Middleton, 1977

Hypothesis
Filtered signal
Corrupted signal
Filter
Decision Rule
We assume perfect estimation of noise model
parameters
21
Wiener Filtering Linear Filter

• Optimal in mean squared error sense when noise is
  Gaussian
• Model
• Design

Minimize Mean-Squared Error E e(n)2
22
Wiener Filtering Finite Impulse Response (FIR)
Case

• Wiener-Hopf equations for FIR Wiener filter of
  order p-1
• General solution in frequency domain

desired signal d(n)power spectrum F(e j w)
correlation of d and x rdx(n)autocorrelation
of x rx(n)Wiener FIR Filter w(n) corrupted
signal x(n)noise z(n)
23
Wiener Filtering 100-tap FIR Filter
Pulse shape10 samples per symbol10 symbols per
pulse
ChannelA 0.35G 0.5 10-3SNR -10
dBMemoryless
24
Wiener Filtering Communication Performance
Pulse shapeRaised cosine10 samples per
symbol10 symbols per pulse
ChannelA 0.35G 0.5 10-3Memoryless
Bit Error Rate (BER)
Optimal Detection RuleDescribed next
SNR (dB)
10
-10
0
-20
-30
-40
25
Coherent Detection

• Hard decision
• Bayesian formulation Spaulding and Middleton,
  1977

Decision Rule ?(X)
corrupted signal
H1 or H2
26
Coherent Detection

• Equally probable source
• Optimal detection rule

N number of samples in vector X
27
Coherent Detection in Class A Noise with G 10-4
A 0.1
Correlation Receiver Performance
SNR (dB)
SNR (dB)
28
Coherent Detection Small Signal Approximation

• Expand pdf pZ(z) by Taylor series about Sj 0
  (for j1,2)
• Optimal decision rule threshold detector for
  approximation
• Optimal detector for approximation is logarithmic
  nonlinearity followed by correlation receiver
  (see next slide)

We use 100 terms of the series expansion
ford/dxi ln pZ(xi) in simulations
29
Coherent Detection Small Signal Approximation
AntipodalA 0.35G 0.510-3

• Near-optimal for small amplitude signals
• Suboptimal for higher amplitude signals

Communication performance of approximation vs.
upper boundSpaulding Middleton, 1977, pt. I
30
V. Conclusion

• Radio frequency interference from computing
  platform
• Affects wireless data communication subsystems
• Models include Middleton noise models and alpha
  stable processes
• RFI cancellation
• Extends range of communication systems
• Reduces bit error rates
• Initial RFI interference cancellation methods
  explored
• Linear optimal filtering (Wiener)
• Optimal detection rules (26 dB gain for coherent
  detection)

31
VI. Future Work

• Offline methods
• Estimator for single symmetric alpha-stable
  process plus Gaussian
• Estimator for mixture of alpha stable processes
  plus Gaussian (requires blind source separation
  for 1-D time series)
• Estimator for Middleton Class B parameters
• Quantify communication performance vs. complexity
  tradeoffs for Middleton Class A detection
• Online methods
• Develop fixed-point (embedded) methods for
  parameter estimation
• Middleton noise models
• Mixtures of alpha-stable processes
• Develop embedded implementations of detection
  methods

32
References

• 1 D. Middleton, Non-Gaussian noise models in
  signal processing for telecommunications New
  methods and results for Class A and Class B noise
  models, IEEE Trans. Info. Theory, vol. 45, no.
  4, pp. 1129-1149, May 1999
• 2 S. M. Zabin and H. V. Poor, Efficient
  estimation of Class A noise parameters via the EM
  Expectation-Maximization algorithms, IEEE
  Trans. Info. Theory, vol. 37, no. 1, pp. 60-72,
  Jan. 1991
• 3 G. A. Tsihrintzis and C. L. Nikias, "Fast
  estimation of the parameters of alpha-stable
  impulsive interference", IEEE Trans. Signal
  Proc., vol. 44, Issue 6, pp. 1492-1503, Jun. 1996
• 4 A. Spaulding and D. Middleton, Optimum
  Reception in an Impulsive Interference
  Environment-Part I Coherent Detection, IEEE
  Trans. Comm., vol. 25, no. 9, Sep. 1977
• 5 A. Spaulding and D. Middleton, Optimum
  Reception in an Impulsive Interference
  Environment-Part II Incoherent Detection, IEEE
  Trans. Comm., vol. 25, no. 9, Sep. 1977
• 6 B. Widrow et al., Principles and
  Applications, Proc. of the IEEE, vol. 63, no.12,
  Sep. 1975.

33
BACKUP SLIDES
34
Potential Impact

• Improve communication performance for wireless
  data communication subsystems embedded in PCs and
  laptops
• Extend range from the wireless data communication
  subsystems to the wireless access point
• Achieve higher bit rates for the same bit error
  rate and range, and lower bit error rates for the
  same bit rate and range
• Extend the results to multiple RF sources on a
  single chip

35
Symmetric Alpha Stable Process PDF

• Closed-form expression does not exist in general
• Power series expansions can be derived in some
  cases
• Standard symmetric alpha stable model for
  localization parameter d 0

36

• Middleton Class B Model
• Envelope Statistics
• Envelope exceedance probability density (APD)
  which is 1 cumulative distribution function

37
Class B Envelope Statistics
38
Parameters for Middleton Class B Noise
Parameters Description Typical Range
Impulsive Index AB ? 10-2, 1
Ratio of Gaussian to non-Gaussian intensity GB ? 10-6, 1
Scaling Factor NI ? 10-1, 102
Spatial density parameter a ? 0, 4
Effective impulsive index dependent on a A a ? 10-2, 1
Inflection point (empirically determined) eB gt 0
39
Accuracy of Middleton Noise Models
Magnetic Field Strength, H (dB relative to
microamp per meter rms)
e0 (dB gt erms)
Percentage of Time Ordinate is Exceeded
P(e gt e0)
Soviet high power over-the-horizon radar
interference Middleton, 1999
Fluorescent lights in mine shop office
interference Middleton, 1999
40
Class B Exceedance Probability Density Plot
41
Class A Parameter Estimation Based on APD
(Exceedance Probability Density) Plot
42
Class A Parameter Estimation Based on Moments

• Moments (as derived from the characteristic
  equation)
• Parameter estimates

Odd-order momentsare zeroMiddleton, 1999
2
43

• Expectation Maximization Overview

44
Maximum Likelihood for Sum of Densities
45
Results of EM Estimator for Class A Parameters
46
Extreme Order Statistics
47
Estimator for Alpha-Stable
0 lt p lt a
48

• Incoherent Detection
• Bayes formulation Spaulding Middleton, 1997,
  pt. II

Small signal approximation
49

• Incoherent Detection
• Optimal Structure

Incoherent Correlation Detector
The optimal detector for the small signal
approximation is basically the correlation
receiver preceded by the logarithmic nonlinearity.
50
Coherent Detection Class A Noise

• Comparison of performance of correlation receiver
  (Gaussian optimal receiver) and nonlinear
  detector Spaulding Middleton, 1997, pt. II

51
Volterra Filters

• Non-linear (in the signal) polynomial filter
• By Stone-Weierstrass Theorem, Volterra signal
  expansion can model many non-linear systems, to
  an arbitrary degree of accuracy. (Similar to
  Taylor expansion with memory).
• Has symmetry structure that simplifies
  computational complexity Np (Np-1) C p
  instead of Np. Thus for N8 and p8 Np16777216
  and (Np-1) C p 6435.

52
Adaptive Noise Cancellation

• Computational platform contains multiple antennas
  that can provide additional information regarding
  the noise
• Adaptive noise canceling methods use an
  additional reference signal that is correlated
  with corrupting noise

s signalsn0 corrupted signaln0 noisen1
reference inputz system output