1. Mitigating Near-field Interference in Laptop Embedded Wireless Transceivers
Marcel Nassar(1), Kapil Gulati(1) , Arvind K. Sujeeth(1),
Navid Aghasadeghi(1), Brian L. Evans(1), Keith R. Tinsley(2)‏
(1) The University of Texas at Austin, Austin, Texas, USA
(2) System Technology Lab, Intel, Hillsborough, Oregon, USA
2008 IEEE International Conference on Acoustics, Speech, and Signal Processing
3rd April, 2008 1

2. We’ll be using noise and interference interchangeably
Problem Definition
Within computing platforms, wireless transceivers experience radio frequency interference (RFI) from clocks/busses
PCI Express busses
LCD clock harmonics
Approach
Statistical modelling of RFI
Filtering/detection based on estimation of model parameters
Past Research
Potential reduction in bit error rates by factor of 10 or more [Spaulding & Middleton, 1977]
Backup
We’ll be using noise and interference interchangeably 2 2

3. Computer Platform Noise Modelling
RFI is combination of independent radiation events
Has predominantly non-Gaussian statistics
Statistical-Physical Models (Middleton Class A, B, C)‏
Independent of physical conditions (universal)‏
Sum of independent Gaussian and Poisson interference
Models electromagnetic interference
Alpha-Stable Processes
Models statistical properties of “impulsive” noise
Approximation for Middleton Class B (broadband) noise
Backup 3 3

4. Proposed Contributions
Computer Platform Noise Modelling
Evaluate fit of measured RFI data to noise models
Narrowband Interference: Middleton Class A model
Broadband Interference: Symmetric Alpha Stable
Parameter Estimation
Evaluate estimation accuracy vs complexity tradeoffs
Filtering / Detection
Evaluate communication performance vs. complexity tradeoffs
Middleton Class A: Correlation receiver, Wiener filtering and Bayesian detector
Symmetric Alpha Stable: Correlation receiver Wiener filtering and Myriad filtering 4

5. Middleton Class A Model
Backup
Probability Density Function for A = 0.15, = 0.8
Power Spectral Density for A = 0.15, = 0.8
Parameter
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
Γ  [10-6, 1] 5 5

6. Symmetric Alpha Stable Model
Backup
Probability Density Function for  = 1.5,  = 0 and  = 10
Power Spectral Density for = 1.5,  = 0 and  = 10
Parameter
Description
Range
Characteristic Exponent. Amount of impulsiveness
Localization. Analogous to mean
Dispersion. Analogous to variance 6 6

7. Estimation of Noise Model Parameters
For Middleton Class A Model
Expectation maximization (EM) [Zabin & Poor, 1991]
Finds roots of second and fourth order polynomials at each iteration
Advantage Small sample size required (~1000 samples)‏
Disadvantage Iterative algorithm, computationally intensive
For Symmetric Alpha Stable Model
Based on extreme order statistics [Tsihrintzis & Nikias, 1996]
Parameter estimators require computations similar to mean and standard deviation.
Advantage Fast / computationally efficient (non-iterative)‏
Disadvantage Requires large set of data samples (~ 10,000 samples)‏
Backup
Backup 7 7

8. Symmetric Alpha Stable Model Middleton Class A Model
Results of Measured RFI Data for Broadband Noise
Backup
Data set of 80,000 samples collected using 20 GSPS scope
Estimated Parameters
Symmetric Alpha Stable Model
Localization (δ)
0.0043
Characteristic exp. (α)
1.2105
Dispersion (γ)
0.2413
Middleton Class A Model
Overlap Index (A)
0.1036
Gaussian Factor (Γ)
0.7763
Gaussian Model
Mean (µ)
Variance (σ2) 1 8 8

9. Alternate Adaptive Model
Filtering and Detection – System Model
Alternate Adaptive Model
Signal Model
Multiple samples/copies of the received signal are available:
N path diversity [Miller, 1972]
Oversampling by N [Middleton, 1977]
Using multiple samples increases gains vs. Gaussian case because impulses are isolated events over symbol period
Impulsive Noise
Backup
s[n]
gtx[n]
v[n]
grx[n]
Λ(.)‏
Pulse Shape
Pre-Filtering
Matched Filter
Decision Rule
N samples per symbol 9

10. We assume perfect estimation of noise model parameters
Filtering and Detection
We assume perfect estimation of noise model parameters
Class A Noise
Correlation Receiver (linear)‏
Wiener Filtering (linear)‏
Coherent Detection using MAP (Maximum A posteriori Probability) detector [Spaulding & Middleton, 1977]
Small Signal Approximation to MAP Detector [Spaulding & Middleton, 1977]
Alpha Stable Noise
Myriad Filtering [Gonzalez & Arce, 2001]
MAP Approximation
Hole Puncher
Backup
Backup
Backup
Backup
Backup
Backup 10 10

11. Class A Detection - Results
Pulse shape Raised cosine 10 samples per symbol 10 symbols per pulse
Channel A =  = 0.5 × Memoryless
Method
Comp.
Detection Perform.
Correl.
Low
Wiener
Medium
Approx.
High
MAP 11

12. Alpha Stable Results Method Comp. Detection Perform. Hole Punching Low
Medium
Selection Myriad
MAP Approx.
High
Optimal Myriad 12

13. Conclusion Class A Noise MAP High Performance High Complexity
MAP approximation
Medium Complexity
Correlation Receiver
Low Performance
Low Complexity
Wiener Filtering
Alpha Stable Noise
MAP Approximation
Optimal Myriad
Medium Performance
Selection Myriad
Hole Puncher T 13

14. Thank you,
Questions?

15. 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 , 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 , 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 , Jun
[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
[6] B. Widrow et al., “Principles and Applications”, Proc. of the IEEE, vol. 63, no.12, Sep
[7] J.G. Gonzalez and G.R. Arce, “Optimality of the Myriad Filter in Practical Impulsive- Noise Environments”, IEEE Trans. on Signal Processing, vol 49, no. 2, Feb 2001 15 15

16. References (cont…)‏
[8] S. Ambike, J. Ilow, and D. Hatzinakos, “Detection for binary transmission in a mixture of gaussian noise and impulsive noise modeled as an alpha-stable process,” IEEE Signal Processing Letters, vol. 1, pp. 55–57, Mar
[9] J. G. Gonzalez and G. R. Arce, “Optimality of the myriad filter in practical impulsive- noise enviroments,” IEEE Trans. on Signal Proc, vol. 49, no. 2, pp. 438–441, Feb 2001.
[10] E. Kuruoglu, “Signal Processing In Alpha Stable Environments: A Least Lp Approach,” Ph.D. dissertation, University of Cambridge, 1998.
[11] J. Haring and A.J. Han Vick, “Iterative Decoding of Codes Over Complex Numbers for Impuslive Noise Channels”, IEEE Trans. On Info. Theory, vol 49, no. 5, May 2003
[12] G. Beenker, T. Claasen, and P. van Gerwen, “Design of smearing filters for data transmission systems,” IEEE Trans. on Comm., vol. 33, Sept
[13] G. R. Lang, “Rotational transformation of signals,” IEEE Trans. Inform. Theory, vol. IT–9, pp. 191–198, July 1963.
[14] Ping Gao and C. Tepedelenlioglu. “Space-time coding over mimo channels with impulsive noise”, IEEE Trans. on Wireless Comm., 6(1):220–229, January 2007.
[15] K.F. McDonald and R.S. Blum. “A physically-based impulsive noise model for array observations”, Proc. IEEE Asilomar Conference on Signals, Systems& Computers, vol 1, 2-5 Nov 16

17. BACKUP SLIDES 17

18. Interfering Clocks and Busses
Common Spectral Occupancy
Standard
Carrier (GHz)‏
Wireless Networking
Interfering Clocks and Busses
Bluetooth
2.4
Personal Area Network
Gigabit Ethernet, PCI Express Bus, LCD clock harmonics
IEEE b/g/n
Wireless LAN (Wi-Fi)‏
IEEE e
2.5– –3.8
5.725–5.85
Mobile Broadband (Wi-Max)‏
PCI Express Bus, LCD clock harmonics
IEEE a
5.2 18 18

19. Extend results to multiple RF sources on single chip
Potential Impact
Improve communication performance for wireless data communication subsystems embedded in PCs and laptops
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 range from wireless data communication subsystems to wireless access point
Extend results to multiple RF sources on single chip 19 19

20. Accuracy of Middleton Noise Models
Magnetic Field Strength, H (dB relative to
microamp per meter rms)‏
ε0 (dB > εrms)‏
Percentage of Time Ordinate is Exceeded
P(ε > ε0)‏
Soviet high power over-the-horizon radar interference [Middleton, 1999]
Fluorescent lights in mine shop office interference [Middleton, 1999] 20 20

21. 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)‏ 21 21

22. Probability Density Function for A = 0.15, G = 0.1
Middleton Class A Model
Probability density function (pdf)
Probability Density Function for A = 0.15, G = 0.1
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
Γ  [10-6, 1]

23. Symmetric Alpha Stable Model Characteristic function:
Parameters
Characteristic exponent indicative of thickness of tail of impulsiveness
Localization (analogous to mean)
Dispersion (analogous to variance)
No closed-form expression for pdf except for α = 1 (Cauchy), α = 2 (Gaussian), α = 1/2 (Levy) and α = 0 (not very useful)
Could approximate pdf using inverse transform of power series expansion of characteristic function

24. Symmetric Alpha Stable Model Middleton Class A Model
Results of Measured RFI Data for Broadband Noise
Data set of 80,000 samples collected using 20 GSPS scope
Estimated Parameters
Symmetric Alpha Stable Model
Localization (δ)
0.0043
KL Divergence
0.0514
Characteristic exp. (α)
1.2105
Dispersion (γ)
0.2413
Middleton Class A Model
Overlap Index (A)
0.1036
0.0825
Gaussian Factor (Γ)
0.7763
Gaussian Model
Mean (µ)
0.2217
Variance (σ2) 1 24 24

25. Coherent Detection – Small Signal Approximation
Expand noise pdf pZ(z) by Taylor series about Sj = 0 (j=1,2)‏
Optimal decision rule & threshold detector for approximation
Optimal detector for approximation is logarithmic nonlinearity followed by correlation receiver
We use 100 terms of the series expansion for d/dxi ln pZ(xi) in simulations
Backup 25 25

26. Hole Punching (Blanking) Filter
Sets sample to 0 when sample exceeds threshold [Ambike, 1994]
Intuition:
Large values are impulses and true value cannot be recovered
Replace large values with zero will not bias (correlation) receiver
If additive noise were purely Gaussian, then the larger the threshold, the lower the detrimental effect on bit error rate 26

27. Filtering and Detection – Alpha Stable Model
MAP detection: remove nonlinear filter
Decision rule is given by (p(.) is the SαS distribution)‏
Approximations for SαS distribution:
Method
Shortcomings
Reference
Series Expansion
Poor approximation when series length shortened
[Samorodnitsky, 1988]
Polynomial Approx.
Poor approximation for small x
[Tsihrintzis, 1993]
Inverse FFT
Ripples in tails when α < 1
Simulation Results 27

28. MAP Detector – PDF Approximation
SαS random variable Z with parameters  ,  can be written Z = X Y½ [Kuruoglu, 1998]
X is zero-mean Gaussian with variance 2 
Y is positive stable random variable with parameters depending on 
Pdf of Z can be written as a mixture model of N Gaussians [Kuruoglu, 1998]
Mean can be added back in
Obtain fY(.) by taking inverse FFT of characteristic function & normalizing
Number of mixtures (N) and values of sampling points (vi) are tunable parameters 28

29. Bit Error Rate (BER) Performance in Alpha Stable Noise29

30. 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  = 0 30

31. 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 Γ). Root 2nd-order polynomial.
Given K, maximize A. Root 4th-order poly. (after approximation).
Backup
Backup 31 31

32. 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 Frechet’s 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 ~ 10,000)‏
Backup
Backup
Backup 32 32

33. Class A Parameter Estimation Based on APD (Exceedance Probability Density) Plot33 33

34. Odd-order moments are zero [Middleton, 1999]
Class A Parameter Estimation Based on Moments
Moments (as derived from the characteristic equation)‏
Parameter estimates
e2 =
e4 =
e6 =
Odd-order moments are zero [Middleton, 1999] 2 34 34

35. Middleton Class B Model Envelope Statistics
Envelope exceedance probability density (APD) which is 1 – cumulative distribution function 35 35

36. Class B Envelope Statistics36

37. Parameters for Middleton Class B Noise
Description
Typical Range
Impulsive Index
AB  [10-2, 1]
Ratio of Gaussian to non-Gaussian intensity
ΓB  [10-6, 1]
Scaling Factor
NI  [10-1, 102]
Spatial density parameter
α  [0, 4]
Effective impulsive index dependent on α
A α  [10-2, 1]
Inflection point (empirically determined)‏
εB > 0 37 37

38. Class B Exceedance Probability Density Plot38 38

39. Expectation Maximization Overview39 39

40. Maximum Likelihood for Sum of Densities40 40

41. EM Estimator for Class A Parameters Using 1000 Samples
Normalized Mean-Squared Error in A
×10-3
PDFs with 11 summation terms
50 simulation runs per setting
Convergence criterion:
Example learning curve
Iterations for Parameter A to Converge 41

42. Results of EM Estimator for Class A Parameters42

43. Extreme Order Statistics43 43

44. Estimator for Alpha-Stable44 44

45. Results for Symmetric Alpha Stable Parameter Estimator
Data length (N) was 10,000 samples
Results averaged over 100 simulation runs
Estimate α and “mean” δ directly from data
Estimate “variance” γ from α and δ estimates
Continued next slide
Mean squared error in estimate of characteristic exponent α 45

46. Results for Symmetric Alpha Stable Parameter Estimator
Mean squared error in estimate of localization (“mean”) 
 = 10
Mean squared error in estimate of dispersion (“variance”) 
 = 5 46

47. Wiener Filtering – Linear Filter
Optimal in mean squared error sense when noise is Gaussian
Model
Design
d(n): desired signal d(n): filtered signal e(n): error w(n): Wiener filter x(n): corrupted signal z(n): noise
d(n): ^
d(n)‏
z(n)‏ ^
w(n)‏
x(n)‏
w(n)‏
x(n)‏
d(n)‏ ^
e(n)‏
Minimize Mean-Squared Error E { |e(n)|2 } 47 47

48. 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: (e j ) correlation of d and x: rdx(n) autocorrelation of x: rx(n) Wiener FIR Filter: w(n) corrupted signal: x(n) noise: z(n)‏ 48 48

49. Raised Cosine Pulse Shape
Wiener Filtering – 100-tap FIR Filter
Pulse shape 10 samples per symbol 10 symbols per pulse
Raised Cosine Pulse Shape
Transmitted waveform corrupted by Class A interference
Received waveform filtered by Wiener filter n
Channel A =  = 0.5 × SNR = -10 dB Memoryless 49 49

50. Bayes formulation [Spaulding & Middleton, 1997, pt. II]
Incoherent Detection
Bayes formulation [Spaulding & Middleton, 1997, pt. II]
Small signal approximation 50 50

51. 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. 51 51

52. Coherent Detection – Class A Noise
Comparison of performance of correlation receiver (Gaussian optimal receiver) and nonlinear detector [Spaulding & Middleton, 1997, pt. II] 52 52

53. Coherent Detection – Small Signal Approximation
Near-optimal for small amplitude signals
Suboptimal for higher amplitude signals
Correlation Receiver
Antipodal A =  = 0.5×10-3
Communication performance of approximation vs. upper bound [Spaulding & Middleton, 1977, pt. I] 53 53

54. Non-linear (in the signal) polynomial filter
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 = (N+p-1) C p instead of Np. Thus for N=8 and p=8; Np= and (N+p-1) C p = 6435. 54 54

55. 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
[Widrow et al., 1975]
s : signal s+n0 :corrupted signal n0 : noise n1 : reference input z : system output 55 55

56. Haring’s Receiver Simulation Results56

57. Coherent Detection in Class A Noise with Γ = 10-4
Correlation Receiver Performance
SNR (dB)‏
SNR (dB)‏ 57 57

58. Myriad Filtering
Myriad Filters exhibit high statistical efficiency in bell-shaped impulsive distributions like the SαS distributions.
Have been used as both edge enhancers and smoothers in image processing applications.
In the communication domain, they have been used to estimate a sent number over a channel using a known pulse corrupted by additive noise. (Gonzalez 1996)‏
In this work, we used a sliding window version of the myriad filter to mitigate the impulsiveness of the additive noise. (Nassar et. al 2007)‏ 58

59. Bayesian formulation [Spaulding and Middleton, 1977]
MAP Detection
corrupted signal
Decision Rule Λ(X)‏
Hard decision
Bayesian formulation [Spaulding and Middleton, 1977]
H1 or H2
Equally probable source 59 59

60. Results 60

61. MAP Detector – PDF Approximation
SαS random variable Z with parameters a , d, g can be written Z = X Y½ [Kuruoglu, 1998]
X is zero-mean Gaussian with variance 2 g
Y is positive stable random variable with parameters depending on a
Pdf of Z can be written as a mixture model of N Gaussians [Kuruoglu, 1998]
Mean d can be added back in
Obtain fY(.) by taking inverse FFT of characteristic function & normalizing
Number of mixtures (N) and values of sampling points (vi) are tunable parameters

62. Sliding window algorithm Outputs myriad of sample window
Myriad Filtering
Sliding window algorithm
Outputs myriad of sample window
Myriad of order k for samples x1, x2, … , xN [Gonzalez & Arce, 2001]
As k decreases, less impulsive noise gets through myriad filter
As k→0, filter tends to mode filter (output value with highest freq.)
Empirical choice of k: [Gonzalez & Arce, 2001]

63. Myriad Filtering – Implementation
Given a window of samples x1,…,xN, find β  [xmin, xmax]
Optimal myriad algorithm
Differentiate objective function polynomial p(β) with respect to β
Find roots and retain real roots
Evaluate p(β) at real roots and extremum
Output β that gives smallest value of p(β)
Selection myriad (reduced complexity)
Use x1,…,xN as the possible values of β
Pick value that minimizes objective function p(β)
Backup

64. Hole Punching (Blanking) Filter
Sets sample to 0 when sample exceeds threshold [Ambike, 1994]
Intuition:
Large values are impulses and true value cannot be recovered
Replace large values with zero will not bias (correlation) receiver
If additive noise were purely Gaussian, then the larger the threshold, the lower the detrimental effect on bit error rate

65. N is oversampling factor S is constellation size W is window size
Complexity Analysis
Method
Complexity per symbol
Analysis
Hole Puncher + Correlation Receiver
O(N+S)
A decision needs to be made about each sample.
Optimal Myriad + Correlation Receiver
O(NW3+S)
Due to polynomial rooting which is equivalent to Eigen-value decomposition.
Selection Myriad + Correlation Receiver
O(NW2+S)
Evaluation of the myriad function and comparing it.
MAP Approximation
O(MNS)
Evaluating approximate pdf (M is number of Gaussians in mixture)
N is oversampling factor S is constellation size W is window size