1. Texas Wireless Summit, Austin, Texas
Wireless Networking and Communications Group
Improving Wireless Data Transmission Speed and Reliability to Mobile Computing Platforms
Prof. Brian L. Evans
Lead Graduate Students
Aditya Chopra, Kapil Gulati and Marcel Nassar
In collaboration with Keith R. Tinsley and Chaitanya Sreerama at Intel Labs
28 November November 2018
Texas Wireless Summit, Austin, Texas

2. We will use noise and interference interchangeably
Problem Definition
Within computing platforms, wireless transceivers experience radio frequency interference (RFI) from clocks and busses
Objectives
Develop offline methods to improve communication performance in presence of computer platform RFI
Develop adaptive online algorithms for these methods
Approach
Statistical modeling of RFI
Filtering/detection based on estimated model parameters
We will use noise and interference interchangeably
Wireless Networking and Communications Group

3. Common Spectral Occupancy
Standard
Band (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
Wireless Networking and Communications Group

4. Impact of RFI
Impact of LCD noise on throughput performance for a g embedded wireless receiver [Shi et al., 2006]
Backup
Wireless Networking and Communications Group

5. Our Contributions
Mitigation of computational platform noise in single carrier, single antenna systems [Nassar et al., ICASSP 2008]
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: Myriad filtering, hole punching, and Bayesian detector
Wireless Networking and Communications Group

6. Power Spectral Densities
Middleton Class A
Symmetric Alpha Stable
Parameter values: A = 0.15 and G = 0.1
Parameter values: a = 1.5, d = 0 and g = 10

7. Fitting Measured RFI Data
Broadband RFI data
80,000 samples collected using 20GSPS scope
Backup
Estimated Parameters
Symmetric Alpha Stable Model
Localization (δ)
0.0043
Distance
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
Distance: Kullback-Leibler divergence
Wireless Networking and Communications Group

8. Fitting Measured RFI Data
Best fit for other 25 data sets under different conditions
Return

9. Filtering and Detection Methods
Middleton Class A noise
Symmetric Alpha Stable noise
Filtering
Wiener Filtering (Linear)
Detection
Correlation Receiver (Linear)
MAP (Maximum a posteriori probability) detector [Spaulding & Middleton, 1977]
Small Signal Approximation to MAP detector [Spaulding & Middleton, 1977]
Filtering
Myriad Filtering [Gonzalez & Arce, 2001]
Hole Punching
Detection
Correlation Receiver (Linear)
MAP approximation
Backup
Backup
Backup
Backup
Backup
Wireless Networking and Communications Group

10. Results: Class A Detection
Pulse shape Raised cosine 10 samples per symbol 10 symbols per pulse
Channel A = 0.35  = 0.5 × 10-3 Memoryless
Method
Comp. Complexity
Detection Perform.
Correl.
Low
Wiener
Medium
MAP Approx.
High
MAP
Wireless Networking and Communications Group

11. Results: Alpha Stable Detection
Backup
Method
Comp. Complexity
Detection Perform.
Hole Punching
Low
Medium
Selection Myriad
MAP Approx.
High
Optimal Myriad
Backup
Use dispersion parameter g in place of noise variance to generalize SNR
Wireless Networking and Communications Group

12. Results: Class A for 2  2 MIMO
Improvement in communication performance over conventional Gaussian ML receiver at symbol error rate of 10-2
Complexity Analysis A
Noise Characteristic
Improve-ment
0.01
Highly Impulsive
~15 dB
0.1
Moderately Impulsive
~8 dB 1
Nearly Gaussian
~0.5 dB
Communication Performance (A = 0.1, 1= 0.01, 2= 0.1, k = 0.4)
Wireless Networking and Communications Group

13. Conclusions Radio frequency interference from computing platform
Affects wireless data communication transceivers
Fit Middleton Class A and symmetric alpha stable models
RFI mitigation can reduce bit error rate by a factor of
100 for Middleton Class A model, single carrier system
10 for Middleton Class A model, 2 x 2 MIMO system
10 for Symmetric Alpha Stable model, single carrier system
Other applications of impulsive noise models
Co-channel interference
Adjacent channel interference
Wireless Networking and Communications Group

14. Contributions Publications Software Releases
M. Nassar, K. Gulati, A. K. Sujeeth, N. Aghasadeghi, B. L. Evans and K. R. Tinsley, “Mitigating Near-field Interference in Laptop Embedded Wireless Transceivers”, Proc. IEEE Int. Conf. on Acoustics, Speech, and Signal Proc., Mar. 30-Apr. 4, 2008, Las Vegas, NV USA.
K. Gulati, A. Chopra, R. W. Heath Jr., B. L. Evans, K. R. Tinsley, and X. E. Lin, ”MIMO Receiver Design in the Presence of Radio Frequency Interference”, Proc. IEEE Int. Global Communications Conf., Nov. 30-Dec. 4th, 2008, New Orleans, LA USA, accepted for publication.
A. Chopra, K. Gulati, B. L. Evans, K. R. Tinsley, and C. Sreerama, ``Performance Bounds of MIMO Receivers in the Presence of Radio Frequency Interference'', Proc. IEEE Int. Conf. on Acoustics, Speech, and Signal Proc., Apr , 2009, Taipei, Taiwan, submitted.
Software Releases
RFI Mitigation Toolbox
Version 1.1 Beta (Released November 21st, 2007) Version 1.0 (Released September 22nd, 2007)
Project Website
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15. Thank You, Questions ?
Wireless Networking and Communications Group

16. References RFI Modeling Parameter Estimation
[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] 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
[3] K. Furutsu and T. Ishida, “On the theory of amplitude distributions of impulsive random noise,” J. Appl. Phys., vol. 32, no. 7, pp. 1206–1221, 1961.
[4] J. Ilow and D . Hatzinakos, “Analytic alpha-stable noise modeling in a Poisson field of interferers or scatterers”,  IEEE transactions on signal processing, vol. 46, no. 6, pp , 1998.
Parameter Estimation
[5] 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
[6] 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. 1996
RFI Measurements and Impact
[7] J. Shi, A. Bettner, G. Chinn, K. Slattery and X. Dong, "A study of platform EMI from LCD panels - impact on wireless, root causes and mitigation methods,“ IEEE International Symposium on Electromagnetic Compatibility, vol.3, no., pp , Aug. 2006
Wireless Networking and Communications Group

17. References (cont…) Filtering and Detection
[8] 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
[9] 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
[10] 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
[11] S. Ambike, J. Ilow, and D. Hatzinakos, “Detection for binary transmission in a mixture of Gaussian noise and impulsive noise modelled as an alpha-stable process,” IEEE Signal Processing Letters, vol. 1, pp. 55–57, Mar
[12] J. G. Gonzalez and G. R. Arce, “Optimality of the myriad filter in practical impulsive-noise environments,” IEEE Trans. on Signal Proc, vol. 49, no. 2, pp. 438–441, Feb 2001.
[13] E. Kuruoglu, “Signal Processing In Alpha Stable Environments: A Least Lp Approach,” Ph.D. dissertation, University of Cambridge, 1998.
[14] J. Haring and A.J. Han Vick, “Iterative Decoding of Codes Over Complex Numbers for Impulsive Noise Channels”, IEEE Trans. On Info. Theory, vol 49, no. 5, May 2003
[15] 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.
Wireless Networking and Communications Group

18. Backup Slides Most backup slides are linked to the main slides
Miscellaneous topics not covered in main slides
Performance bounds for single carrier single antenna system in presence of RFI
Backup
Wireless Networking and Communications Group

19. Outline Problem definition Single carrier single antenna systems
Radio frequency interference modeling
Estimation of interference model parameters
Filtering/detection
Multi-input multi-output (MIMO) single carrier systems
Conclusions
Wireless Networking and Communications Group

20. Impact of RFI Calculated in terms of desensitization (“desense”)
Interference raises noise floor
Receiver sensitivity will degrade to maintain SNR
Desensitization levels can exceed 10 dB for a/b/g due to computational platform noise [J. Shi et al., 2006]
Case Sudy: b, Channel 2, desense of 11dB
More than 50% loss in range
Throughput loss up to ~3.5 Mbps for very low receive signal strengths (~ -80 dbm)
Return
Wireless Networking and Communications Group

21. Statistical Modeling of RFI
Radio Frequency Interference (RFI)
Sum of independent radiation events
Predominantly non-Gaussian impulsive statistics
Key Statistical-Physical Models
Middleton Class A, B, C models
Independent of physical conditions (Canonical)
Sum of independent Gaussian and Poisson interference
Model non-linear phenomenon governing RFI
Symmetric Alpha Stable models
Approximation of Middleton Class B model
Backup
Backup
Wireless Networking and Communications Group

22. Assumptions for RFI Modeling
Key Assumptions [Middleton, 1977][Furutsu & Ishida, 1961]
Infinitely many potential interfering sources with same effective radiation power
Power law propagation loss
Poisson field of interferers
Pr(number of interferers = M |area R) ~ Poisson
Poisson distributed emission times
Temporally independent (at each sample time)
Limitations
[Alpha Stable]: Does not include thermal noise
Temporal dependence may exist
Wireless Networking and Communications Group

23. Middleton Class A, B and C Models
Return
Class A Narrowband interference (“coherent” reception) Uniquely represented by 2 parameters
Class B Broadband interference (“incoherent” reception) Uniquely represented by six parameters
Class C Sum of Class A and Class B (approx. Class B)
Backup
Wireless Networking and Communications Group

24. Middleton Class A model
Probability Density Function
PDF 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]
Wireless Networking and Communications Group

25. Middleton Class B Model
Envelope Statistics
Envelope exceedence probability density (APD), which is 1 – cumulative distribution function (CDF)
Return
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26. Middleton Class B Model (cont…)
Middleton Class B Envelope Statistics
Return
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27. Middleton Class B Model (cont…)
Parameters for Middleton Class B Model
Return
Parameters
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
Wireless Networking and Communications Group

28. Accuracy of Middleton Noise Models
Return
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]
Wireless Networking and Communications Group

29. Symmetric Alpha Stable Model
Characteristic Function
Closed-form PDF expression only for α = 1 (Cauchy), α = 2 (Gaussian), α = 1/2 (Levy), α = 0 (not very useful)
Approximate PDF using inverse transform of power series expansion
Second-order moments do not exist for α < 2
Generally, moments of order > α do not exist
Backup
PDF for  = 1.5,  = 0 and  = 10
Backup
Parameter
Description
Range
Characteristic Exponent. Amount of impulsiveness
Localization. Analogous to mean
Dispersion. Analogous to variance
Wireless Networking and Communications Group

30. Symmetric Alpha Stable 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
Return
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31. Symmetric Alpha Stable Model
Heavy tailed distribution
Return
Density functions for symmetric alpha stable distributions for different values of characteristic exponent alpha: a) overall density and b) the tails of densities
Wireless Networking and Communications Group

32. Estimation of Noise Model Parameters
Middleton Class A model
Expectation Maximization (EM) [Zabin & Poor, 1991]
Find roots of second and fourth order polynomials at each iteration
Advantage: Small sample size is required (~1000 samples)
Disadvantage: Iterative algorithm, computationally intensive
Symmetric Alpha Stable Model
Based on Extreme Order Statistics [Tsihrintzis & Nikias, 1996]
Parameter estimators require computations similar to mean and standard deviation computations
Advantage: Fast / computationally efficient (non-iterative)
Disadvantage: Requires large set of data samples (~10000 samples)
Backup
Backup
Wireless Networking and Communications Group

33. Parameter Estimation: Middleton Class A
Expectation Maximization (EM)
E Step: Calculate log-likelihood function \w current parameter values
M Step: Find parameter set that maximizes log-likelihood function
EM Estimator for Class A parameters [Zabin & Poor, 1991]
Express envelope statistics as sum of weighted PDFs
Maximization step is iterative
Given A, maximize K (= AG). Root 2nd order polynomial.
Given K, maximize A. Root 4th order polynomial
Return
Backup
Results
Backup
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34. Expectation Maximization Overview
Return
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35. Results: EM Estimator for Class A
Return
Normalized Mean-Squared Error in A
Iterations for Parameter A to Converge
K = A G
PDFs with 11 summation terms
50 simulation runs per setting
1000 data samples
Convergence criterion:
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36. Results: EM Estimator for Class A
Return
For convergence for A  [10-2, 1], worst-case number of iterations for A = 1
Estimation accuracy vs. number of iterations tradeoff
Wireless Networking and Communications Group

37. Parameter Estimation: Symmetric Alpha Stable
Based on extreme order statistics [Tsihrintzis & Nikias, 1996]
PDFs of max and min of sequence of i.i.d. data samples
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)
Return
Results
Backup
Wireless Networking and Communications Group

38. Results: Symmetric Alpha Stable Parameter Estimator
Return
Data length (N) of 10,000 samples
Results averaged over 100 simulation runs
Estimate α and “mean” g directly from data
Estimate “variance” g from α and δ estimates
Mean squared error in estimate of characteristic exponent α
Wireless Networking and Communications Group

39. Results: Symmetric Alpha Stable Parameter Estimator (Cont…)
Return
Mean squared error in estimate of localization (“mean”) 
Mean squared error in estimate of dispersion (“variance”) 
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40. Extreme Order Statistics
Return
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41. Parameter Estimators for Alpha Stable
Return
0 < p < α
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42. Filtering and Detection
System Model
Assumptions:
Multiple samples of the received signal are available
N Path Diversity [Miller, 1972]
Oversampling by N [Middleton, 1977]
Multiple samples increase gains vs. Gaussian case
Impulses are isolated events over symbol period
Impulsive Noise
Pulse
Shaping
Pre-Filtering
Matched Filter
Detection Rule
N samples per symbol
Wireless Networking and Communications Group

43. Wiener Filtering
Optimal in mean squared error sense in presence of Gaussian noise
Return
Model
d(n)‏
z(n)‏ ^
w(n)‏
x(n)‏ ^
d(n): desired signal d(n): filtered signal e(n): error w(n): Wiener filter x(n): corrupted signal z(n): noise
Design
w(n)‏
x(n)‏
d(n)‏ ^
e(n)‏
Minimize Mean-Squared Error E { |e(n)|2 }
Wireless Networking and Communications Group

44. Wiener Filter Design Infinite Impulse Response (IIR)
Finite Impulse Response (FIR)
Wiener-Hopf equations for order p-1
Return
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)‏
Wireless Networking and Communications Group

45. Results: Wiener Filtering
100-tap FIR Filter
Return
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
Wireless Networking and Communications Group

46. Filtering for Alpha Stable Noise
Myriad Filtering
Sliding window algorithm outputs myriad of a sample window
Myriad of order k for samples x1,x2,…,xN [Gonzalez & Arce, 2001]
As k decreases, less impulsive noise passes through the myriad filter
As k→0, filter tends to mode filter (output value with highest frequency)
Empirical Choice of k [Gonzalez & Arce, 2001]
Developed for images corrupted by symmetric alpha stable impulsive noise
Wireless Networking and Communications Group

47. Filtering for Alpha Stable Noise (Cont..)
Myriad Filter 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 extreme points
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)
Wireless Networking and Communications Group

48. MAP Detection for Class A
Hard decision
Bayesian formulation [Spaulding & Middleton, 1977]
Equally probable source
Return
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49. MAP Detection for Class A: Small Signal Approx.
Expand noise PDF pZ(z) by Taylor series about Sj = 0 (j=1,2)‏
Approximate MAP detection rule
Logarithmic non-linearity + correlation receiver
Near-optimal for small amplitude signals
Return
We use 100 terms of the series expansion for d/dxi ln pZ(xi) in simulations
Correlation Receiver
Wireless Networking and Communications Group

50. Incoherent Detection
Baye’s formulation [Spaulding & Middleton, 1997, pt. II]
Small Signal Approximation
Return
Correlation receiver
Wireless Networking and Communications Group

51. Filtering for Alpha Stable Noise (Cont..)
Hole Punching (Blanking) Filters
Set sample to 0 when sample exceeds threshold [Ambike, 1994]
Large values are impulses and true values can be recovered
Replacing large values with zero will not bias (correlation) receiver for two-level constellation
If additive noise were purely Gaussian, then the larger the threshold, the lower the detrimental effect on bit error rate
Communication performance degrades as constellation size (i.e., number of bits per symbol) increases beyond two
Return
Wireless Networking and Communications Group

52. MAP Detection for Alpha Stable: PDF Approx.
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
Return
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53. Results: Alpha Stable Detection
Return
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54. Complexity Analysis for Alpha Stable Detection
Return
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)
Wireless Networking and Communications Group

55. Performance Bounds (Single Antenna)
Channel Capacity
Return
System Model
Case I
Shannon Capacity in presence of additive white Gaussian noise
Case II
(Upper Bound) Capacity in the presence of Class A noise
Assumes that there exists an input distribution which makes output distribution Gaussian (good approximation in high SNR regimes)
Case III
(Practical Case) Capacity in presence of Class A noise
Assumes input has Gaussian distribution (e.g. bit interleaved coded modulation (BICM) or OFDM modulation [Haring, 2003])
Wireless Networking and Communications Group

56. Performance Bounds (Single Antenna)
Channel Capacity in presence of RFI
Return
System Model
Capacity
Parameters A = 0.1, Γ = 10-3
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57. Performance Bounds (Single Antenna)
Probability of error for uncoded transmissions
Return
[Haring & Vinck, 2002]
BPSK uncoded transmission
One sample per symbol
A = 0.1, Γ = 10-3
Wireless Networking and Communications Group

58. Performance Bounds (Single Antenna)
Chernoff factors for coded transmissions
Return
PEP: Pairwise error probability
N: Size of the codeword
Chernoff factor:
Equally likely transmission for symbols
Wireless Networking and Communications Group

59. Extensions to MIMO systems
RFI Modeling
Middleton Class A Model for two-antenna systems [McDonald & Blum, 1997]
Closed form PDFs for M x N MIMO system not published
Prior Work
Much prior work assumes independent noise at antennas
Performance analysis of standard MIMO receivers in impulsive noise [Li, Wang & Zhou, 2004]
Space-time block coding over MIMO channels with impulsive noise [Gao & Tepedelenlioglu,2007]
Wireless Networking and Communications Group

60. Our Contributions
2 x 2 MIMO receiver design in the presence of RFI [Gulati et al., Globecom 2008]
RFI Modeling
Evaluated fit of measured RFI data to the bivariate Middleton Class A model [McDonald & Blum, 1997]
Includes noise correlation between two antennas
Parameter Estimation
Derived parameter estimation algorithm based on the method of moments (sixth order moments)
Performance Analysis
Demonstrated communication performance degradation of conventional receivers in presence of RFI
Bounds on communication performance [Chopra et al., submitted to ICASSP 2009]
Receiver Design
Derived Maximum Likelihood (ML) receiver
Derived two sub-optimal ML receivers with reduced complexity
Backup
Wireless Networking and Communications Group

61. Performance Bounds (2x2 MIMO)
Channel Capacity [Chopra et al., submitted to ICASSP 2009]
Return
System Model
Case I
Shannon Capacity in presence of additive white Gaussian noise
Case II
(Upper Bound) Capacity in presence of bivariate Middleton Class A noise. Assumes that there exists an input distribution which makes output distribution Gaussian for all SNRs.
Case III
(Practical Case) Capacity in presence of bivariate Middleton Class A noise
Assumes input has Gaussian distribution
Wireless Networking and Communications Group

62. Performance Bounds (2x2 MIMO)
Channel Capacity in presence of RFI for 2x2 MIMO [Chopra et al., submitted to ICASSP 2009]
Return
System Model
Capacity
Parameters: A = 0.1, G1 = 0.01, G2 = 0.1, k = 0.4
Wireless Networking and Communications Group

63. Performance Bounds (2x2 MIMO)
Probability of symbol error for uncoded transmissions [Chopra et al., submitted to ICASSP 2009]
Return
Pe: Probability of symbol error
S: Transmitted code vector
D(S): Decision regions for MAP detector
Equally likely transmission for symbols
Parameters: A = 0.1, G1 = 0.01, G2 = 0.1, k = 0.4
Wireless Networking and Communications Group

64. Performance Bounds (2x2 MIMO)
Chernoff factors for coded transmissions [Chopra et al., submitted to ICASSP 2009]
Return
PEP: Pairwise error probability N: Size of the codeword Chernoff factor: Equally likely transmission for symbols
Parameters: G1 = 0.01, G2 = 0.1, k = 0.4
Wireless Networking and Communications Group

65. Results: RFI Mitigation in 2 x 2 MIMO
Complexity Analysis for decoding M-QAM modulated signal
Receiver
Quadratic Forms
Exponential
Comparisons
Gaussian ML M2
Optimal ML
2M2
Sub-optimal ML (Four-Piece)
3M2
Sub-optimal ML (Two-Piece)
Complexity Analysis
Communication Performance (A = 0.1, 1= 0.01, 2= 0.1, k = 0.4)
Wireless Networking and Communications Group

66. Extensions to Multicarrier Systems
Impulse noise with impulse event followed by “flat” region
Coding may improve communication performance
In multicarrier modulation, impulsive event in time domain spreads out over all subcarriers, reducing the effect of impulse
Complex number (CN) codes [Lang, 1963]
Unitary transformations
Gaussian noise is unaffected (no change in 2-norm Distance)
Orthogonal frequency division multiplexing (OFDM) is a special case: Inverse Fourier Transform
[Haring 2003] As number of subcarriers increase, impulsive noise case approaches the Gaussian noise case.
Return
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67. Future Work Modeling RFI to include
Computational platform noise
Co-channel interference
Adjacent channel interference
Multi-input multi-output (MIMO) single carrier systems
RFI modeling and receiver design
Multicarrier communication systems
Coding schemes resilient to RFI
Circuit design guidelines to reduce computational platform generated RFI
Backup
Wireless Networking and Communications Group