1. MIMO Receiver Design in the Presence of Radio Frequency Interference
Wireless Networking and Communications Group
MIMO Receiver Design in the Presence of Radio Frequency Interference
Kapil Gulati†, Aditya Chopra†, Robert W. Heath Jr. †, Brian L. Evans†, Keith R. Tinsley ‡ and Xintian E. Lin‡
†The University of Texas at Austin ‡ Intel Corporation
2 December 2008
IEEE Globecom 2008

2. We will use the terms noise and interference interchangeably
Problem Definition
Within computing platforms, wireless transceivers experience radio frequency interference (RFI) from clocks and busses.
Major sources of interference:
LCD clock harmonics
PCI Express busses
We will use the terms noise and interference interchangeably
Our approach
Statistical modeling of RFI
Detection based on estimated model parameters
We consider a 2 x 2 MIMO system in presence of RFI
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3. Radio Frequency Interference Modeling and Receiver Design
Prior Work
Radio Frequency Interference Modeling and Receiver Design
RFI Model
Spatial Corr.
Physical Model
Comments
Middleton Class A No
Yes
Uni-variate model
Assume independent or uncorrelated noise for multiple antennas
Receiver design:
[Gao & Tepedelenlioglu, 2007] Space-Time Coding [Li, Wang & Zhou, 2004] Performance degradation in receivers
Weighted Mixture of Gaussian Densities
Not derived based on physical principles
Receiver design: [Blum et al., 1997] Adaptive Receiver Design
Bivariate Middleton Class A [McDonald & Blum, 1997]
Extensions of Class A model to two-antenna systems
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4. Proposed Contributions
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
Performance Analysis
Demonstrated communication performance degradation of conventional receivers in presence of RFI
Receiver Design
Derived Maximum Likelihood (ML) receiver
Derived two sub-optimal ML receivers with reduced complexity
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5. Bivariate Middleton Class A Model
Joint Spatial Distribution
Parameter
Description
Typical Range
Overlap Index. Product of average number of emissions per second and mean duration of typical emission
Ratio of Gaussian to non-Gaussian component intensity at each of the two antennas
Correlation coefficient between antenna observations
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6. Results on Measured RFI Data
50,000 baseband noise samples represent broadband interference
Backup
Estimated Parameters
Bivariate Middleton Class A
Overlap Index (A)
0.313
2D- KL Divergence 1.004
Gaussian Factor (G1)
0.105
Gaussian Factor (G2)
0.101
Correlation (k)
-0.085
Bivariate Gaussian
Mean (µ)
2D- KL Divergence
Variance (s1) 1
Variance (s2)
Marginal PDFs of measured data compared with estimated model densities
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7. Sub-optimal ML Receivers
System Model
2 x 2 MIMO System
Maximum Likelihood (ML) Receiver
Log-Likelihood Function
Sub-optimal ML Receivers
approximate
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8. Sub-Optimal ML Receivers
Two-Piece Linear Approximation
Four-Piece Linear Approximation
Approximation of
chosen to minimize
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9. Results: Performance Degradation
Performance degradation in receivers designed assuming additive Gaussian noise in the presence of RFI
Simulation Parameters
4-QAM for Spatial Multiplexing (SM) transmission mode
16-QAM for Alamouti transmission strategy
Noise Parameters: A = 0.1, 1= 0.01, 2= 0.1, k = 0.4
Severe degradation in communication performance in high-SNR regimes
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10. Results: RFI Mitigation in 2 x 2 MIMO
Improvement in communication performance over conventional Gaussian ML receiver at symbol error rate of 10-2 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)
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11. 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)
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12. Conclusions RFI Modeling Used bivariate Middleton Class A model
Fits measured RFI data better than Gaussian model
Parameter Estimation
Derived parameter estimation algorithm based on the method of moments
Performance Analysis
Severe degradation in communication performance in the presence of RFI
Receiver Design
Optimal and two sub-optimal ML receivers proposed
Improvement over Gaussian ML (at SER of 10-2)
~15 dB [Highly Impulsive]
~ 8 dB [Moderately Impulsive]
Same as Gaussian ML in presence of Gaussian noise
Backup
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13. Thank You, Questions ?
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14. 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
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15. 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.
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16. Parameter Estimation
Return
Parameter Estimator for Bivariate Middleton Class A model
Moment Generating Function
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17. Parameter Estimation (cont…)
Return
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18. Parameter Estimators Wireless Networking and Communications Group
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19. Measured Fitting Notes on measured RFI data
Radio used to listen to the platform noise only (when no data communication ongoing)
Noise assumed to be broadband
Do not expect bivariate Middleton Class A to fit perfectly
Expect bivariate Class A to model much better than Gaussian
Kullback-Leibler (KL) divergence
Return
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20. Impact of RFI
Impact of LCD noise on throughput performance for a g embedded wireless receiver [Shi et al., 2006]
Backup
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21. 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
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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
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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
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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]
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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
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28. 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
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29. 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
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30. Fitting Measured RFI Data
Best fit for 25 data sets under different conditions
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31. 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
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32. 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
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33. 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
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34. 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
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35. 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
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36. 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
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37. 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
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