MIMO Receiver Design in the Presence ofRadio Frequency Interference
IEEE Globecom 2008
Wireless Networking and Communications Group
2 December 2008
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
Within computing platforms, wireless transceivers experience radio frequency interference (RFI) from clocks and busses.Major sources of interference:• LCD clock harmonics• PCI Express busses
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Problem Definition2
Our approach Statistical modeling of RFI Detection based on estimated model parameters
We consider a 2 x 2 MIMO system in presence of RFI
We will use the terms noise and interference interchangeably
We will use the terms noise and interference interchangeably
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Prior Work3
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Proposed Contributions4
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Bivariate Middleton Class A Model5
Joint Spatial Distribution
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Results on Measured RFI Data6
50,000 baseband noise samples represent broadband interference
-4 -3 -2 -1 0 1 2 3 40
0.2
0.4
0.6
0.8
1
1.2
1.4
Noise amplitude
Pro
ba
bili
ty D
en
sity
Fu
nct
ion
Measured PDFEstimated MiddletonClass A PDFEqui-powerGaussian PDF
Marginal PDFs of measured data compared with estimated model densities
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2 x 2 MIMO System
Maximum Likelihood (ML) Receiver
Log-Likelihood Function
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System Model7
Sub-optimal ML Receiversapproximate
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Sub-Optimal ML Receivers8
Two-Piece Linear Approximation
Four-Piece Linear Approximation
-5 -4 -3 -2 -1 0 1 2 3 4 50
0.5
1
1.5
2
2.5
3
3.5
4
4.5
5
z
Ap
pro
xma
tion
of
(z)
(z)
1(z)
2(z)
chosen to minimizeApproximation of
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Results: Performance Degradation9
Performance degradation in receivers designed assuming additive Gaussian noise in the presence of RFI
-10 -5 0 5 10 15 2010
-5
10-4
10-3
10-2
10-1
100
SNR [in dB]
Vec
tor
Sym
bol E
rror
Rat
e
SM with ML (Gaussian noise)SM with ZF (Gaussian noise)Alamouti coding (Gaussian noise)SM with ML (Middleton noise)SM with ZF (Middleton noise)Alamouti coding (Middleton noise)
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, = 0.4
Severe degradation in communication performance in
high-SNR regimes
-10 -5 0 5 10 15 20
10-3
10-2
10-1
SNR [in dB]
Vec
tor
Sym
bol E
rror
Rat
e
Optimal ML Receiver (for Gaussian noise)Optimal ML Receiver (for Middleton Class A)Sub-Optimal ML Receiver (Four-Piece)Sub-Optimal ML Receiver (Two-Piece)
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Results: RFI Mitigation in 2 x 2 MIMO 10
Improvement in communication performance over conventional Gaussian ML receiver at symbol
error rate of 10-2
Communication Performance (A = 0.1, 1= 0.01, 2= 0.1, = 0.4)
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Results: RFI Mitigation in 2 x 2 MIMO 11
Complexity Analysis
Complexity Analysis for decoding M-QAM modulated signal
Communication Performance (A = 0.1, 1= 0.01, 2= 0.1, = 0.4)
-10 -5 0 5 10 15 20
10-3
10-2
10-1
SNR [in dB]
Vec
tor
Sym
bol E
rror
Rat
e
Optimal ML Receiver (for Gaussian noise)Optimal ML Receiver (for Middleton Class A)Sub-Optimal ML Receiver (Four-Piece)Sub-Optimal ML Receiver (Two-Piece)
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Conclusions12
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13
Thank You,Questions ?
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References14
RFI Modeling[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] 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. 1997.
[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. 1601-1611, 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. 60-72, Jan. 1991
[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. 1492-1503, 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. 626-631, 14-18 Aug. 2006
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References (cont…)15
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. 1994.
[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.
Parameter Estimation
Parameter Estimator for Bivariate Middleton Class A model
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16
Moment Generating Function
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Parameter Estimation (cont…)
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17
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Parameter Estimators
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18
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Measured Fitting
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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
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Impact of RFI20
Impact of LCD noise on throughput performance for a 802.11g embedded wireless receiver [Shi et al., 2006]
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Impact of RFI21
Calculated in terms of desensitization (“desense”) Interference raises noise floor Receiver sensitivity will degrade to maintain SNR
Desensitization levels can exceed 10 dB for 802.11a/b/g due to computational platform noise [J. Shi et al., 2006]Case Sudy: 802.11b, 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)
floor noise RX
ceInterferenfloor noise RXlog10 10desense
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Assumptions for RFI Modeling22
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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Middleton Class A, B and C Models23
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)
[Middleton, 1999]
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Middleton Class A model24
Probability Density Function
1
2!)(
2
2
02
2
2
Am
where
em
Aezf
m
z
m m
mA
Zm
-10 -5 0 5 100
0.1
0.2
0.3
0.4
0.5
0.6
0.7
Noise amplitude
Pro
bability d
ensity f
unction
PDF for A = 0.15, = 0.8
A
Parameter
Description RangeOverlap 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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Middleton Class B Model25
Envelope Statistics Envelope exceedence probability density (APD), which is 1 – cumulative
distribution function (CDF)
Bm
mBA
IIB
BB
BBB
i
B
mm
mIB
mBB em
AeP
GG
AA
G
N
Fwhere
mF
m
m
AP
00
)2/(01
''
200
11
00110
001
220
!)(
2
4
)1(4
1;
2ˆ;
2ˆ
function trichypergeomeconfluent theis,
ˆ;2;2
1.2
1.!
ˆ)1(ˆ1)(
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Middleton Class B Model (cont…)26
Middleton Class B Envelope Statistics
0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 10
0.5
1
1.5
2
2.5
3
3.5
4
4.5
Exceedance Probability Density Graph for Class B Parameters: A = 10-1, A
B = 1,
B = 5, N
I = 1, = 1.8
No
rma
lize
d E
nve
lop
e T
hre
sho
ld (
E 0 /
Erm
s)
P(E > E0)
PB-I
PB-II
B
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Middleton Class B Model (cont…)27
Parameters for Middleton Class B Model
B
I
B
B
A
N
A
Parameters
Description Typical RangeImpulsive 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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Symmetric Alpha Stable Model28
Characteristic Function
Closed-form PDF expression only forα = 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
||)( je
PDF for = 1.5, = 0 and = 10
-50 0 500
0.01
0.02
0.03
0.04
0.05
0.06
0.07
Noise amplitude
Pro
babili
ty d
ensity f
unction
Parameter Description Range
Characteristic Exponent. Amount of impulsiveness
Localization. Analogous to mean
Dispersion. Analogous to variance
αδ
]2,0[α
),( ),0(
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Fitting Measured RFI Data29
Broadband RFI data 80,000 samples collected using 20GSPS scope
-5 -4 -3 -2 -1 0 1 2 3 4 50
0.2
0.4
0.6
0.8
1
Measured Data Fitting
Noise amplitude
Pro
babi
lity
Den
sity
Fun
ctio
n
Measured PDF
Estimated AlphaStable PDFEstimated MiddletonClass A PDF
Estimated Equi-powerGaussian PDF
Estimated ParametersSymmetric Alpha Stable Model
Localization (δ) 0.0043Distance 0.0514Characteristic exp. (α) 1.2105
Dispersion (γ) 0.2413
Middleton Class A Model
Overlap Index (A) 0.1036 Distance0.0825Gaussian Factor (Γ) 0.7763
Gaussian Model
Mean (µ) 0 Distance0.2217Variance (σ2) 1
Distance: Kullback-Leibler divergence
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Fitting Measured RFI Data
Best fit for 25 data sets under different conditions
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30
Filtering and Detection Methods
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
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Middleton Class A noise Symmetric Alpha Stable noise
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Results: Class A Detection32
Pulse shapeRaised cosine
10 samples per symbol10 symbols per pulse
ChannelA = 0.35
= 0.5 × 10-3
Memoryless
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Results: Alpha Stable Detection33
-10 -5 0 5 10 15 20
10-2
10-1
100
Generalized SNR
BE
R
Communication Performance (=0.9, =0, M=12)
Matched FilterHole PunchingMAPMyriad
Use dispersion parameter in place of noise variance to generalize SNRUse dispersion parameter in place of noise variance to generalize SNR
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Performance Bounds (2x2 MIMO)34
Channel Capacity [Chopra et al., submitted to ICASSP 2009]
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 noiseAssumes input has Gaussian distribution
NXY System Model
)()(
)|()(
);(max}}{),({ 2
NhYh
XYhYh
YXICsX EXExf
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Performance Bounds (2x2 MIMO)35
Channel Capacity in presence of RFI for 2x2 MIMO[Chopra et al., submitted to ICASSP 2009]
NXY System Model
Capacity
)()(
)|()(
);(max}}{),({ 2
NhYh
XYhYh
YXICsX EXExf
-40 -30 -20 -10 0 10 200
5
10
15
20
25
SNR [in dB]
Mut
ual I
nfor
mat
ion
(bits
/sec
/Hz)
Channel Capacity with Gaussian noiseUpper Bound on Mutual Information with Middleton noiseGaussian transmit codebook with Middleton noise
Parameters:A = 0.1, 1 = 0.012 = 0.1, = 0.4
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Performance Bounds (2x2 MIMO)36
Probability of symbol error for uncoded transmissions[Chopra et al., submitted to ICASSP 2009]
Parameters:A = 0.1, 1 = 0.012 = 0.1, = 0.4
Pe: Probability of symbol error
S: Transmitted code vector
D(S): Decision regions for MAP detector
Equally likely transmission for symbols
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Performance Bounds (2x2 MIMO)37
Chernoff factors for coded transmissions[Chopra et al., submitted to ICASSP 2009]
N
ttt ssC
ssPPEP
1
'
'
),,(min
)(
PEP: Pairwise error probabilityN: Size of the codewordChernoff factor:Equally likely transmission for symbols
),,(min ' kk ccC
-30 -20 -10 0 10 20 30 4010
-8
10-6
10-4
10-2
100
dt2 / N
0 [in dB]
Che
rnof
f Fac
tor
Middleton noise (A = 0.5)Middleton noise (A = 0.1)Middleton noise (A = 0.01)Gaussian noise
Parameters:1 = 0.012 = 0.1, = 0.4
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