MIMO Receiver Design in the Presence of Radio Frequency Interference

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


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


Prior Work3


Proposed Contributions4


Bivariate Middleton Class A Model5

Joint Spatial Distribution


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

Backup

2 x 2 MIMO System

Maximum Likelihood (ML) Receiver

Log-Likelihood Function


System Model7

Sub-optimal ML Receiversapproximate


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


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)


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)


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)


Conclusions12

Backup


13

Thank You,Questions ?


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


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


16

Moment Generating Function

Return

Parameter Estimation (cont…)


17

Return

Parameter Estimators


18

Return

Measured Fitting


19

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


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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Backup


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]


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

Return


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

Return


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(

Backup

Backup


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

Backup

Fitting Measured RFI Data

Best fit for 25 data sets under different conditions


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

31


Middleton Class A noise Symmetric Alpha Stable noise

BackupBackup

Backup

Backup

Backup


Results: Class A Detection32

Pulse shapeRaised cosine

10 samples per symbol10 symbols per pulse

ChannelA = 0.35

= 0.5 × 10-3

Memoryless


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

Backup

Backup


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

Return



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

Return



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

Return



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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Documents

MIMO Receiver Design in the Presence of Radio Frequency Interference