design of interference-aware wireless communication systems

Design of Interference-Aware Wireless Communication Systems

Wireless Networking and Communications Group

2 Dec 2010

Brian L. EvansLead Graduate Students

Aditya Chopra, Kapil Gulati, and Marcel Nassar

Collaborators from Intel LabsCurrent: Nageen Himayat, Kirk Skeba, and Srikathyayani Srikanteswara

Past: Chaitanya Sreerama, Eddie X. Lin, Alberto A. Ochoa, and Keith R. Tinsley

Outline

Introduction Problem definition Summary of last talk (in Apr. 2010) at Intel Labs Recent results

RFI Modeling: Spatial and Temporal dependence RFI Mitigation: Multi-carrier systems

Conclusions Future work


2

Radio FrequencyInterference

(RFI)

Introduction


3

Wireless Communication Sources

• Closely located sources• Coexisting protocols

Non-CommunicationSources

Electromagnetic radiations

Computational Platform• Clocks, busses, processors• Co-located transceivers

antenna

baseband processor

(Wi-Fi)(WiMAX Basestation)

(WiMAX Mobile)

(Bluetooth)

(Microwave)

(Wi-Fi) (WiMAX)

Problem Definition

Problem: Co-channel and adjacent channel interference, and platform noise degrade communication performance

Approach: Statistical modeling of RFI Solution: Receiver design

Listen to the environment Estimate parameters for RFI statistical models Use parameters to mitigate RFI

Goal: Improve communication performance 10-100x reduction in bit error rate 10-100x improvement in network throughput


4

Designing Interference-Aware Receivers


5

RTS

CTS

RTS / CTS: Request / Clear to send

Guard zone

Example: Dense WiFi Networks

Medium Access Control (MAC) Layer• Interference sense and avoid• Optimize MAC parameters

(e.g. guard zone size, transmit power)

Physical (PHY) Layer• Receiver pre-filtering• Receiver detection• Forward error correction

Statistical Modeling of RFI• Derive analytically• Estimate parameters at receiver

Statistical Models (isotropic, zero centered)

Symmetric Alpha Stable [Furutsu & Ishida, 1961] [Sousa, 1992]

Characteristic function

Gaussian Mixture Model [Sorenson & Alspach, 1971]

Amplitude distribution

Middleton Class A (w/o Gaussian component) [Middleton, 1977]


6

Summary of Last Talk: RFI Modeling


7

• Sensor networks• Ad hoc networks

• Dense Wi-Fi networks

• Cluster of hotspots (e.g. marketplace)

• In-cell and out-of-cell femtocell users

• Out-of-cell femtocell users

• Cellular networks• Hotspots (e.g. café)

Symmetric Alpha Stable

Ad hoc and Cellular networks

• Single Antenna• Instantaneous statistics

Femtocell networks• Single Antenna• Instantaneous statistics

Gaussian Mixture Model

Summary of Last Talk: RFI Modeling

Validated for Laptop radiated RFI

Slides available at:http://users.ece.utexas.edu/~bevans/projects/rfi/talks/April2010RFIMitigationTalk.html


8

Smaller KL divergence• Closer match in distribution• Does not imply close match in

tail probabilities

Radiated platform RFI• 25 RFI data sets from Intel• 50,000 samples at 100 MSPS• Laptop activity unknown to us

0 5 10 15 20 250

0.05

0.1

0.15

0.2

0.25

0.3

0.35

0.4

Measurement Set

Kul

lbac

k-Le

ible

r div

erge

nce

Symmetric Alpha StableMiddleton Class AGaussian Mixture ModelGaussian

Summary of Last Talk: RFI Mitigation

Communication Performance


9

Pulse Shaping Pre-filtering Matched

FilterDetection

Rule

Interference + Thermal noise

-10 -5 0 5 10 15 20

10-3

10-2

10-1

SNR [in dB]

Vec

tor S

ymbo

l Err

or R

ate

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)

-40 -35 -30 -25 -20 -15 -10 -5

10-3

10-2

10-1

100

Signal to Noise Ratio (SNR) [in dB]

Sym

bol E

rror

Rat

e

Correlation ReceiverBayesian DetectionMyriad Pre-filtering

Single carrier, single antenna (SISO) Single carrier, two antenna (2x2 MIMO)

~ 20 dB ~ 8 dB

10 – 100x reduction in Bit Error Rate

Extended to include spatial and temporal dependence

Multivariate extensions of Symmetric Alpha Stable Gaussian mixture model

RFI Modeling: Extensions


10

Statistical Modeling of RFISingle Antenna

Instantaneous statisticsSpatial Dependence Temporal Dependence

• Multi-antenna receivers• Symbol errors • Burst errors• Coded transmissions• Delays in network

RFI Modeling: Spatial Dependence

System Model Common and exclusive interferers Characterizes receiver separation

and directional shielding

Joint RFI statistics helpful in choosing spatial transmit and receive techniques


11

1

1

1

11

11

22

2

2

2

2

3

33

3

3

ReceiverInterferers impact all receiversInterferers impact receiver1

RFI Modeling: Spatial Dependence

An impulsive event at one antenna increases probability of impulse event at other antennae

Translated environmental parameters to spatial dependence


12

0 0.05 0.1 0.15 0.2 0.250

0.05

0.1

0.15

0.2

0.25

|Y1|

|Y2|

0 0.05 0.1 0.15 0.2 0.250

0.05

0.1

0.15

0.2

0.25

|Y1|

|Y2|

0 0.05 0.1 0.15 0.2 0.250

0.05

0.1

0.15

0.2

0.25

|Y1|

|Y2|

|RFI at antenna 2|

|RFI

at a

nten

na 1

|

|RFI

at a

nten

na 1

|

|RFI

at a

nten

na 1

|

|RFI at antenna 2||RFI at antenna 2|

SPATIALLY INDEPENDENT SPATIALLY ISOTROPIC

RFI Modeling: Temporal Dependence

System Model

Interference is dependent across time slots


13

RFI Modeling: Joint Interference Statistics

Throughput performance of ad hoc networks


14

Ad hoc networksMultivariate Symmetric Alpha Stable

Cellular networksMultivariate Gaussian Mixture Model

2 4 6 8 10 12 14 162

3

4

5

6

7

8

9

10

Expected ON Time of a User (time slots)

Net

wor

k Th

roug

hput

(nor

mal

ized

)[ b

ps/H

z/ar

ea ]

With RFI MitigationWithout RFI Mitigation

Network throughput improved by optimizing distribution of ON Time of users (MAC parameter)

~1.6x

RFI Mitigation: Multi-carrier systems

Single Carrier vs. Multi-Carrier: Intuition


15

Symbols

Impulsive Noise

Symbols

Impulsive Noise

High Amplitude Impulse

High Amplitude Impulse

• Impulse energy concentrated in one symbol• Symbol Lost

• Impulse energy spread across symbols• Noise dependent across subcarriers• Optimal decoding: exponential complexity!

Single Carrier Multi Carrier (OFDM)

RFI Mitigation: Multi-carrier systems

Proposed Receiver Iterative Expectation Maximization (EM) based on noise model

Communication Performance


16

-10 -5 0 5 10 15 20

10-4

10-3

10-2

10-1

100


Bit

Erro

r Rat

e

OFDM ReceiverSingle CarrierProposed EM-based Receiver

Simulation Parameters

• BPSK Modulation• Interference Model

2-term Gaussian Mixture Model~ 5 dB

Summary


17

Physical (PHY) Layer

Single Antenna (past work) Multi-Antenna Receivers Temporal Modeling

Statistical Modeling of RFI: (a) Uni- or Multi-variate Gaussian Mixture(b) Uni- or Multi-variate Symmetric Alpha Stable

Medium Access Control (MAC) Layer

(a) Detection and Pre-filtering methods(b) Single- and Two-antenna receivers(c) Single- and Multi-carrier systems

RFI Mitigation:(a) Microwave Oven Interference(b) Performance of Ad hoc Networks

RFI Avoidance and Mitigation:

Impact: 10-100x improvement in communication performance

Current and Future Work


18

Physical (PHY) Layer Medium Access Control (MAC) Layer

RFI Avoidance and Mitigation:

Statistical Modeling of RFI: (a) Multi-carrier Multi-antenna systems(b) Non-stationary RFI

Communication Performance Analysis• MIMO transmit and receive strategiesImproving Communication Performance• Detection and Pre-filtering methods• Error correction coding Interference Avoidance• Spectrum Sensing

Impact: Improved communication performance

RFI Avoidance and Mitigation:Network Performance Analysis• Different MAC strategiesImproving Network Performance• Optimizing MAC parameters• MAC algorithms to reduce interferenceInterference Avoidance• Resource Allocation (time, frequency)

Impact: Improved network-wide performance

Cognitive Radios

UT Austin RFI Modeling & Mitigation Toolbox

Freely distributable toolbox in MATLAB Simulation environment for RFI modeling and mitigation

RFI generation Measured RFI fitting Parameter estimation algorithms Filtering and detection methods Demos for RFI modeling and mitigation

Latest Toolbox ReleaseVersion 1.5, Aug. 16, 2010


19

http://users.ece.utexas.edu/~bevans/projects/rfi/software/index.html

Snapshot of a demo

Related Publications

Journal Publications• K. Gulati, B. L. Evans, J. G. Andrews, and K. R. Tinsley, “Statistics of Co-Channel

Interference in a Field of Poisson and Poisson-Poisson Clustered Interferers”, IEEE Transactions on Signal Processing, to be published, Dec., 2010.

• M. Nassar, K. Gulati, M. R. DeYoung, B. L. Evans and K. R. Tinsley, “Mitigating Near-Field Interference in Laptop Embedded Wireless Transceivers”, Journal of Signal Processing Systems, Mar. 2009, invited paper.

Conference Publications• M. Nassar, X. E. Lin, and B. L. Evans, “Stochastic Modeling of Microwave Oven

Interference in WLANs”, Int. Conf. on Comm., Jan. 5-9, 2011, Kyoto, Japan, submitted.• K. Gulati, B. L. Evans, and K. R. Tinsley, “Statistical Modeling of Co-Channel

Interference in a Field of Poisson Distributed Interferers”, Proc. IEEE Int. Conf. on Acoustics, Speech, and Signal Proc., Mar. 14-19, 2010.

• K. Gulati, A. Chopra, B. L. Evans, and K. R. Tinsley, “Statistical Modeling of Co-Channel Interference”, Proc. IEEE Int. Global Communications Conf., Nov. 30-Dec. 4, 2009.

Cont…

20


Related Publications

Conference Publications (cont…)• 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. 19-24, 2009.

• 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.

• 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.

21


Software Releases• K. Gulati, M. Nassar, A. Chopra, B. Okafor, M. R. DeYoung, N. Aghasadeghi, A. Sujeeth,

and B. L. Evans, "Radio Frequency Interference Modeling and Mitigation Toolbox in MATLAB", version 1.5, Aug. 16, 2010.

Thanks !

22


References

RFI Modeling1. 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. 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.

3. 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.

4. E. S. Sousa, “Performance of a spread spectrum packet radio network link in a Poisson field of interferers,” IEEE Transactions on Information Theory, vol. 38, no. 6, pp. 1743–1754, Nov. 1992.

5. X. Yang and A. Petropulu, “Co-channel interference modeling and analysis in a Poisson field of interferers in wireless communications,” IEEE Transactions on Signal Processing, vol. 51, no. 1, pp. 64–76, Jan. 2003.

6. E. Salbaroli and A. Zanella, “Interference analysis in a Poisson field of nodes of finite area,” IEEE Transactions on Vehicular Technology, vol. 58, no. 4, pp. 1776–1783, May 2009.

7. M. Z. Win, P. C. Pinto, and L. A. Shepp, “A mathematical theory of network interference and its applications,” Proceedings of the IEEE, vol. 97, no. 2, pp. 205–230, Feb. 2009.

23


References

Parameter Estimation1. 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 .

2. 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.

Communication Performance of Wireless Networks3. R. Ganti and M. Haenggi, “Interference and outage in clustered wireless ad hoc networks,” IEEE

Transactions on Information Theory, vol. 55, no. 9, pp. 4067–4086, Sep. 2009.4. A. Hasan and J. G. Andrews, “The guard zone in wireless ad hoc networks,” IEEE Transactions on

Wireless Communications, vol. 4, no. 3, pp. 897–906, Mar. 2007.5. X. Yang and G. de Veciana, “Inducing multiscale spatial clustering using multistage MAC contention

in spread spectrum ad hoc networks,” IEEE/ACM Transactions on Networking, vol. 15, no. 6, pp. 1387–1400, Dec. 2007.

6. S. Weber, X. Yang, J. G. Andrews, and G. de Veciana, “Transmission capacity of wireless ad hoc networks with outage constraints,” IEEE Transactions on Information Theory, vol. 51, no. 12, pp. 4091-4102, Dec. 2005.

24


References

Communication Performance of Wireless Networks (cont…)5. S. Weber, J. G. Andrews, and N. Jindal, “Inducing multiscale spatial clustering using multistage MAC

contention in spread spectrum ad hoc networks,” IEEE Transactions on Information Theory, vol. 53, no. 11, pp. 4127-4149, Nov. 2007.

6. J. G. Andrews, S. Weber, M. Kountouris, and M. Haenggi, “Random access transport capacity,” IEEE Transactions On Wireless Communications, Jan. 2010, submitted. [Online]. Available: http://arxiv.org/abs/0909.5119

7. M. Haenggi, “Local delay in static and highly mobile Poisson networks with ALOHA," in Proc. IEEE International Conference on Communications, Cape Town, South Africa, May 2010.

8. F. Baccelli and B. Blaszczyszyn, “A New Phase Transitions for Local Delays in MANETs,” in Proc. of IEEE INFOCOM, San Diego, CA,2010, to appear.

Receiver Design to Mitigate RFI9. A. Spaulding and D. Middleton, “Optimum Reception in an Impulsive Interference Environment-

Part I: Coherent Detection”, IEEE Trans. Comm., vol. 25, no. 9, Sep. 197710.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

25


http://arxiv.org/abs/0909.5119

References

Receiver Design to Mitigate RFI (cont…)3. 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.

4. G. R. Arce, Nonlinear Signal Processing: A Statistical Approach, John Wiley & Sons, 2005.5. Y. Eldar and A. Yeredor, “Finite-memory denoising in impulsive noise using Gaussian mixture

models,” IEEE Transactions on Circuits and Systems II: Analog and Digital Signal Processing, vol. 48, no. 11, pp. 1069-1077, Nov. 2001.

6. J. H. Kotecha and P. M. Djuric, “Gaussian sum particle ltering,” IEEE Transactions on Signal Processing, vol. 51, no. 10, pp. 2602-2612, Oct. 2003.

7. 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.

8. 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.

RFI Measurements and Impact9. 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

26


Backup Slides

Introduction Interference avoidance , alignment, and cancellation methods Femtocell networks

Statistical Modeling of RFI Computational platform noise Impact of RFI Assumptions for RFI Modeling Transients in digital FIR filters Poisson field of interferers Poisson-Poisson cluster field of interferers

Measured RFI FittingWireless Networking and Communications Group

27

Backup

Backup

Backup

Backup

Backup

Backup

Backup

Backup

Backup

Backup Slides (cont…)

Gaussian Mixture vs. Alpha Stable Middleton Class A, B, and C models

Middleton Class A model Expectation maximization overview Results: EM for Middleton Class A

Symmetric Alpha Stable Extreme order statistics based estimator for Alpha Stable

Video over impulsive channels Demonstration #1 Demonstration #2


28

Backup

Backup

Backup

Backup

Backup

Backup

Backup

Backup

Backup


RFI mitigation in SISO systems Our contributions Results: Class A Detection Results: Alpha Stable Detection

RFI mitigation in MIMO systems Our contributions

Performance bounds for SISO systems Performance bounds for MIMO systems Extensions for multicarrier systems Turbo codes in impulsive channels


29

Backup

Backup

Backup

Backup

Backup

Backup

Backup

Backup


RFI Toolbox


30

Backup

Interference Mitigation Techniques

Interference avoidance CSMA / CA

Interference alignment Example:

[Cadambe & Jafar, 2007]


31

Return

Interference Mitigation Techniques (cont…)

Interference cancellationRef: J. G. Andrews, ”Interference Cancellation for Cellular Systems: A Contemporary Overview”, IEEE Wireless Communications Magazine, Vol. 12, No. 2, pp. 19-29, April 2005


32

Return

Femtocell Networks

Reference:V. Chandrasekhar, J. G. Andrews and A. Gatherer, "Femtocell Networks: a Survey", IEEE Communications Magazine, Vol. 46, No. 9, pp. 59-67, September 2008


33

Return

Common Spectral Occupancy


34

Standard Carrier (GHz)

Wireless Networking Interfering Clocks and Busses

Bluetooth 2.4 Personal Area Network

Gigabit Ethernet, PCI Express Bus, LCD clock harmonics

IEEE 802. 11 b/g/n 2.4 Wireless LAN

(Wi-Fi)Gigabit Ethernet, PCI Express Bus,

LCD clock harmonics

IEEE 802.16e

2.5–2.69 3.3–3.8

5.725–5.85

Mobile Broadband(Wi-Max)

PCI Express Bus,LCD clock harmonics

IEEE 802.11a 5.2 Wireless LAN

(Wi-Fi)PCI Express Bus,

LCD clock harmonics

Return

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 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)


35

floor noise RX

ceInterferenfloor noise RXlog10 10desense

Return

Impact of LCD clock on 802.11g

Pixel clock 65 MHz LCD Interferers and 802.11g center frequencies


36

LCD Interferers

802.11g Channel

Center Frequency

Difference of Interference from Center Frequencies

Impact

2.410 GHz Channel 1 2.412 GHz ~2 MHz Significant

2.442 GHz Channel 7 2.442 GHz ~0 MHz Severe

2.475 GHz Channel 11 2.462 GHz ~13 MHz Just outside Ch. 11. Impact minor

Return

Assumptions for RFI Modeling

Key assumptions for Middleton and Alpha Stable models[Middleton, 1977][Furutsu & Ishida, 1961] Infinitely many potential interfering sources with same effective

radiation power Power law propagation loss Poisson field of interferers with uniform intensity l Pr(number of interferers = M |area R) ~ Poisson(M; lR)

Uniformly distributed emission times Temporally independent (at each sample time)

Limitations Alpha Stable models do not include thermal noise Temporal dependence may exist


37

Return

50 100 150 200

-0.5

0

0.5

Inpu

t

50 100 150 200-1

-0.5

0

0.5

1

Filte

r Out

put

Transients in Digital FIR Filters


38

25-Tap FIR Filter• Low pass• Stopband freq. 0.22 (normalized)

Input Output

Freq = 0.16

Interference duration = 10 * 1/0.22 Interference duration = 100 x 1/0.22

Transients

Transients Significant w.r.t. Steady State

100 200 300 400 500 600

-0.5

0

0.5

Inpu

t

100 200 300 400 500 600-1

-0.5

0

0.5

1

Filte

r Out

put

Transients Ignorable w.r.t. Steady State

Return

Poisson Field of Interferers

Interferers distributed over parametric annular space

Log-characteristic function


39

Return



40

Return



41

• Cellular networks• Hotspots (e.g. café)

• Sensor networks• Ad hoc networks

• Dense Wi-Fi networks• Networks with contention

based medium access

Symmetric Alpha Stable Middleton Class A (form of Gaussian Mixture)

Return


Simulation Results (tail probability)


42

0.1 0.2 0.3 0.4 0.5 0.6 0.710

-3

10-2

10-1

100

Interference amplitude (y)

Tail

Pro

babi

lity

[ P (|

Y| >

y) ]

SimulatedSymmetric Alpha Stable

0.1 0.2 0.3 0.4 0.5 0.6 0.710

-15

10-10

10-5

100


Tail

Pro

babi

lity

[ P (|

Y| >

y) ]

SimulatedSymmetric Alpha StableGaussianMiddleton Class A

Gaussian and Middleton Class A models are not applicable since mean intensity is infinite

Case I: Entire Plane Case III: Infinite-area with guard zone

Return




43

Case II: Finite area annular region

0 0.1 0.2 0.3 0.4 0.5 0.6 0.710

-15

10-10

10-5

100


Tail

Pro

babi

lity

[P(|Y

| > y

)]

SimulatedSymmetric Alpha StableGaussianMiddleton Class A

Return

Poisson-Poisson Cluster Field of Interferers

Cluster centers distributed as spatial Poisson process over

Interferers distributed as spatial Poisson process


44

Return


Log-Characteristic function


45

Return



46

• Cluster of hotspots (e.g. marketplace)

• In-cell and out-of-cell femtocell users in femtocell networks

• Out-of-cell femtocell users in femtocell networks

Symmetric Alpha Stable Gaussian Mixture Model

Return




47

0.1 0.2 0.3 0.4 0.5 0.6 0.710

-12

10-10

10-8

10-6

10-4

10-2

100


Tail

Pro

babi

lity

[ P (|

Y| >

y) ]

SimulatedSymmetric Alpha StableGaussianGaussian Mixture Model

0.1 0.2 0.3 0.4 0.5 0.6 0.710

-4

10-3

10-2

10-1

100


Tail

Pro

babi

lity

[ P (|

Y| >

y) ]

SimulatedSymmetric Alpha Stable

Gaussian and Gaussian mixture models are not applicable since mean intensity is infinite

Case I: Entire Plane Case III: Infinite-area with guard zone

Return




48

Case II: Finite area annular region

0 0.1 0.2 0.3 0.4 0.5 0.6 0.710

-15

10-10

10-5

100


Tail

Pro

babi

lity

[P(|Y

| > y

)]

SimulatedSymmetric Alpha StableGaussianGaussian Mixture Model

Return

Fitting Measured Laptop RFI Data

Statistical-physical models fit data better than Gaussian


49

Smaller KL divergence• Closer match in distribution• Does not imply close match in

tail probabilities

Radiated platform RFI• 25 RFI data sets from Intel• 50,000 samples at 100 MSPS• Laptop activity unknown to us

0 5 10 15 20 250

0.05

0.1

0.15

0.2

0.25

0.3

0.35

0.4

Measurement Set

Kul

lbac

k-Le

ible

r div

erge

nce

Symmetric Alpha StableMiddleton Class AGaussian Mixture ModelGaussian

Platform RFI sources• May not be Poisson distributed• May not have identical emissions

Return

Results on Measured RFI Data

For measurement set #2350


Tail probability governs communication performance• Bit error rate• Outage probability

0 1 2 3 4 5 6 7 8 910

-20

10-15

10-10

10-5

100

Threshold Amplitude (a)

Tail

Pro

babi

litie

s [P

(X >

a)]

EmpiricalMiddleton Class ASymmteric Alpha StableGaussianGaussian Mixture Model

Return

Gaussian Mixture vs. Alpha Stable

Gaussian Mixture vs. Symmetric Alpha Stable


51

Gaussian Mixture Symmetric Alpha StableModeling Interferers distributed with Guard

zone around receiver (actual or virtual due to pathloss function)

Interferers distributed over entire plane

Pathloss Function

With GZ: singular / non-singularEntire plane: non-singular

Singular form

Thermal Noise

Easily extended(sum is Gaussian mixture)

Not easily extended (sum is Middleton Class B)

Outliers Easily extended to include outliers Difficult to include outliers

Return

52


Middleton Class A, B and C Models

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]

Return

53


Middleton Class A model

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

babi

lity

dens

ity fu

nctio

n

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]

Return

Expectation Maximization Overview


5454

Return


Results: EM Estimator for Class A55

PDFs with 11 summation terms50 simulation runs per setting

1000 data samplesConvergence criterion:

1e-006 1e-005 0.0001 0.001 0.01

10

15

20

25

30

K

Num

ber o

f Ite

ratio

ns

Number of Iterations taken by the EM Estimator for A

A = 0.01A = 0.1A = 1

Iterations for Parameter A to Converge

1e-006 1e-005 0.0001 0.001 0.01

0.8

1

1.2

1.4

1.6

1.8

2

2.2

2.4

2.6

x 10-3

K

Frac

tiona

l MS

E =

| (A

- A

est) /

A |

2

Fractional MSE of Estimator for A

A = 0.01A = 0.1A = 1

Normalized Mean-Squared Error in A

2

)(AAAANMSE est

est

7

1

1 10ˆˆˆ

n

nn

AAA

K = A

Return

56


Results: EM Estimator for Class A

• For convergence for A [10-2, 1], worst-case number of iterations for A = 1

• Estimation accuracy vs. number of iterations tradeoff

Return

57


Symmetric Alpha Stable Model

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, = 10

-50 0 500

0.01

0.02

0.03

0.04

0.05

0.06

0.07

Noise amplitude

Pro

babi

lity

dens

ity fu

nctio

n

Parameter Description Range

Characteristic Exponent. Amount of impulsiveness

Localization. Analogous to mean

Dispersion. Analogous to variance

αδ

]2,0[α

),( ),0(

Backup

Backup

Return

58


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)

)( )](1[ )(

)( )( )(1

:

1:

xfxFNxf

xfxFNxf

XN

Nm

XN

NM

Return

Parameter Estimators for Alpha Stable


5959

0 < p < α

Return

60


Parameter Est.: Symmetric Alpha Stable Results

• Data length (N) of 10,000 samples

• Results averaged over 100 simulation runs

• Estimate α and “mean” directly from data

• Estimate “variance” from α and δ estimates

0 0.2 0.4 0.6 0.8 1 1.2 1.4 1.6 1.8 20

0.01

0.02

0.03

0.04

0.05

0.06

0.07

0.08

0.09MSE in estimates of the Characteristic Exponent ()

Characteristic Exponent:

Mea

n S

quar

ed E

rror (

MS

E)

Mean squared error in estimate of characteristic exponent α

Return

61


Parameter Est.: Symmetric Alpha Stable Results

0 0.2 0.4 0.6 0.8 1 1.2 1.4 1.6 1.8 20

1

2

3

4

5

6

7MSE in estimates of the Dispersion Parameter ()


Mea

n S

quar

ed E

rror (

MS

E)

Mean squared error in estimate of dispersion (“variance”)

Mean squared error in estimate of localization (“mean”)

0 0.2 0.4 0.6 0.8 1 1.2 1.4 1.6 1.8 20

1

2

3

4

5

6

7MSE in estimates of the Dispersion Parameter ()


Mea

n S

quar

ed E

rror (

MS

E)

Return

Extreme Order Statistics


62

Return

63

Video over Impulsive Channels

Video demonstration for MPEG II video stream 10.2 MB compressed stream from camera (142 MB uncompressed) Compressed file sent over additive impulsive noise channel Binary phase shift keying

Raised cosine pulse10 samples/symbol10 symbols/pulse length

Composite of transmitted and received MPEG II video streamshttp://www.ece.utexas.edu/~bevans/projects/rfi/talks/video_demo19dB_correlation.wmv Shows degradation of video quality over impulsive channels with

standard receivers (based on Gaussian noise assumption)Wireless Networking and Communications Group

Additive Class A Noise ValueOverlap index (A) 0.35Gaussian factor () 0.001SNR 19 dB

Return

http://www.ece.utexas.edu/~bevans/projects/rfi/talks/video_demo19dB_correlation.wmv

http://www.ece.utexas.edu/~bevans/projects/rfi/talks/video_demo19dB_correlation.wmv

Video over Impulsive Channels #2

Video demonstration for MPEG II video stream revisited 5.9 MB compressed stream from camera (124 MB uncompressed) Compressed file sent over additive impulsive noise channel Binary phase shift keying

Raised cosine pulse10 samples/symbol10 symbols/pulse length

Composite of transmitted video stream, video stream from a correlation receiver based on Gaussian noise assumption, and video stream for a Bayesian receiver tuned to impulsive noise

http://www.ece.utexas.edu/~bevans/projects/rfi/talks/video_demo19dB.wmv


64

Additive Class A Noise ValueOverlap index (A) 0.35Gaussian factor () 0.001SNR 19 dB

Return



65

Video over Impulsive Channels #2

Structural similarity measure [Wang, Bovik, Sheikh & Simoncelli, 2004]

Score is [0,1] where higher means better video quality

Frame number

Bit error rates for ~50 million bits sent:

6 x 10-6 for correlation receiver

0 for RFI mitigating receiver (Bayesian)

Return

66


Our Contributions

Computer Platform Noise Modelling

Evaluate fit of measured RFI data to noise models• Middleton Class A model• 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

Mitigation of computational platform noise in single carrier, single antenna systems [Nassar, Gulati, DeYoung, Evans & Tinsley, ICASSP 2008, JSPS 2009]

Return

67


Filtering and Detection

Pulse Shaping Pre-Filtering Matched

FilterDetection

Rule

Impulsive Noise

Middleton Class A noise Symmetric Alpha Stable noise

Filtering Wiener Filtering (Linear)

Detection Correlation Receiver (Linear) Bayesian Detector

[Spaulding & Middleton, 1977] Small Signal Approximation to

Bayesian detector[Spaulding & Middleton, 1977]

Filtering Myriad Filtering

Optimal Myriad [Gonzalez & Arce, 2001]

Selection Myriad Hole Punching

[Ambike et al., 1994]Detection

Correlation Receiver (Linear) MAP approximation

[Kuruoglu, 1998]

AssumptionMultiple samples of the received signal are available• N Path Diversity [Miller, 1972]• Oversampling by N [Middleton, 1977]

Return

RFI Mitigation in SISO systems

Communication performance


68

Pulse Shaping Pre-filtering Matched

FilterDetection

Rule

Interference + Thermal noise

Pulse shapeRaised cosine

10 samples per symbol10 symbols per pulse

ChannelA = 0.35 = 5 × 10-3

Memoryless

Method Comp. Complexity

Detection Perform.

Correlation Low Low

Bayesian detection High High

Myriad pre-filtering Medium Medium

Binary Phase Shift Keying

-40 -35 -30 -25 -20 -15 -10 -5

10-3

10-2

10-1

100


Sym

bol E

rror

Rat

e

Correlation ReceiverBayesian DetectionMyriad Pre-filtering

Return

69


Results: Class A Detection

Pulse shapeRaised cosine

10 samples per symbol10 symbols per pulse

ChannelA = 0.35

= 0.5 × 10-3

Memoryless


Detection Perform.

Correl. Low LowWiener Medium LowBayesian S.S. Approx.

Medium High

Bayesian High High-35 -30 -25 -20 -15 -10 -5 0 5 10 15

10-5

10-4

10-3

10-2

10-1

100

SNR

Bit

Err

or R

ate

(BE

R)

Correlation ReceiverWiener FilteringBayesian DetectionSmall Signal Approximation

Communication Performance Binary Phase Shift KeyingReturn

70


Results: Alpha Stable Detection

Use dispersion parameter in place of noise variance to generalize SNR


Detection Perform.

Hole Punching

Low Medium

Selection Myriad

Low Medium

MAP Approx.

Medium High

Optimal Myriad

High Medium

-10 -5 0 5 10 15 20

10-2

10-1

100

Generalized SNR (in dB)

Bit

Err

or R

ate

(BE

R)

Matched FilterHole PunchingMAPMyriad

Communication Performance Same transmitter settings as previous slideReturn

71


MAP Detection for Class A

Hard decision Bayesian formulation [Spaulding & Middleton, 1977]

Equally probable source

Z+S=X:H

Z+S=X:H

22

11 1

2

1

11

22

H

H

)H|X)p(p(H)H|X)p(p(H=)XΛ(

1

2

1

1

2

H

H

Z

Z

)SX(p)SX(p

=)XΛ(

Return


MAP Detection for Class A: Small Signal Approx.72

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

ji

N

=i i

ZZj

ΤZZjZ s

x)X(p

)X(p=S)X(p)X(p)SX(p

1

Correlation Receiver

1 ln1

ln1

2

1

11i

12i

H

H

N

=iiZ

i

N

=iiZ

i

)(xpdxds

)(xpdxds

)XΛ(

We use 100 terms of the series expansion for

d/dxi ln pZ(xi) in simulations

Return

73


Incoherent Detection

Bayesian formulation [Spaulding & Middleton, 1997, pt. II]

Small signal approximation

Z(t)+θ)(t,S=X(t):H

Z(t)+θ)(t,S=X(t):H

22

11

1

2

1

1

2

1

2

H

H

θ

θ

)X(p)X(p=

)p(θp(θH|Xp(

)p(θp(θH|Xp(=)XΛ(

phase :φamplitude:a

φ

a=θ and where

ln

1 sincos

sincos

2

1

2

11

2

11

2

12

2

12

)(xpdxd=)l(xwhere

tω)l(x+tω)l(x

tω)l(x+tω)l(x

iZi

i

H

H

N

=iii

N

=iii

N

=iii

N

=iii

Correlation receiver

Return

74


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

22

11 minargˆ,,

i

N

ikNM xkxxg

1

2),(

k

Return


Filtering for Alpha Stable Noise (Cont..)75

Myriad filter implementation Given a window of samples, x1,…,xN, find β [xmin, xmax] Optimal Myriad algorithm

1. Differentiate objective function polynomial p(β) with respect to β

2. Find roots and retain real roots3. Evaluate p(β) at real roots and extreme points4. Output β that gives smallest value of p(β)

Selection Myriad (reduced complexity)1. Use x1, …, xN as the possible values of β2. Pick value that minimizes objective function p(β)

22

1)(

i

N

ixkp

Return

76


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

hp

hp

T>nxTnxnx

][0][][

hhp

Return

77


MAP Detection for Alpha Stable: PDF Approx.

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

N

iiY

iY

N

i

vz

vf

vfezp

i

1

2

2

1

2

,0,

2

2

2

Return

78


Results: Alpha Stable Detection

Return

79


Complexity Analysis for Alpha Stable Detection

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)

Return

80


Extensions to MIMO systems

Radio Frequency Interference Modeling and Receiver Design for MIMO systemsRFI Model Spatial

Corr.Physical Model

Comments

Middleton Class A No Yes • Uni-variate model• Assume independent or uncorrelated

noise for multiple antennasReceiver design:[Gao & Tepedelenlioglu, 2007] Space-Time Coding[Li, Wang & Zhou, 2004] Performance degradation in receivers

Weighted Mixture of Gaussian Densities

Yes No • Not derived based on physical principles

Receiver design:[Blum et al., 1997] Adaptive Receiver Design

Bivariate Middleton Class A[McDonald & Blum, 1997]

Yes Yes • Extensions of Class A model to two-antenna systems

Return

81


Our 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 (sixth order moments)

Performance Analysis

• Demonstrated communication performance degradation of conventional receivers in presence of RFI

• Bounds on communication performance[Chopra , Gulati, Evans, Tinsley, and Sreerama, ICASSP 2009]

Receiver Design • Derived Maximum Likelihood (ML) receiver• Derived two sub-optimal ML receivers with reduced

complexity

2 x 2 MIMO receiver design in the presence of RFI[Gulati, Chopra, Heath, Evans, Tinsley & Lin, Globecom 2008]

Return

82


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

Return

83


Results on Measured RFI Data

50,000 baseband noise samples represent broadband interference

Estimated Parameters

Bivariate Middleton Class A

Overlap Index (A) 0.313

2D-KL Divergence

1.004

Gaussian Factor (1) 0.105

Gaussian Factor (2) 0.101

Correlation (k) -0.085

Bivariate Gaussian

Mean (µ) 0

2D-KL Divergence

1.6682

Variance (1) 1

Variance (2) 1

Correlation (k) -0.085

-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

babi

lity

Den

sity

Fun

ctio

n

Measured PDFEstimated MiddletonClass A PDFEqui-powerGaussian PDF

Marginal PDFs of measured data compared with estimated model densities

Return

84

2 x 2 MIMO System

Maximum Likelihood (ML) receiver

Log-likelihood function


System Model

Sub-optimal ML Receiversapproximate

Return


Sub-Optimal ML Receivers85

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

App

roxm

atio

n of

(z

)

(z)

1(z)

2(z)

chosen to minimizeApproximation of

Return

86


Results: Performance Degradation

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 S

ymbo

l Err

or R

ate

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, k = 0.4

Severe degradation in communication performance in

high-SNR regimes

Return

87

-10 -5 0 5 10 15 20

10-3

10-2

10-1

SNR [in dB]

Vec

tor S

ymbo

l Err

or R

ate



Results: RFI Mitigation in 2 x 2 MIMO

A Noise Characteristic

Improve-ment

0.01 Highly Impulsive ~15 dB0.1 Moderately

Impulsive ~8 dB

1 Nearly Gaussian ~0.5 dB

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, k = 0.4)

Return


Results: RFI Mitigation in 2 x 2 MIMO 88

Complexity AnalysisReceiver

Quadratic Forms

Exponential

Comparisons

Gaussian ML M2 0 0

Optimal ML 2M2 2M2 0

Sub-optimal ML (Four-Piece) 2M2 0 2M2

Sub-optimal ML (Two-Piece) 2M2 0 M2

Complexity Analysis for decoding M-level QAM modulated signal

Communication Performance (A = 0.1, 1= 0.01, 2= 0.1, k = 0.4)

-10 -5 0 5 10 15 20

10-3

10-2

10-1

SNR [in dB]

Vec

tor S

ymbo

l Err

or R

ate


Return

89


Performance Bounds (Single Antenna)

Channel capacity

Case I Shannon Capacity in presence of additive white Gaussian noise

Case II (Upper Bound) Capacity in the presence of Class A noiseAssumes 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 noiseAssumes input has Gaussian distribution (e.g. bit interleaved coded modulation (BICM) or OFDM modulation [Haring, 2003])

NXY System Model

)()()|()(

);(max}}{),({ 2

NhYhXYhYh

YXICsX EXExf

Return

90



Channel capacity in presence of RFI

NXY

-40 -30 -20 -10 0 10 200

5

10

15

SNR [in dB]

Cap

acity

(bits

/sec

/Hz)

Channel Capacity

X: Gaussian, N: Gaussian

Y:Gaussian, N:ClassA (A = 0.1, = 10-3)

X:Gaussian, N:ClassA (A = 0.1, = 10-3)

System Model

ParametersA = 0.1, Γ = 10-3

Capacity

)()()|()(

);(max}}{),({ 2

NhYhXYhYh

YXICsX EXExf

Return

91



Probability of error for uncoded transmissions

)(!

2

0m

AWGNe

m

mA

e PmAeP

-40 -30 -20 -10 0 10 2010

-7

10-6

10-5

10-4

10-3

10-2

10-1

100

dmin / [in dB]

Pro

babi

lity

of e

rror

Probability of error (Uncoded Transmission)

AWGN

Class A: A = 0.1, = 10-3

12 A

m

m

BPSK uncoded transmissionOne sample per symbolA = 0.1, Γ = 10-3

[Haring & Vinck, 2002]

Return

92



Chernoff factors for coded transmissions

N

kkk ccC

PPEP

1

'

'

),,(min

)(

ll

cc

-20 -15 -10 -5 0 5 10 1510

-3

10-2

10-1

100

dmin / [in dB]

Che

rnof

f Fac

tor

Chernoff factors for real channel with various parameters of A and MAP decoding

Gaussian

Class A: A = 0.1, = 10-3

Class A: A = 0.3, = 10-3

Class A: A = 10, = 10-3

PEP: Pairwise error probability

N: Size of the codeword

Chernoff factor:

Equally likely transmission for symbols

),,(min ' ll kk ccC

Return

93

Performance Bounds (2x2 MIMO)


Return

94



Channel capacity

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

System Model

Return

95



Channel capacity in presence of RFI for 2x2 MIMO

System Model

Capacity

-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 = 0.01, 2 = 0.1, k = 0.4

Return

96



Probability of symbol error for uncoded transmissions

Parameters:A = 0.1, 1 = 0.01,2 = 0.1, k = 0.4

Pe: Probability of symbol error

S: Transmitted code vector

D(S): Decision regions for MAP detector

Equally likely transmission for symbols

Return

97



Chernoff factors for coded transmissions

N

ttt ssC

ssPPEP

1

'

'

),,(min

)(

ll

PEP: Pairwise error probabilityN: Size of the codewordChernoff factor:Equally likely transmission for symbols

),,(min ' ll kk ccC

-30 -20 -10 0 10 20 30 4010

-8

10-6

10-4

10-2

100

dt2 / N0 [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 = 0.01,2 = 0.1, k = 0.4

Return

98


Cutoff rates for coded transmissions Similar measure as channel capacity Relates transmission rate (R) to Pe for a length T codes


Return

99



Cutoff rate

-30 -20 -10 0 10 20 30 400

0.5

1

1.5

2

2.5

3

3.5

4

SNR [in dB]

Cut

off R

ate

[bits

/tran

smis

sion

]

BPSK, Middleton noiseBPSK, Gaussian noiseQPSK, Middleton noiseQPSK, Gaussian noise16QAM, Middleton noise16QAM, Gaussian noise

Return

100


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 over all subcarriers, reducing 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 As number of subcarriers increase, impulsive noise case

approaches the Gaussian noise case [Haring 2003]

Return

Turbo Codes in Presence of RFI


101

Decoder 1Parity 1Systematic Data

Decoder 2

Parity 2

1

-

-

-

-

A-priori Information

Depends on channel statistics

Independent of channel statistics

Gaussian channel:

Middleton Class A channel:

Independent of channel statistics

Extrinsic Information

Leads to a 10dB improvement at BER of 10-5 [Umehara03]

Return

RFI Mitigation Using Error Correction


102

Decoder 1Parity 1

Systematic Data

Decoder 2

Interleaver

Parity 2 Interleaver

-

-

-

-

Interleaver

Turbo decoder

Decoding depends on the RFI statistics 10 dB improvement at BER 10-5 can be achieved using

accurate RFI statistics [Umehara, 2003]

Return

Usage Scenario #1


103

User System Simulator(e.g. WiMAX simulator)

RFI Generation•RFI_MakeDataClassA.m•RFI_MakeDataAlphaStable.m….….

Parameter Estimation

•RFI_EstMethodofMoments.m•RFI_EstAlphaS_Alpha.m….….

Receivers•RFI_myriad_opt.m•RFI_BiVarClassAMLRx.m….….

RFI Toolbox

Return

Usage Scenario #2104

Measured RFI data

RFI Toolbox Statistical Modeling DEMO

SISO Communication Performance DEMO File Transfer DEMOMIMO Communication

Performance DEMO


Return

design of interference-aware wireless communication systems

Documents

presence of class

noise modelsmiddleton

communications groupresults

yesyesextensions of

communications groupextensions

gaussian distribution

uncorrelated noise

input distribution