narrowband interference parameterization for sparse

Narrowband Interference Parameterization forSparse Bayesian Recovery

Anum Ali1, Hesham Elsawy1, Tareq Y. Al-Naffouri1,2, andMohamed-Slim Alouini1

1King Abdullah University of Science and Technology, Thuwal, Saudi Arabia.2King Fahd University of Petroleum and Minerals, Dhahran, Saudi Arabia.

June 09, 2015

Bayesian Interference Mitigation for SC-FDMA Anum Ali et. al. 1/17

Content

1 Introduction

2 Bayesian Sparse Recovery

3 Interference Parameterization

4 Simulation Results

InterferenceMitigation

CompressedSensing

StochasticGeometry


Introduction

Single Carrier-FDMA (SC-FDMA) is used in LTE uplink [1]

Narrowband Interfer-ence (NBI) Sources

Coexistingsystems inunlicensed bands

Garage dooropeners

Cordless phonesetc


[1] H. G. Myung, J. Lim, and D. Goodman, “Single carrier FDMA for uplink wireless transmission,” IEEEVeh. Technol. Mag., vol. 1, no. 3, pp. 30-38, 2006.

Introduction

Interference Impact on SC-FDMA

A single strong interference source can completely destroy thedata in single carrier-FDMA

0 32 64 96 128

0

0.2

0.4

0.6

0.8

1

Subcarrier Index

Nor

mal

ized

Rec

eive

dS

ign

al SC-FDMAInterference


Bayesian Sparse Recovery

How and Why?

Active interference on few frequencies −→ CompressedSensing based recovery is possible

Randomly chosen data points are kept data free to senseinterference at the receiver

Size M observation

vector

Measurement matrix

Sparse NBI

noiseThe unknown size

N NBI vector

Active NBI Sources



Sparse Signal Recovery Approaches

Bayesian (utilizeprior statistics)

• FBMP

• SBL

Convex optimization(robust)

• BP

• BPDN

• LASSO

Greedy (fast)

• OMP

• CoSaMP

• StOMP

Use Bayesian schemesfor sparse recovery

Low computationalcomplexityGood reconstructionaccuracyAcknowledgeGaussianity of noise



Fast Bayesian Matching Pursuit (FBMP) [2]

Low complexity

minimum meansquared error(MMSE) estimation

Gaussian prior

FBMP

statistics

Simple,Accurate

no statistics

Boostrap,Complex


[2] P. Schniter, L. C. Potter, and J. Ziniel, “Fast Bayesian matching pursuit,” in Proc. Inform. Theory &Appl. Workshop, 2008, pp. 326-333.


Fast Bayesian Matching Pursuit (FBMP) [2]

Low complexity

minimum meansquared error(MMSE) estimation

Gaussian prior

FBMP

statistics

Simple,Accurate

no statistics

Boostrap,Complex

73Challenge: → How to estimate mean, variance, and sparsity rate.


[2] P. Schniter, L. C. Potter, and J. Ziniel, “Fast Bayesian matching pursuit,” in Proc. Inform. Theory &Appl. Workshop, 2008, pp. 326-333.

Interference Parameterization


1: Transmiter Power2: PathLoss Coefficient3: Location



1: Transmiter Power X2: PathLoss Coefficient X3: Location ?


Homogenous Poisson Point Process

Tractable Analysis [3]

Accurate expressions

Widely used

Applicable to diverse typesof networks

ad-hoc networkscellular networks

Process→ Ψ, Intensity→ λ

Iagg=∑

i∈Ψ

√E si hi

AggregateInterference

TransmittedEnergy

ChannelIncludingPathloss

TransmittedSymbol


[3] H. ElSawy, E. Hossain, and M. Haenggi, “Stochastic geometry for modeling, analysis, and design ofmulti-tier and cognitive cellular wireless networks: A survey,” IEEE Commun. Surveys and Tutorials, vol.15, no. 3, pp. 996-1019, 2013.


For interference Iagg =∑

i∈Ψ

√Esihi , Characteristic Function (CF) is

Φ(ω) = exp

−λπγ2

+∞∑q=1

ΥqE[|s|2q

]( |ω|2EΩ

γ2b

)q

Obtain mean and variance by differentiating the CF

µIagg = E [Iagg] = −1Φ′(0) = 0

σ2Iagg = E

[|Iagg|2

]= −2Φ′′(0) = 2πλγ2Υ1E

[|s|2] (

EΩγ2b

)



Gaussian Assumption

Sparsity Rate

ρ dominant elements

N − ρ elements atnoise level

Decide a threshold ξa.

Assume Gaussianityon interference

0 16 32 48 640

0.2

0.4

0.6

0.8

1

Subcarrier Index

Normalized

Interferen

ce

Threshold ξ

s =2ρ

NQ(4√INR−1) + 2

N − ρN

Q(4)

INR: Impulse-to-noise ratio, Q(·) is Q function.


a. We use ξ = 4√σ2z .

Results

Mean and Variance as a function of intensity λ

10−1 100 101−1

−0.5

0

0.5

1

λ

µI a

gg

SimulationAnalysis

10−1 100 1010

1

2

3

4

λ

σ2 I a

gg

SimulationAnalysis

SimulationParameters:

b=2

γ=2m

R=20m

Subcarriers=256

Users=2

Modulation=64QAM


Results

Mean and Variance as a function of pathloss coefficient b

1.5 2 2.5 3 3.5 4−1

−0.5

0

0.5

1

b

µI a

gg

SimulationAnalysis

1.5 2 2.5 3 3.5 4

0

0.5

1

b

σ2 I a

gg

SimulationAnalysis


λ=1

γ=2m

R=20m

Subcarriers=256

Users=2

Modulation=64QAM


Results

Sparsity rate as a function of INR and dominant elements ρ

30 35 40 45 500

0.05

0.1

Impulse-to-Noise Ratio (dB)

Sparsity

SimulationAnalysis

ρ = 10

8 24 40 56 720

0.15

0.3

Dominant elements - ρ

Sparsity

SimulationAnalysis

INR=40dB


ξ = 4√σ2Z

γ=2m

R=20m

Subcarriers=256

Users=2

Modulation=64QAM


Results

BER performance of the proposed scheme

5 10 15 20 25

10−3

10−2

10−1

Eb/N0 (dB)

BER

ImpairedPoor Init.

Poor Init. (Ref) (L = 10)AnalyticalNumericalInterference free

5 10 15 20 25

0.2

0.4

0.6

0.8

1

Eb/N0 (dB)

Normalized

RunTim

e

Poor Init. (Ref) (L = 10)AnalyticalNumericalPoor Init.

Simulation Parameters:Measurements= 25%,SIR=−10dB, ρ=4,Subcarriers=256, Users=2,Modulation=64 QAM


Summary

Interference has a dire impact of SC-FDMA systems

Compressed sensing can be used to mitigate interference

Bayesian compressed sensing has good performance and lowcomplexity

Bayesian schemes require interference parameters

Parameters can be obtained analytically using stochasticgeometry

Analytical parameter estimation reduces computationalcomplexity significantly


Thank you for your Attention!


narrowband interference parameterization for sparse

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