narrowband interference parameterization for sparse
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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
Bayesian Interference Mitigation for SC-FDMA Anum Ali et. al. 2/17
Introduction
Single Carrier-FDMA (SC-FDMA) is used in LTE uplink [1]
Narrowband Interfer-ence (NBI) Sources
Coexistingsystems inunlicensed bands
Garage dooropeners
Cordless phonesetc
Bayesian Interference Mitigation for SC-FDMA Anum Ali et. al. 3/17
[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 Interference Mitigation for SC-FDMA Anum Ali et. al. 4/17
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
Bayesian Interference Mitigation for SC-FDMA Anum Ali et. al. 5/17
Bayesian Sparse Recovery
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
Bayesian Interference Mitigation for SC-FDMA Anum Ali et. al. 6/17
Bayesian Sparse Recovery
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
Bayesian Interference Mitigation for SC-FDMA Anum Ali et. al. 6/17
Bayesian Sparse Recovery
Fast Bayesian Matching Pursuit (FBMP) [2]
Low complexity
minimum meansquared error(MMSE) estimation
Gaussian prior
FBMP
statistics
Simple,Accurate
no statistics
Boostrap,Complex
Bayesian Interference Mitigation for SC-FDMA Anum Ali et. al. 7/17
[2] P. Schniter, L. C. Potter, and J. Ziniel, “Fast Bayesian matching pursuit,” in Proc. Inform. Theory &Appl. Workshop, 2008, pp. 326-333.
Bayesian Sparse Recovery
Fast Bayesian Matching Pursuit (FBMP) [2]
Low complexity
minimum meansquared error(MMSE) estimation
Gaussian prior
FBMP
statistics
Simple,Accurate
no statistics
Boostrap,Complex
Bayesian Interference Mitigation for SC-FDMA Anum Ali et. al. 7/17
[2] P. Schniter, L. C. Potter, and J. Ziniel, “Fast Bayesian matching pursuit,” in Proc. Inform. Theory &Appl. Workshop, 2008, pp. 326-333.
Bayesian Sparse Recovery
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.
Bayesian Interference Mitigation for SC-FDMA Anum Ali et. al. 7/17
[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
Bayesian Interference Mitigation for SC-FDMA Anum Ali et. al. 8/17
1: Transmiter Power2: PathLoss Coefficient3: Location
Interference Parameterization
Bayesian Interference Mitigation for SC-FDMA Anum Ali et. al. 8/17
1: Transmiter Power X2: PathLoss Coefficient X3: Location ?
Interference Parameterization
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
Bayesian Interference Mitigation for SC-FDMA Anum Ali et. al. 9/17
[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.
Interference Parameterization
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
)
Bayesian Interference Mitigation for SC-FDMA Anum Ali et. al. 10/17
Interference Parameterization
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.
Bayesian Interference Mitigation for SC-FDMA Anum Ali et. al. 11/17
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
Bayesian Interference Mitigation for SC-FDMA Anum Ali et. al. 12/17
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
SimulationParameters:
λ=1
γ=2m
R=20m
Subcarriers=256
Users=2
Modulation=64QAM
Bayesian Interference Mitigation for SC-FDMA Anum Ali et. al. 13/17
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
SimulationParameters:
ξ = 4√σ2Z
γ=2m
R=20m
Subcarriers=256
Users=2
Modulation=64QAM
Bayesian Interference Mitigation for SC-FDMA Anum Ali et. al. 14/17
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
Bayesian Interference Mitigation for SC-FDMA Anum Ali et. al. 15/17
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
Bayesian Interference Mitigation for SC-FDMA Anum Ali et. al. 16/17
Thank you for your Attention!
Bayesian Interference Mitigation for SC-FDMA Anum Ali et. al. 17/17
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