using multiple power spectrum measurements to sense...

UsingMultiplePowerSpectrumMeasurementstoSenseSignalswith

PartialSpectralOverlapMihirLaghateandProf.Danijela Cabric

7th March2017IEEEDySPAN 2017,Baltimore

D. Markovic / Slide 2

Outline

w Goals,Motivation,andExistingWorkw SystemModel

– Assumptions– Time-FrequencyMap

w Non-NegativeMatrixFactorization(NNMF)– Challengeswithexistingalgorithms

w ProposedAlgorithm:GreedyEnergyMinimizingNNMFw MATLABSimulationResultsw USRPMeasurementResultsw ConclusionsandFutureWork

2


Goals

Thatis,w Countnumberofsignalsrcvdw Detectsets ofdiscreteFourier

transformbinsoccupiedbyeachsignal

3

[1] M. Laghate and D. Cabric, “Using the Time Dimension toSense Signals with Partial Spectral Overlap,” in IEEEGLOBECOM, Washington, USA, 2016.

Estimatenoisepowerspectrum

Challenges:– Colorednoise– Spursandalways-oninterferers

DistinguishSignalswithSpectralOverlap


MotivatingApplications

– IEEE802.11nin5GHzbands– LTE-Advanced

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Image Source:Wikipedia“ListofWLANchannels”

LTECarrierAggregation [2][2] H. J. Wu et al., “A wideband digital pre-distortion platform with 100 MHz instantaneous bandwidth for LTE-advanced applications,” in 2012 Workshop on Integrated Nonlinear Microwave and Millimetre-Wave Circuits, 2012, pp. 1–3.

– IEEE802.11b/gchannelsin2.4GHz

– ChannelbondinginIEEE802.11n

LackofGuardBands

Spectraloverlapbydesign Measurements@UCLA


ExistingWorkforDistinguishingSignals

5

Based on Blind SingleAntenna

SpectralOverlap

DetectBands

BlindtoChannel

Transmission protocols[4],[5] û ü ü ü ü

Cyclicfrequency[7] û ü ü û ü

Channelmodel &location[6] û ü ü û û

Angle ofArrival[8] ü û ü û û

RandomMatrixTheory[9] ü û ü û ü

MultipleCRs[10],[11] ü û û ü ü

PowerSpectrumThreshold[12] ü ü û ü üMultiplePowerSpectrumMeasurements ü ü ü ü ü

Proposedmethodandourpriorwork[1]


SystemModel

Widebandsensorw BasebandbandwidthW Hzw AdditivewidesensestationaryGaussiannoise𝜈 𝑡 ∈ ℝ%&

w WelchpowerspectrumestimatorusingFFToflengthF

IncumbentUsersw M distinctfrequencybandsw mth bandhasUm transmitterswithfreq.supportBm DFTbins

– Powerspectrumreceivedfromuth transmitter:𝑋(,* ∈ ℝ%&

– Activity𝑎(,* 𝑡 ∈ 0,1 isfractionoftth measurementthatuth

transmitterinmth bandisactive

w Receivedpowerspectrum:

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Time-FrequencyMap:1user/bandw Time-Freq.mapE ofreceivedenergy:E = [Y[1] Y[2] … Y[T]]T

w Definematrices:Atm= am[t],Smf = Xm( f ),andΔ/0 = 𝜈 𝑡 𝑓

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=

+

+

E A= S +D

E

(1) (1)A ´S

Output computed by Non-Negative Matrix Factorization (NNMF) when given M = 3

Input:SimulatedPowerSpectrum

Output:Time-FreqofEachTx

(2) (2)A ´S

(3) (3)A ´S

Example:M = 3, F = 512, T = 30 Y [t] = am,u

u=1

Um

∑m=1

M

∑ [t]Xm,u[t]+ν[t]


Non-NegativeMatrixFactorization(NNMF)

w Let𝑀4 =Estimatednumberofreceivedsignalsw NNMFfinds,tominimize

Challenges:w Estimating𝑀4 ishardwhen

w Non-convexcostfunctionÞ convergencetoglobalminimanotguaranteed

w CostfunctionisnotprobabilisticÞ Notrobusttonoise

w Non-uniquesolutionandisnotbinaryÞ ,i.e.,thresholdingwillnotdetectalloccupiedDFTbins

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2ˆ ˆ FE A- S

T F<

AS » S/ S

A∈! +T ×M Σ ∈! M×F


PriorWork:NNMF-basedAlgorithm

9

Initialization

NNMFofwith signals

Increment

No

DetectOccupiedBandsYes

ˆ 1M =

EnergyDetectionE

'E'E

Mˆ ˆ,A S

M

{ }ˆ1 2ˆ ˆ ˆ, ,..., 0,..., 1MB B B FÌ -

Noisebanddetected?

ˆ 4M =

Significantsignalenergy

NoiseBand

ReconstructedFactorsfor

“Leaked”energy


MotivatingNNMFAlgorithm:RobustXRay

i.e.,conewithreceivedpowerspectraasextremerays

RecursiveAlgorithm:1. Choosepointwithmaximum residual

asextremeray2. Measureresidualtoallmeasurements3. Repeat1untilallmeasurementsliewithincone

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[13] A. Kumar, V. Sindhwani, and P. Kambadur, “Fast conical hull algorithms for near-separable non-negative matrix factorization,” in International Conference on Machine Learning, 2013.

Image source: [13]

E Y [t] | a[t][ ] = am,u[t]E Xm,u[t]⎡⎣ ⎤⎦u=1

Um

∑m=1

M

∑ + E ν[t][ ]


Separability Assumption

i.e.,conewithreceivedpowerspectraasextremerays

Separability Assumption:Requiresatleastonemeasurementofeachextremerayw Atleastonenoiseonlymeasurementw Foreachtransmitter,atleastonemeasurementwhereitisthe

onlyactivetransmitter

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[14] D. Donoho and V. Stodden, “When Does Non-Negative Matrix Factorization Give a Correct Decomposition into Parts?,” in Advances in Neural Information Processing Systems, MIT Press, 2004, pp. 1141–1148.

Image source: [13]

E Y [t] | a[t][ ] = am,u[t]E Xm,u[t]⎡⎣ ⎤⎦u=1

Um

∑m=1

M

∑ + E ν[t][ ]


ProposedGreedyEnergyMinimizingNNMF

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Welch Power Spectrum Estimator

No

Energy Detection on Detected Signals

Yes

Received Signal

Append to Time Frequency Map E

Ø Center FrequencyØ Bandwidth

Detect Noise-Only Measurements ℒ

ℒ ≜ Measurements that are linear combinations

of Detected Signals

Noise power spectrum learned from data1. Initialize noise estimate as min. energy measurement2. Estimate noise as mean of measurements with

Mahalanobis distance < t to est. noise distribution3. Repeat Step 2 until convergence

Index in 1,… , 𝑇 \ℒ with Lowest Energy labelled

as Detected Signal

ℒ = 𝑇?


ProposedGreedyEnergyMinimizingNNMF

13

Welch Power Spectrum Estimator

No

Energy Detection on Detected Signals

Yes

Received Signal

Append to Time Frequency Map E

Ø Center FrequencyØ Bandwidth

Detect Noise-Only Measurements ℒ

ℒ ≜ Measurements that are linear combinations

of Detected Signals

Noise power spectrum learned from data1. Initialize noise estimate as min. energy measurement2. Estimate noise as mean of measurements with

Mahalanobis distance < t to est. noise distribution3. Repeat Step 2 until convergence

Index in 1,… , 𝑇 \ℒ with Lowest Energy labelled

as Detected Signal

ℒ = 𝑇?

Constrained least squares minimization estimates activity1. Activity for noise ∈ (−∞, 1]2. Activity for detected signals ∈ [0,∞)

»0.3´ +0.2´ + 0.5´

Measurement Detected Signal 1 Detected Signal 2 Noise Estimate


PerformanceMetrics

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w Numberofdetectedbandsw Numberofextrabandsdetectedw RelativeErrorsinCenterFrequencyandBandwidth


PerformanceMetrics

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OurOutput

GroundTruthFullyConnectedBipartiteGraph

ComputedusingMaximumWeightMatching

EdgeWeights:

SymmetricDifference

1B 2B

2B 3B1B

9 564 8 10

w Numberofdetectedbandsw Numberofextrabandsdetectedw RelativeErrorsinCenterFrequencyandBandwidth

δ Bm1 , Bm2( ) = F − Bm1 ! Bm2


MATLABSimulations:Performancevs.TReceiver:w Bandwidth100MHzw 512lengthFFT,averageof64

windowedoverlappingsegmentsw Upto50measurements,i.e.,8.32msw Parameters:Pfa = 0.01, 𝜏r = 0.1

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802.11gTransmitters:w Eachnetwork=1AP+2STAsw Channels1,4,6,8,11w Saturateduplinkanddownlinkflowsw Shadowfadingchannelswith6dB

variance

NumberofDetectedSignals NumberofExtraSignals


Simulation:Performancevs.SpectralOverlap

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NumberofDetectedSignals

NumberofExtraSignals

RelativeErrorinBandwidth

FrequencyError


USRPMeasurements:Example

w Device:USRPN210withCBXdaughtercard

w Measurementsat2.452GHzw 8-bitsamples@50MS/s

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ColoredNoiseLearnt

802.11SignalsDetected

USRPMeasurements

Black arrows: detected supportsLabels: corresponding 802.11 channels


MultipleUSRPMeasurements

w Contourplotof2Dhistogramofdetectedcenterfrequenciesandbandwidths

w [email protected]

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AndroidWiFiAnalyzerusedtoconfirm802.11channels6,7,8,and11inuse


ConclusionsandFutureWork

w Noisepowerspectrumcanbeestimatedautomaticallywhensensingcommunicatingincumbentusers

w Multiplepowerspectrummeasurementscandistinguishrealworldspectrallyoverlappedsignalseveninunknownchannels

w Conventionalsignaldetectionandestimationtheorymaynotbesufficient

FutureWork:w Findstructuralpropertiesofoptimizationproblemtoreduce

computationalcomplexityw Estimatetimeofactivity,i.e.,,foruseintrafficestimation

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A

Thankyou!

Questions?

ThismaterialisbaseduponworksupportedbytheNationalScienceFoundationunderGrantNo.1527026:DynamicSpectrumAccessbyLearningPrimaryNetworkTopology


SelectedReferences[1] M. Laghate and D. Cabric, “Using the Time Dimension to Sense Signals with Partial Spectral Overlap,” in IEEE GLOBECOM, Washington, USA, 2016.[2] H. J. Wu et al., “A wideband digital pre-distortion platform with 100 MHz instantaneous bandwidth for LTE-advanced applications,” in 2012 Workshop on Integrated Nonlinear Microwave and Millimetre-Wave Circuits, 2012, pp. 1–3.[3] Z. Quan, S. Cui, A. H. Sayed, and H. V. Poor, “Optimal Multiband Joint Detection for Spectrum Sensing in Cognitive Radio Networks,” IEEE Transactions on Signal Processing, 2009.[4] I. Bisio, M. Cerruti, F. Lavagetto, M. Marchese, M. Pastorino, A. Randazzo, and A. Sciarrone, “A Trainingless WiFi Fingerprint Positioning Approach Over Mobile Devices,” IEEE Antennas Wirel. Propag. Lett., vol. 13, pp. 832–835, 2014.[5] M. Ibrahim and M. Youssef, “CellSense: An Accurate Energy-Efficient GSM Positioning System,” Veh. Technol. IEEE Trans. On, vol. 61, no. 1, pp. 286–296, Jan. 2012.[6] H. Yilmaz, T. Tugcu, F. Alago¨z, and S. Bayhan, “Radio environment map as enabler for practical cognitive radio networks,” IEEE Commun. Mag., vol. 51, no. 12, pp. 162–169, Dec. 2013.[7] S. Chaudhari and D. Cabric, “Cyclic weighted centroid localization for spectrally overlapped sources in cognitive radio networks,” in 2014 IEEE Global Communications Conference (GLOBECOM), Dec. 2014, pp. 935–940.[8] J. Wang and D. Cabric, “A cooperative DoA-based algorithm for localization of multiple primary-users in cognitive radio networks,” in IEEE GLOBECOM, Dec. 2012, pp. 1266–1270.[9] L. Wei, P. Dharmawansa, and O. Tirkkonen, “Multiple Primary User Spectrum Sensing in the Low SNR Regime,” IEEE Transactions on Communications, vol. 61, no. 5, pp. 1720–1731, May 2013.[10] M. Laghate and D. Cabric, “Identifying the presence and footprints of multiple incumbent transmitters,” in 2015 49th Asilomar Conference on Signals, Systems and Computers, 2015, pp. 146–150.[11] M. Laghate and D. Cabric, “Cooperatively Learning Footprints of Multiple Incumbent Transmitters by Using Cognitive RadioNetworks,” submitted to IEEE Transactions on Cognitive Communications and Networking, Sept. 2015.[12] T.-H. Yu, O. Sekkat, S. Rodriguez-Parera, D. Markovic, and D. Cabric, “A Wideband Spectrum-Sensing Processor With Adaptive Detection Threshold and Sensing Time,” IEEE Transactions on Circuits and Systems I: Regular Papers, vol. 58, no. 11,pp. 2765–2775, Nov. 2011.[13] A. Kumar, V. Sindhwani, and P. Kambadur, “Fast conical hull algorithms for near-separable non-negative matrix factorization,” in International Conference on Machine Learning, 2013.[14] D. Donoho and V. Stodden, “When Does Non-Negative Matrix Factorization Give a Correct Decomposition into Parts?,” in Advances in Neural Information Processing Systems, MIT Press, 2004, pp. 1141–1148.

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