Fading Modeling, MIMO Channel Generation, and Spectrum Sensing for Wireless Communications

1
Fading Modeling, MIMO Channel Generation, and
Spectrum Sensing for Wireless Communications

• Wei-Ho Chung
• Electrical Engineering
• University of California, Los Angeles
• April 2009
• whc_at_ee.ucla.edu

2
Outline

• Introduction-Fading Channels
• Fading Channel Model by Modified Hidden
  Semi-Markov Model
• Generating Correlated MIMO Fading Channel
• Detection and Decision Fusion in Fading
  Environment
• Sequential Likelihood Ratio Test for Spectrum
  Sensing
• Future Work
• Conclusions

3
Fading Effects

• In wireless communications, the signals traverse
  from the transmitter to the receiver
• The medium (channel) physically influences the
  signals, including
• Reflection
• Signal impinges on the smooth surface
• Surface dimension much larger
• than Wavelength
• Diffraction
• Signals impinges the edge or corner of the dense
  entity
• Secondary signals spread out from the impinged
  edge
• Non-line-of-sight (NLOS) communications
• Scatter
• Signals impinge a rough surface
• The roughness at the order of the wavelength or
  less

B. Sklar, IEEE Communications Magazine, 1997.
4
Fading Models and Applications

• The fading channel model is the mathematical
  description of the fading channel
• Stochastic
• Mobile communication systems
• Mobile node moving, various fading effects
• Quasi-deterministic
• Transmitter and receiver are relatively static
• Fading effects can be approximately deterministic
• Applications of fading channel model include
• Performance analyses, e.g. bit error rate
• Channel capacity Biglieri 98
• Outage probability
• Power control Caire 99
• Channel coding Hall 98
• Adaptive modulation Goldsmith 98

5
Flat Fading

• Fading channel is modeled as a linear
  time-variant system with the impulse response
• represents the time index of filter
  response
• represents the time dependence of the
  filter response
• Delay spread of the filter response , the
  coherence bandwidth
• Flat fading channel, bandwidth of input signal
  smaller than coherence bandwidth
• Multiplicative effect on the transmitted signal
• The fading channel model is focused on modeling
  the statistical properties of

S. Stein, IEEE JSAC, 1987
6
Related Work

• Rayleigh, Rice, and Nakagami distributions have
  been investigated to model flat fading channel
  P. Beckman, 1967
• Rayleigh model
• Large amount of scattered signals
• Central limit theorem
• Rician model
• Dominant impinging signal
• Larger amount of scattered signals
• Markov Chain Tan and Beaulieu, IEEE Tran. Comm.,
  2000
• Gilbert-Elliott model
• Two states, the good (high SNR) and bad states
  (low SNR).
• The Ray-Tracing Model Rizk 97
• Trace the geometry in signal propagation
• Trace reflections, diffractions, and scatters
• Site-specific information

7
Outline

• Introduction-Fading Channels
• Fading Channel Model by Modified Hidden
  Semi-Markov Model
• Generating Correlated MIMO Fading Channel
• Detection and Decision Fusion in Fading
  Environment
• Sequential Likelihood Ratio Test for Spectrum
  Sensing
• Conclusions

8
Multi-Modal Observations

• Envelope PDFs can have multi-modes
• LOS v.s. NLOS
• Time-Variant Fading Conditions
• Simulation
• Experiment

9
Modified Hidden Semi-Markov Model

• Amplitude-based Finite-State Markov Chains Model
  (AFSMCM)
• Output channel amplitude
• Hidden Markov Model (HMM)
• Output channel amplitude probabilistically
• Hidden Semi-Markov Model (HSMM)
• State duration probability

10
Properties

• AFSMCM
• Output vector
• Transition matrix P
• ACF
• PDF Steady-state probability
• HMM
• Independent samples
• PDF Mixtures of steady-state prob. and output
  PDF
• HSMM
• Independent samples

11
Modified Hidden Semi-Markov Model

• Model scenarios
• LOS v.s. NLOS
• High speed v.s. Low speed
• Segmentation by features
• Channel gain
• Entropy of energy distribution

W. Chung and K. Yao, "Modified Hidden
Semi-Markov Model for Modelling the Flat Fading
Channel," IEEE Tran. Comm., June, 2008.
12
Parameter Estimation of MHSMM
13
Clustering in the Feature Domain

• Perform k-means Clustering
• For a specific k, generate clusters and centers
• Detect Number of States
• Davis-Bouldin Bezdek 98
• Within-cluster scatter/Between-cluster
  separation
• Pursue small Davis-Bouldin Index for good
  clustering
• Dunn Dunn 73
• Min inter-cluster distance/Cluster diameter
• Pursue large Dunn Index for good clustering
• Percentage of residual explained Aldenderfer 84
• Between-group variance/Total variance
• Elbow rule

14
Parameter estimation

• ACF Sample ACF, i.e.,
• PDF

15
Segmentation Example
16
Clustering
17
Estimated pdf

• Kolgomorov D-statistic

MHSMM 0.02
AFSMCM 0.06
HMM 0.17
18
Estimated ACFs
19
Experiment
20
Experimental Data-Hallway

• Hallway inside building
• Rush hours
• Numerous reflectors and scatters
• Non-cooperative disturbances

21
Summary

• Model Nonstationary Fading Processes
• Various channel conditions
• Piece-wise stationary processes
• Model the PDFs and ACFs
• Model Estimation Scheme
• Channel segmentation
• Parameter estimation

22
Outline

• Introduction-Fading Channels
• Fading Channel Model by Modified Hidden
  Semi-Markov Model
• Generating Correlated MIMO Fading Channel
• Detection and Decision fusion in Fading
  Environment
• Sequential Likelihood Ratio Test for Spectrum
  Sensing
• Future Work
• Conclusions

23
Generating Correlated MIMO Channels

• Motivations
• Channels Codes
• Modulations
• Diversity Combining
• MIMO systems
• Generate multiple channels that have specific
• Auto-correlation function (ACF)
• Cross-correlation function (CCF)
• Envelope pdfs

24
Multiple Channels

• Space-Time correlation model
• Jakes model by Bessel function Jakes 94
• Spatial and temporal correlations
• Multiple mobile fading channels Abidi 02
• MIMO channel for non-isotropic scattering
  environment
• MIMO channel for omnidirectional antennas Rad
  05

25
Example of Time-Space model
Rad and Gazor, 05
26
Channel Generation by Autoregressive Processes

• Channels and Covariance Matrix
• AR processes

Baddour and Beaulieu, "Accurate Simulation of
multiple cross-correlated Rician fading
channels," IEEE Tran. on Comm., Nov. 2004.
27
Solve AR parameters

• AR Coefficient
• Covariance of Noise

28
Simulation by Autoregressive Processes
29
Generating Correlated Nakagami

• Nakagami channels
• Measurements M. Nakagami,1960 H. Suzuki, 1977
• Modulation Alouini and Goldsmith, 2000
• Diversity Combining Beaulieu and Abu-Dayya,
  1991
• Gaussian Random Variable is Well Researched
• Operate on Gaussian RV
• Notation
• Process
• Problem

Q. T. Zhang, "A decomposition technique for
efficient generation of correlated Nakagami
fading channels, IEEE JSAC, 2000.
30
Generating Correlated Nakagami

• Generate
• Relating covariance matrices

31
Heterogeneous MIMO channel generation

• Previous works focus on PDFs of the same family,
  e.g., Rayleigh Baddour 2004 , Nakagami Zhang
  2000
• Fading environment causes channels of various
  properties-channels of different families
• Generate multiple channels that have specific
• Auto-correlation function (ACF)
• Cross-correlation function (CCF)
• Heterogeneous envelope PDFs

32
Illustration of the problem

• ?

33
Inverse Transform Sampling

• Framework
• Probability density functions
• Correlations
• Inverse Transform Sampling
• Generate x with CDF
• y has CDF

34
Proposed approachInverse Transform Sampling
W. Chung, K. Yao, and R. E. Hudson, The Unified
Approach for Generating Multiple Cross-correlated
and Auto-correlated Fading Envelope Processes.
Accepted. IEEE Tran. Comm., 2009.
35
Sketch of derivation

• Definition of correlation
• Jacobian
• Correlations of input and output

36
Example- Heterogeneous channels of Nakagami,
Rician, and Rayleigh pdfs

• Three channels
• Nakagami
• Rician
• Rayleigh
• Correlations
• ACF
• CCF

37
Results
38
Example- Heterogeneous Channels of Nakagami,
Rician, and Rayleigh pdfs
39
Example- 2x2 Rayleigh MIMO Channels

• PDF
• ACFs

40
Example- 2x2 Rayleigh MIMO Channels

• CCFs

41
Example-Single Nakagami Channel

• ACF
• High sampling rate
• Low sampling rate

42
Outline

• Introduction-Fading Channels
• Fading Channel Model by Modified Hidden
  Semi-Markov Model
• Generating Correlated MIMO Fading Channel
• Detection and Decision Fusion in Fading
  Environment
• Sequential Likelihood Ratio Test for Spectrum
  Sensing
• Future Work
• Conclusions

43
Detection and Decision Fusion in Fading
Environment

• Detection by Single sensor
• Hypothesis test
• Cognitive radio
• Decision Fusion using Multiple Sensors
• Detection by Single Sensor under Fading
• Multi-Sensor Decision Fusion under Fading

44
Hypothesis Test

• Hypothesis Test applications
• Surveillance
• Target Detection
• Spectrum Sensing
• Example-Matched Filter Detection
• Signal model

45
Receiver Operating Curve

• Receiver Operating Curve v.s.
• Setting Threshold
• Criteria
• Neyman-Pearson
• upper-bounded
• Bayes
• Priors and costs

46
Spectrum Sensing in Cognitive Radio

• Wireless communications rely on spectra.
• Current usage model frequency bands are
  licensed.
• The licensed bands are often vacant- low
  utilizations.
• Cognitive Radio-to increase the spectrum
  utilization.
• Allows secondary user to access the spectrum when
  it is vacant.
• Secondary users sense the spectrum before
  accessing.
• Accuracies of the spectrum sensing is crucial.
• Formulated as binary hypothesis test problem
• H0 Spectrum Vacant
• H1 Spectrum Occupied

S. Haykin, "Cognitive radio brain-empowered
wireless communications," IEEE JSAC. 2005.
47
Detection Criteria and Implications in Cognitive
Radio

• Interpretations of PD and PFA in cognitive radio
• Detection performed by the secondary users
• H1 Spectrum used by the primary users
• Secondary users access the spectrum if decision
  is H0
• Channel conflict Decision H0 under the truth H1
• Miss of the spectrum opportunity Decision H1
  under the truth H0
• Neyman-Pearson
• Upper-bound probability of false alarm while
  maximizing probability of detection
• Protect the spectrum opportunities of the
  secondary users while minimizing the channel
  conflicts
• Lower-Bounded Probability of Detection (LBPD)
  Chung 08
• Lower-bound probability of detection while
  minimizing probability of false alarm
• Protect the primary users while maximizing the
  spectrum opportunities for the secondary users

48
Decision Fusion Framework

• Sensors make binary decisions.
• Many applications require binary decisions.
• Accuracy of a single sensor is limited.
• Fusion of multiple decisions increases
  accuracies.

R. Viswanathan and P. K. Varshney,
"Distributed Detection with Multiple sensors I.
Fundamentals," Proceedings of the IEEE, 1997.
49
Decision Fusion Framework

• N sensors make binary decisions.
• Probability of False Alarm
• Probability of Detection
• Sensor decisions
• The fusion center makes final decision.
• Fusion Rule
• Fusion Rule with random strategy
• Solve the parameters of the Fusion Rule

50
Algorithm for Computing the Fusion Rule

• For each element , we denote
  
• by
• by
• The likelihood ratio, associated with , is
  defined as

W. Chung and K. Yao, Decision Fusion in Sensor
Networks for Spectrum Sensing based on Likelihood
Ratio Tests, Proceedings of SPIE, 2008.
51
Fusion of Two Sensors

• Two Sensors
• Operating points
• Goal (Lower-Bounded Probability of Detection
  Criterion) Minimizing while
  is lower bounded by 0.91
• Result

52
Fusion of Two Sensors
53
Examples
3 sensors

• Proposed algorithm
• K out of N
• FC declares H1 if k or more than k sensors
  declare H1. Otherwise, FC declares H0.
• Decision Space search
• All possible combinations of decision fusion rule

4 sensors
54
Detection under Fading---Likelihood Ratio Test
with Fading Statistics (LRFS)

• Signal Model
• Fading Gains
• Rayleigh
• Rician
• Test Statistic

55
LRFS

• Explicit Expressions of the test statistics
• Rayleigh
• Rician

56
Multi-Sensor Decision Fusion under Fading

• Signal Model
• Likelihood Ratio
• Reformulate by fading statistics
• Under H1
• Under H0
• Test Statistics

57
Numerical Examples

• LRT with Fading Statistics
• LRFS under Rayleigh
• LRFS under Rician
• Matched Filter
• Decision Fusion with Fading Statistics
• 3 Sensors
• 2 Sensors

58
Summary

• Explicit Algorithms
• Neyman-Pearson
• Lowered-Bounded Probability of Detection
• Test Statistics under Rayleigh and Rician Fading.
• Performance Improvements by Incorporating Fading
  Statistics
• Single-Sensor Detection under Fading
• Decision Fusion under Fading

59
Outline

• Introduction-Fading Channels
• Fading Channel Model by Modified Hidden
  Semi-Markov Model
• Generating Correlated MIMO Fading Channel
• Detection and Decision Fusion in Fading
  Environment
• Sequential Likelihood Ratio Test for Spectrum
  Sensing
• Future Work
• Conclusions

60
Sequential Likelihood Ratio Testfor Spectrum
Sensing

• Problem Spectrum Sensing under Fading
• Goal
• Faster decision
• Allow setting both probability of false alarm and
  probability of detection
• Conventional Approaches
• Collect fixed amount of data
• Uncertain signal strength in fading
• Can we reach faster decision when signal is
  strong?
• Sequential Likelihood Ratio Test

W. Chung and K. Yao, Sequential Likelihood
Ratio Test under Incomplete Signal Model for
Spectrum Sensing,
61
Formulation

• Signal Model
• Received
• Signal (primary user)
• Signal follows AR model
• Received signal follows ARMA

62
Sequential Decision

• Decision at time t
• Log LR
• Sequential decision

63
Decision and Thresholds

• Decision
• Thresholds
• Expected termination time can be derived as a
  function of accuracy and SNR

64
Example 1-Scenario

• SNR uniformly distributed between -20 dB to 10 dB
• Prior 0.5 for H1 and H0
• Jakes ACF

65
Example 1-results
66
Example 2fixed SNR at -20 dB
67
Conclusion

• Modified Hidden Semi-Markov Model
• ACFs and Durations
• Channel Segmentations
• Parameter Estimation
• Multiple Channel Generation
• Correlated Heterogeneous Channels
• Detection and Decision Fusion under Fading
• Single Detector
• Sensor Network
• Sequential LRT allows faster decision while
  maintaining targeted detection accuracies

68
Future Works

• Detection, Estimation, and Learning
• Demodulation under Correlated Heterogeneous
  Channels
• Joint Detection and Estimation of Information and
  Environment
• Cognitive Radio
• Sequential Detection
• Quickest Detection
• Protocol Enforcement
• Game-Theoretical
• Sniffer

69

• Thank you

70
Publications

• Wei-Ho Chung, Kung Yao, and Ralph E. Hudson, "The
  Unified Approach for Generating Multiple
  Cross-correlated and Auto-correlated Fading
  Envelope Processes." Accepted for publication in
  IEEE Transactions on Communications, Oct. 2008.
  To appear.
• Wei-Ho Chung and Kung Yao, "Decision Fusion in
  Sensor Networks for Spectrum Sensing based on
  Likelihood Ratio Tests," Proceedings of SPIE,
  Vol. 7074, No. 70740H, Aug. 2008.
• Wei-Ho Chung and Kung Yao, "Modified Hidden
  Semi-Markov Model for Modelling the Flat Fading
  Channel," Accepted for publication in IEEE
  Transactions on Communications, Feb. 2008. To
  appear.
• Wei-Ho Chung and Kung Yao, "Empirical
  Connectivity for Mobile Ad Hoc Networks under
  Square and Rectangular Covering Scenarios," IEEE
  Proc. International Conference on Communications,
  Circuits, and Systems, Vol. 3, pp. 1482-1486,
  June 2006.
• Wei-Ho Chung, "Probabilistic Analysis of Routes
  on Mobile Ad Hoc Networks," IEEE Communications
  Letters, Vol.8, Issue 8, pp.506-508, Aug. 2004.
• Wei-Ho Chung, Sy-Yen Kuo, and Shih-I Chen,
  "Direction-Aware Routing Protocol for Mobile Ad
  Hoc Networks," Proceedings of IEEE International
  Conference on Communications, Circuits and
  Systems, Vol. 1, pp. 165-169, June 2002.

71
References

• P. Beckman, Probability In Communication
  Engineering. New York Harcourt Brace and World,
  1967.
• E. Biglieri, J. Proakis, and S. Shamai, Fading
  channels information-theoretic and
  communications aspects," IEEE Transactions on
  Information Theory, vol. 44, issue 6, pp.
  2619-2692, Oct. 1998.
• Bernard Sklar, "Rayleigh fading channels in
  mobile digital communication systems. I.
  Characterization, "IEEE Communications
  Magazine,Vol. 35, Issue 7, pp.90-100,Jul. 1997.
• Seymour Stein, "Fading Channel Issues in System
  Engineering," IEEE Journal on Selected Areas in
  Communications, Vol. 5, Issue 2, pp.68-89, Feb.
  1987.
• C. C. Tan, N. C. Beaulieu, "On first-order Markov
  modeling for the Rayleigh fading channel," IEEE
  Transactions on Communications,Vol. 48, Issue
  12,pp. 2032-2040, Dec 2000.
• E. K. Hall and S. G. Wilson, "Design and analysis
  of turbo codes on Rayleigh fading channels," IEEE
  Journal on Selected Areas in Communications, vol.
  16, issue 2, pp. 160-174, Feb. 1998.
• A. J. Goldsmith, S. G. Chua, "Adaptive coded
  modulation for fading channels," IEEE
  Transactions on Communications, vol.46, issue 5,
  pp. 595-602, May 1998.
• J. C. Bezdek, N.R. Pal, "Some new indexes of
  cluster validity," IEEE Transactions on Systems,
  Man and Cybernetics, Part B, Volume 28, Issue 3,
  pp. 301-315, Jun. 1998.
• M. S. Aldenderfer and R.K. Blashfield, Cluster
  Analysis, Newbury Park, California U.S.A., Sage
  Press, 1984.
• J. C. Dunn, "A fuzzy relative of the ISODATA
  process and its use in detecting compact
  well-separated clusters," Journal of Cybernetics,
  vol. 3, no. 3, pp. 3257, 1973.

72
References

• K. E. Baddour and N. C. Beaulieu, "Accurate
  Simulation of multiple cross-correlated Rician
  fading channels," IEEE Transactions on
  Communications, Vol. 52, Issue 11, pp. 1980-1987,
  Nov. 2004.
• A. Abdi and M. Kaveh, "A space-time correlation
  model for multielement antenna systems in mobile
  fading channels," IEEE Journal on Selected Areas
  in Communications, Vol. 20, Issue 3, pp. 550-560,
  Apr. 2002.
• H. S. Rad and S. Gazor, "A cross-correlation MIMO
  channel model for non-isotropic scattering
  environment and non-omnidirectional antennas,"
  Canadian Conference on Electrical and Computer
  Engineering, pp. 25-28, May 2005.
• M. Alouini and A. J. Goldsmith, "Adaptive
  Modulation over Nakagami Fading Channels,"
  Wireless Personal Communications, Vol. 13, pp.
  119-143, Springer Netherlands, May 2000.
• E. K. Hall and S. G. Wilson, "Design and analysis
  of turbo codes on Rayleigh fading channels," IEEE
  Journal on Selected Areas in Communications, Vol.
  16, Issue 2, pp. 160-174, Feb. 1998.
• P. Beckman, Probability In Communication
  Engineering. New York Harcourt Brace and World,
  1967.
• A. Goldsmith, S. A. Jafar, N. Jindal, and S.
  Vishwanath, "Capacity limits of MIMO channels,"
  IEEE Journal on Selected Areas in Communications,
  Vol. 21, Issue 5, pp. 684-702, June 2003.
• Q. T. Zhang, "A decomposition technique for
  efficient generation of correlated Nakagami
  fading channels," IEEE Journal on Selected Areas
  in Communications, Vol. 18, Issue 11, pp.
  2385-2392, Nov. 2000.
• W. C. Jakes, Microwave mobile communication, 2nd
  ed., IEEE Press, 1994.
• S. Haykin,"Cognitive radio brain-empowered
  wireless communications," IEEE Journal on
  Selected Areas in Communications, Volume 23,
  Issue 2, pp. 201-220, Feb. 2005.

73
References

• M. Nakagami, The m-distribution, a general
  formula of intensity distribution of rapid
  fading, in Statistical Methods in Radio Wave
  Propagation, W. G. Hoffman, Ed. Oxford, England
  Pergamon, 1960.
• H. Suzuki, A statistical model for urban radio
  channel model, IEEE Trans. Commun., vol. 25, pp.
  673680, July 1977.

74
Cooperative Spectrum Sensing Scheme based on
Nash Equilibrium

• Wei-Ho Chung
• Electrical Engineering
• University of California, Los Angeles
• March 2009
• whc_at_ee.ucla.edu

75
Decision Fusion using Nash equilibrium

• Detection by Single sensor
• Hypothesis test
• Cognitive radio
• Decision Fusion using Multiple Sensors
• Increase detection accuracy for spectrum sensing
• Nash equilibrium to enforce cooperative scheme

76
Hypothesis Test

• Hypothesis Test applications
• Surveillance
• Target Detection
• Spectrum Sensing
• Example-Matched Filter Detection
• Signal model

77
Receiver Operating Curve

• Receiver Operating Curve v.s.
• Setting Threshold
• Criteria
• Neyman-Pearson
• upper-bounded
• Bayes
• Priors and costs

78
Spectrum Sensing in Cognitive Radio

• Wireless communications rely on spectra.
• Current usage model frequency bands are
  licensed.
• The licensed bands are often vacant- low
  utilizations.
• Cognitive Radio-to increase the spectrum
  utilization.
• Allows secondary user to access the spectrum when
  it is vacant.
• Secondary users sense the spectrum before
  accessing.
• Accuracies of the spectrum sensing is crucial.
• Formulated as binary hypothesis test problem
• H0 Spectrum Vacant
• H1 Spectrum Occupied

S. Haykin, "Cognitive radio brain-empowered
wireless communications," IEEE JSAC. 2005.
79
Detection Criteria and Implications in Cognitive
Radio

• Interpretations of PD and PFA in cognitive radio
• Detection performed by the secondary users
• H1 Spectrum used by the primary users
• Secondary users access the spectrum if decision
  is H0
• Channel conflict Decision H0 under the truth H1
• Miss of the spectrum opportunity Decision H1
  under the truth H0
• Neyman-Pearson
• Upper-bound probability of false alarm while
  maximizing probability of detection
• Protect the spectrum opportunities of the
  secondary users while minimizing the channel
  conflicts
• Lower-Bounded Probability of Detection (LBPD)
  Chung 08
• Lower-bound probability of detection while
  minimizing probability of false alarm
• Protect the primary users while maximizing the
  spectrum opportunities for the secondary users

80
Decision Fusion Framework

• Sensors make binary decisions.
• Many applications require binary decisions.
• Accuracy of a single sensor is limited.
• Fusion of multiple decisions increases
  accuracies.

R. Viswanathan and P. K. Varshney,
"Distributed Detection with Multiple sensors I.
Fundamentals," Proceedings of the IEEE, 1997.
81
Decision Fusion Framework

• N sensors make binary decisions.
• Probability of False Alarm
• Probability of Detection
• Sensor decisions
• The fusion center makes final decision.
• Fusion Rule
• Fusion Rule with random strategy
• Solve the parameters of the Fusion Rule

82
Algorithm for Computing the Fusion Rule

• For each element , we denote
  
• by
• by
• The likelihood ratio, associated with , is
  defined as

W. Chung and K. Yao, Decision Fusion in Sensor
Networks for Spectrum Sensing based on Likelihood
Ratio Tests, Proceedings of SPIE, 2008.
83
Fusion of Two Sensors

• Two Sensors
• Operating points
• Goal (Lower-Bounded Probability of Detection
  Criterion) Minimizing while
  is lower bounded by 0.91
• Result

84
Fusion of Two Sensors
85
Costs structure and game formulation

• Utility from accessing the channel
• 0 for channel conflict
• for a successful access
• Costs
• for a channel conflict
• for a successful access
• Game
• Users
• Actions
• user perform detection -
  incurs cost
• user not perform detection -
  incurs cost 0
• Utility

86
Operating point and Costs

• Operating point by Bayes criterion--the point on
  the ROC with slope of its tangent line equal to
• Expected Costs
• Individual user
• Overall cost

87
Action profile by Nash equilibrium

• For the action profiles
• Compute costs of each action profile
• Compute Nash equilibrium

88
Results - influences of charges from primary users

• Cost of conflict
• Cost of successful access

89
Results-influence of detection cost

• Detection cost

90
Conclusions

• Propose Decision fusion framework using Nash
  equilibrium
• Increase accuracies of spectrum sensing
• Protocol enforcement by Nash equilibrium
• Framework allows analyzing interactions among
• Prices
• Cost of detection
• Probability of false alarm
• Probability of detection
• Utilities

91
References

• S. Haykin, "Cognitive Radio Brain-Empowered
  Wireless Communications," IEEE Journal on
  Selected Areas in Communications, Volume 23,
  Issue 2, pp. 201-220, Feb. 2005.
• D. Cabric, A. Tkachenko, and R. W. Brodersen,
  "Experimental Study of Spectrum Sensing Based on
  Energy Detection and Network Cooperation,"
  Proceedings of the first international workshop
  on Technology and policy for accessing spectrum,
  Article No. 12, 2006.
• H. P. Shiang and M. van der Schaar, "Distributed
  Resource Management in Multi-hop Cognitive Radio
  Networks for Delay Sensitive Transmission," IEEE
  Trans. Veh. Tech., to appear.
• H. Park and M. van der Schaar, "Coalition based
  Resource Negotiation for Multimedia Applications
  in Informationally Decentralized Networks," IEEE
  Trans. Multimedia, to appear.
• W. Chung and K. Yao, "Decision Fusion in Sensor
  Networks for Spectrum Sensing based on Likelihood
  Ratio Tests," Proceedings of SPIE, Vol. 7074, No.
  70740H, Aug. 2008.
• Q. Zhao, L. Tong, A. Swami, and Y. Chen,
  "Decentralized Cognitive MAC for Opportunistic
  Spectrum Access in Ad Hoc Networks A POMDP
  Framework," IEEE Journal on Selected Areas in
  Communications, Vol. 25, No. 3, pp. 589-600,
  April 2007.
• Z. Ji and K. J. R. Liu, "Dynamic Spectrum
  Sharing A Game Theoretical Overview," IEEE
  Communications Magazine, pp. 88-94, May 2007.
• R. Etkin, A. Parekh, and D. Tse, "Spectrum
  Sharing for Unlicensed Bands," IEEE Journal on
  Selected Areas in Communications, Vol. 25, No. 3,
  pp. 517-528, April 2007.

92
Detecting Number of Coherent Signals in Array
Processing by Ljung-Box Statistic

• Wei-Ho Chung
• Electrical Engineering
• University of California, Los Angeles
• April 2009
• whc_at_ee.ucla.edu

93
Array Signal Processing

• Estimate
• Direction of arrival in far-field
• Localizations near-field
• Likelihood formulation
• Grid search
• Newton method
• Genetic Algorithm
• Detect number of signals

94
Signal Model

• Signals
• Source signal
• Received signal
• Unknown parameters
• DOAs
• Amplitudes
• Maximum Likelihood Estimation

95
Estimate Number of Signals

• Estimations of DOAs are based on the assumed
  number of signals-need to detect number of
  signals.
• Information-theoretical approaches
• Minimum description length (MDL)
• Akaike information criterion (AIC)
• Exploit rank of the signal covariance matrix
• Not applicable to coherent signals

96
Whiteness of the residue

• Residue
• Residuereceived signal-estimated signal
• Residue is approximately white
• Measure whiteness of the residue
• Use whiteness as the goodness of fit of the model
  order (number of signals)

97
Detection statistic

• Sample Autocorrelations
• Ljung-Box statistic
• The whiter, the smaller LB statistic
• Large values for the model order k smaller than
  the true number of signals
• Small values for the model order k equal or
  larger than the true number of signals
• Difference of LB statistic is the good indication
  of true model order
• Q-statistic
• Detection by Q-statistic criterion (QSC)

98
Procedure of detection
99
Examples

• Scenario
• 7 sensors (ULA)
• Half wavelength
• separation
• 100 samples
• Examples
• 2 signals
• 3 signals
• 4 signals

100
Detection results-2 signals
101
Detection results-3 signals
102
Detection results-4 signals
103
References

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• Q. T. Zhang, K. M. Wong, P. C. Yip, and J. P.
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  of information theoretic criteria in the
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104
References

• P. Stoica and K. C. Sharman, "Maximum likelihood
  methods for direction-of-arrival estimation,"
  IEEE Transactions on Acoustics, Speech and Signal
  Processing, Volume 38, Issue 7, pp. 1132-1143,
  Jul. 1990.
• M. Pesavento and A. B. Gershman,
  "Maximum-likelihood direction-of-arrival
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  noise," IEEE Transactions on Signal Processing,
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  unknown sensor locationestimation for wideband
  signals in the near-field," IEEE Transactions on
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