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@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 • New mechanism to describe the dynamics

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

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 • Jake’s 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 approach—Inverse 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.]