Table of Contents
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Introduction..........................................................................................................................1 Fractionally Spaced Blind Equalization ..............................................................................5 2.1 Fractionally Spaced Equalizer....................................................................................6 2.1.1 Multi-Channel Model .....................................................................................6 2.1.2 Transfer Function and Condition for Perfect Equalization (Constraint on the Channel).............................................................................................11 2.1.3 Requirement for Perfect Source Recovery (Constraint on the Equalizer Length) .........................................................................................13 2.2 2.3 Blind Adaptive Algorithm: CMA ............................................................................15 Effect of Initialization on a Blind Equalizer ............................................................18 2.3.1 Conditions for Convergence to Global Minima...........................................21 2.4 Conventional Blind Equalizer ..................................................................................24
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Error Equations for Blind Equalization Schemes .............................................................25 3.1 3.2 Error Signals.............................................................................................................26 Weight Update Equations.........................................................................................29 3.2.1 Type1 ............................................................................................................30 3.2.2 Type2 ............................................................................................................31 3.2.3 Type3 ............................................................................................................31 3.2.4 Type4 ............................................................................................................32 3.3 Simulation Results....................................................................................................34 3.3.1 Minimum Phase Channel with Two Impulses .............................................35 3.3.2 Exponentially Decaying Channel.................................................................37 3.3.3 Symmetric Channel ......................................................................................39 3.4 3.5 Effect of Adaptation Step Size.................................................................................40 Effect of Symmetry About Zero Error.....................................................................42
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3.6 4
Effect of Initialization ..............................................................................................44
Recursive Linear Predictor ................................................................................................51 4.1 4.2 4.3 One Step Ahead Predictor ........................................................................................51 Recursive Method for Changing the Predictor Coefficients....................................53 Prediction of the Fading Envelope...........................................................................57 4.3.1 Non-Stationary Rayleigh Fading Envelope Simulator ................................58 4.3.2 Simulation Results........................................................................................62 4.3.2.1 Fading Envelope with Constant Velocity ..................................... 63 4.3.2.2 Fading Envelope with Constant Acceleration............................... 67
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Proposed System................................................................................................................70 5.1 5.2 5.3 5.4 5.5 5.6 Equalizer Update Equations.....................................................................................72 Convergence Rate of FSBEEP.................................................................................76 Modification of Proposed FSBEEP System ............................................................78 Performance of FSBEEP in the Presence of External Noise...................................81 Equalizing Non-Minimum Phase Channels.............................................................82 Tracking Property of the FSBEEP System ..............................................................85 5.6.1 Linear Change from Minimum to Maximum Phase Channel......................86 5.6.2 Linear Change from Maximum to Minimum Phase Channel......................87
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Conclusion and Suggestions for Future Works.................................................................89
Appendix A ...............................................................................................................................91 Appendix B ...............................................................................................................................94 References .................................................................................................................................98 Vita ..........................................................................................................................................100
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