Chaos Applications in Telecommunications

Contents......Page 8
1.1 Chaos Modeling......Page 10
1.2 Synchronization......Page 12
1.3 Chaotic Communication Techniques......Page 16
1.4 Communication Privacy......Page 20
References......Page 21
2 Chaotic Signal Generation and Transmission......Page 22
2.2 Chaos Theory......Page 23
2.2.1 Discrete Dynamical Systems......Page 24
2.2.2 Chaos Modeling......Page 27
2.2.3 Chaotic Regime......Page 33
2.3 Chaotic Communication......Page 37
2.3.1 NRZ Random Signal......Page 39
2.3.2 Principle of DS- SS Baseband System......Page 43
2.4.1 Transmitter of DS- SS Baseband using NRZ- PN Sequence......Page 46
2.4.2 Transmitter of DS- SS Baseband using NRZ- Chaos Sequence......Page 48
2.4.4 Receiver of DS- SS Baseband using NRZ- Chaos Sequence......Page 50
2.5 Performance DS- SS Baseband Communication......Page 51
2.6 DS- SS Bandpass System with BPSK Modulation......Page 55
2.6.1 Application of NRZ Chaos Sequence to DS- SS BPSK......Page 59
2.6.2 Transmitter of DS- SS BPSK using NRZ- PN Sequence......Page 60
2.6.3 Transmitter of DS- SS BPSK using NRZ Chaos Sequence......Page 62
2.6.4 Receiver of DS- SS BPSK using NRZ- PN Sequence......Page 63
2.6.5 Receiver of DS- SS System with NRZ Chaos Sequence......Page 67
References......Page 68
3 Chaotic Transceiver Design......Page 69
3.1 Introduction......Page 70
3.1.1 The Chaotic Communications System......Page 71
3.2.1.1 Henon Attractor......Page 72
3.2.1.2 Mirrored- Henon Attractor......Page 75
3.2.1.3 Chaotic Dynamics on the Various Parabolic Sections......Page 78
3.2.1.4 The Henon Fixed Point......Page 79
3.2.2 The Transmit PDF Model......Page 81
3.2.2.3 The Transmit PDF......Page 83
3.2.2.4 The Transmit PDF Gaussian Model......Page 84
3.2.2.5 The Transmit Power......Page 88
3.2.3 Henon, Mirrored- Henon, and Transmit Sequence Power Spectral Density Plots......Page 90
3.2.4 Chaotic Reconstruction Plots......Page 92
3.3 The Receiver Design......Page 94
3.3.1.1 Maximum A Posteriori ( MAP) Transmit Value......Page 96
3.3.1.1.1 Transmit PDF Window......Page 99
3.3.1.1.2 MAP Transmit Value Calculation......Page 101
3.3.1.1.3 Simplified MAP Transmit Value Calculation......Page 102
3.3.1.2.1 SNR Maximum Probability Estimator......Page 104
3.3.1.2.2 SNR Look-Up Table......Page 105
3.3.1.2.3 Instantaneous SNR Calculation......Page 106
3.3.1.2.4 Received PDF Model......Page 108
3.3.1.2.5 Determination of Maximum Probability SNR......Page 111
3.3.1.2.6 The Newton–Raphson Technique......Page 112
3.3.1.2.7 The Modified Newton–Raphson Technique......Page 114
3.3.1.2.8 SNR Running Weighted Average......Page 119
3.3.1.3 Decision Feedback......Page 122
3.3.2 The Decision and Weighting Block......Page 124
3.3.3 The Approximation Parabola Map......Page 127
3.3.4 The Receiver Initial Decision State......Page 128
3.3.5 The System- to- Bit MAP......Page 129
3.3.6 Receiver Performance......Page 130
References......Page 131
4 Chaos- Based Modulation and Demodulation Techniques......Page 132
4.1.1 A Simple Communication System......Page 133
4.1.2 Spread- Spectrum Communications......Page 139
4.2 Application of Chaos to Communications......Page 140
4.3.1 Chaos Shift Keying......Page 143
4.3.1.1 Coherent Demodulation Based on Synchronization Error......Page 144
4.3.1.2 Coherent Demodulation Based on Correlation......Page 145
4.3.1.3 Noncoherent Demodulation Based on Bit- Energy Estimation......Page 147
4.3.1.4 Noncoherent Demodulation Based on Return Map......Page 149
4.3.1.4.1 Regression Approach......Page 151
4.3.1.4.2 Probability Approach......Page 154
4.3.2 Differential Chaos Shift Keying......Page 155
4.3.3.2 Frequency- Modulated DCSK......Page 159
4.3.3.3 Correlation Delay Shift Keying......Page 161
4.3.3.4 Symmetric Chaos Shift Keying......Page 162
4.3.3.5 Quadrature Chaos Shift Keying......Page 163
4.3.3.6 Permutation- Based Differential Chaos Shift Keying......Page 164
4.4.1.1 Multiple Access Chaotic Frequency Modulation......Page 168
4.4.1.2 Multiple- Access Chaos Shift Keying......Page 169
4.4.2.1 Time- Delay- Based Multiple- Access DCSK System......Page 170
4.4.2.2 Permutation- Based Multiple- Access DCSK System......Page 172
4.4.2.3 Walsh- Code- Based Multiple- Access System......Page 174
4.5 Summary......Page 175
References......Page 176
5.1 Introduction......Page 180
5.2 Some Tools for Computing Expectations of Quantized Chaotic Trajectories......Page 183
5.3 Asynchronous DS- CDMA Systems Model......Page 189
5.4 System Performance Merit Figure......Page 193
5.5 Performance Optimization in Dispersive and Nondispersive Channels......Page 194
5.6 Chaos- Based Generation of Optimized Spreading Sequences......Page 196
5.7 Chaos- Based DS- CDMA System Prototype and Measurement Results......Page 200
5.7.1 Performance over Nondispersive Channel......Page 202
5.7.2 Performance over Exponential Channel......Page 203
5.8.1 System Model......Page 204
5.8.2 Capacity Comparison......Page 205
5.9 Ultimate Limits — Some Analytical Considerations......Page 207
5.9.1 Capacity Related Performance......Page 208
5.9.2 Average Performance......Page 210
References......Page 211
6 Channel Equalization in Chaotic Communication Systems......Page 214
6.1 Introduction......Page 215
6.2.1 Dynamical Systems......Page 217
6.2.2 Chaotic Systems Definitions......Page 218
6.2.3 Symbolic Dynamics......Page 222
6.3.1 Properties of Chaotic Systems......Page 224
6.3.2.1 Chaotic Modulation......Page 227
6.3.2.2 Chaotic Masking......Page 228
6.3.3 Channel Effects......Page 229
6.4 Optimal Estimation and Sequential Channel Equalization Algorithms Based on the Viterbi Algorithm......Page 230
6.4.1 Chaotic Modulation through Symbolic Dynamics......Page 231
6.4.2 Trellis Diagram Representation......Page 232
6.4.3 Optimal Estimation Algorithm......Page 234
6.4.4 A Sequential Channel Equalization Algorithm......Page 235
6.4.5 Simulations......Page 237
6.5 Estimation and Channel Equalization Algorithms for Multiuser Chaotic Communications Systems......Page 240
6.5.1 A Multiuser Chaotic Communications System......Page 241
6.5.2 Multiuser Trellis Diagram Representation......Page 242
6.5.3 A Multiuser Optimal Estimation Algorithm......Page 244
6.5.4 A Multiuser Channel Equalization Algorithm......Page 245
6.5.5 Simulations......Page 247
6.6 Conclusions......Page 250
References......Page 251
7 Optical Communications using Chaotic Techniques......Page 255
7.1 Introduction......Page 256
7.2 Erbium- Doped Fiber Ring Lasers for Optical Chaotic Communication......Page 257
7.3.1.1 Apparatus and Method......Page 259
7.3.1.2 The Dimensionality of the EDFRL Dynamics......Page 264
7.3.1.3 Message Recovery......Page 268
7.3.2 Message Injection Technique using Polarization Discrimination......Page 271
7.3.3 Message Injection Technique using Wavelength Discrimination......Page 274
7.3.4 Wavelength Discrimination with In- Ring Bandpass Filter......Page 275
7.3.5.1 IdenticalWavelengths for EDFRL and Message Light......Page 278
7.3.5.2 DifferentWavelengths for EDFRL and Message Light......Page 281
7.3.6 Discussion of Message Injection Approach......Page 283
7.4.1 Single Ring Technique......Page 285
7.4.2 Two Ring Technique......Page 289
7.4.2.1 Experimental Results of the Two- Ring Technique......Page 298
7.4.3 Discussion of the Intraring Modulator Technique......Page 304
7.5 Communication using Chaotic Polarization Fluctuations to Carry Information......Page 306
7.5.2 Theory of Operation......Page 308
7.5.3 Interpretation of Results......Page 310
7.5.4 Experimental Results......Page 311
References......Page 316
Appendix A Fundamental Concepts of the Theory of Chaos and Fractals......Page 319
A. 1 Introduction......Page 320
A. 1.1 Nonlinearity and Dynamical Systems......Page 322
A. 1.2 The Geometry of Motion in Phase Space......Page 329
A. 1.3 Fundamental Concepts of Chaos......Page 333
A. 2.1 Parameter- Dependent Systems......Page 337
A. 2.2 The Saddle- Node Bifurcation......Page 343
A. 2.3 The Transcritical Bifurcation......Page 345
A. 2.5 The Period- Doubling Bifurcation......Page 346
A. 3 Three Routes to Chaos......Page 348
A. 3.1 The Period- Doubling Route......Page 349
A. 3.2 Onset of Chaos via Intermittency......Page 352
A. 3.3 The Breakup of Quasiperiodic Motion......Page 355
A. 4 Renormalization and Universality......Page 356
A. 4.1 Renormalization of the Period- Doubling Route......Page 358
A. 4.2 Renormalization of the Intermittency Route to Chaos......Page 361
A. 4.3 Renormalization of the Breakup of a Golden Torus......Page 363
A. 5 The Theory of Fractals......Page 365
A. 5.1 Self- Similarity and Fractal Dimension......Page 366
A. 5.2 Multifractals and Generalized Dimensions......Page 376
A. 6 A New Science or a New Understanding of Nature?......Page 382
Acknowledgements......Page 384
References......Page 385
B. 1 Introduction......Page 388
B. 2 The Logistic Map......Page 394
B. 3 Delay Models......Page 398
B. 3.1 The Hénon Model......Page 400
B. 3.2 Hamiltonian Systems......Page 402
B. 3.3 Rotations/ Translations Based Models......Page 406
B. 3.4 Other Patterns and Chaotic Forms......Page 414
B. 4 Three- Dimensional Models......Page 416
References......Page 418