Telecommunications Systems Engineering

CONTENTS TELECOMMUNICATION NETWORK CONCEPTS 1-1 Introduction 1-2 Telecommunication System Functions in a Tracking and Data Acquisition Network 5 The Signal Acquisition and Tracking Function 5 The Telemetry or Data Acquisition Function 7 The Command Function 7 The Synchronization Function 8 1-3 Telecommunication System Design for Space Applications 8 1-4 Shannon's Theorem and Communication System Efficiency 14 1-5 Spectral Occupancy and Bandwidth Considerations 16 Power Spectral Density of a Random Data Sequence Generated by a Markov Source 17 NRZ Baseband Signaling 19 RZ Baseband Signaling 19 Bi-Phase Baseband Signaling 20 Delay Modulation or Miller Coding 20 1-6 Further Studies 22 2 CARRIER-TRACKING LOOPS EMPLOYING THE PHASE-LOCK PRINCIPLE 26 2-1 Introduction 26 2-2 Phase-Locked Loop Operation 27 Linear PLL Theory 26 Nonlinear PLL Theory 30 Loop Model and Phase Error P.D.F. Reduced Modulo 21t 31 The Phase Error Diffusion Coefficient 40 vii viii CONTENTS Mean Time to First Slip or First Loss of Phase Synchronization 46 2-3 The Second-Order Phase-Locked Loop Preceded by a Band-Pass Limiter 49 Linear PLL Theory and the Effects of Band-Pass Limiting 49 Nonlinear PLL Theory and the Effects of Band-Pass Limiting 54 2-4 Suppressed Carrier-Tracking Loops 56 The Squaring Loop Method 57 The Costas or I-Q Loop 62 Decision-Feedback Loop 64 2-5 Carrier-Tracking Loops for Polyphase Signals 69 The Nth Power Loop 71 The N-Phase Costas (I-Q) Loop 74 N-Phase Decision-Feedback Loops 75 Appendix A. Evaluation of the Autocorrelation Function of vz(t, 2rp) 80 3 PHASE AND DOPPLER MEASUREMENTS IN TWO-WAY PHASE-COHERENT TRACKING SYSTEMS 85 3-1 Introduction 85 3-2 Two-Way Phase Measurements 87 Basic System Model 87 Two-Way Tracking Phase Error 88 Linear PLL Theory 88 Nonlinear PLL Theory 90 Two-Way Tracking Phase Error with Carrier-Tracking Loops Preceded by BPLs 93 Linear PLL Theory 93 Nonlinear PLL Theory 97 3-3 Two-Way Doppler Measurements 97 Two-Way Doppler Error 97 Linear PLL Theory 97 Nonlinear PLL Theory 99 Two-Way Doppler Error with Carrier- Tracking Loops Preceded by BPLs 100 Linear PLL Theory 100 Nonlinear PLL Theory 102 3-4 Downlink Carrier-Suppression Effects Due to Additive Noise on the Uplink 104 Carrier Suppression 104 Linear PLL Theory 104 Nonlinear PLL Theory 105 CONTENTS ix Carrier Suppression with BPLs Preceding the Carrier-Tracking Loop 106 Linear PLL Theory 106 Nonlinear PLL Theory 107 3-5 Diversity Combining to Improve Phase and Doppler Measurements 107 The Signal-Combining Technique 109 Improvements Realized in Phase and Doppler Measurements with the Use of Diversity Techniques 110 3-6 Generalization of Two-Way Phase and Doppler Measurements to an N-Step Network 111 4 RANGE MEASUREMENTS BY PHASE-COHERENT TECHNIQUES 125 4-1 Introduction 125 4-2 Range Estimation 128 4-3 Ranging Techniques 131 The Fixed-Tone Ranging Technique 131 The Swept-Tone Ranging Technique 140 Pseudonoise Ranging Techniques 143 Correlation Properties of Periodic Binary Sequences 144 The Generation of Pseudonoise (PN) Sequences 145 Correlation Properties of PN Sequences 148 The Use of PN Sequences in Forming Ranging Codes 150 Rapid Acquisition Sequences (BINOR Codes) 152 Pulse Signal Ranging 157 4-4 PN Range Tracking Receivers 159 The Delay-Locked Loop 159 The Double-Loop Range Tracking Receiver 165 5 PHASE-COHERENT DETECTION WITH PERFECT REFERENCE SIGNALS 171 5-1 Introduction 177 5-2 The Binary and N-ary Decision Problem 181 The Binary Decision Problem 181 The N-ary Decision Problem 183 5-3 Signal Set Representation and Joint P.D.F. of Correlator Outputs 185 Orthogonal Signal Sets 186 Bi-orthogonal Signal Sets 186 CONTENTS Transorthogonal or Regular Simplex Signal Sets 186 Polyphase Signal Sets 187 L-orthogonal Signal Sets 187 5-4 Generation of Binary Signal Sets, r = 2 188 Orthogonal Codes 190 Bi-orthogonal Codes 192 Transorthogonal Codes 192 5-5 Performance Characterization of Phase-Coherent Receivers 192 The Set of Equiprobable, Equal Energy, Orthogonal Signals 195 The Set of Equiprobable, Equal Energy, Bi-orthogonal Signals 198 The Set of Equiprobable, Equal Energy, Transorthogonal Signals 212 Limiting Error Probability Performance of Block Codes as N -00 226 The Set of Equiprobable, Equal Energy, Polyphase Signals (MPSK) 228 The Set of Equiprobable, Equal Energy, L-orthogonal Signals 235 5-6 Coherent and Differentially Coherent Detection of Differentially Encoded MPSK Signals 240 Error Probability for Coherent Detection of Differentially Encoded MPSK 242 Error Probability for Differentially Coherent Detection of Differentially Encoded MPSK 246 5-7 Bit Error Probability for Differentially Encoded Data and Coherent Detection of Orthogonal and Bi-orthogonal Signals 253 5-8 Convolutional Codes 253 Encoding Procedure (Terminated-Tree Structure) 254 The Trellis and State Diagram Representations 259 Maximum-Likelihood Decoding of Convolutional Codes (The Viterbi Algorithm) 261 Other Methods of Decoding Convolutional Codes 263 Sequential Decoding 264 Feedback Decoding 266 Error Probability Performance of Convolutional Codes 266 5-9 Self-Synchronizable Codes 272 Appendix A. Abstract Vector Space Concepts 277 Appendix B. Derivation of the Word Error Probability for Polyphase Signals 279 Appendix C. The Distance Structure of Convolutional Codes and Other Criteria for the Selection of Good Codes 280 Appendix D. Error Probability Bounds for Maximum­Likelihood Decoding of an Arbitrary Convolutional Code 285 CONTENTS 6 PHASE-COHERENT DETECTION WITH NOISY REFERENCE SIGNALS 302 6-1 Introduction 302 6-2 System Model 303 6-3 Differenced Cross-Correlator Output Statistics (N = 2) 305 6-4 Performance of the Data Detector, N = 2 (Carrier Tracking with a PLL) 311 Phase Error Constant During the Symbol Interval 312 Phase Error Varies Rapidly Over the Symbol Interval 317 Phase Error Varies Moderately Over the Symbol Interval 319 6-5 Performance of the Data Detector, N = 2 (Suppressed Carrier Tracking with a Squaring Loop or Costas Loop) 320 6-6 Data Detection Performance of Block-Coded Systems 324 6-7 The Noisy Reference Problem for Detection of Polyphase Signals 327 6-8 Coherent Detection of Differentially Encoded MPSK with Suppressed Carrier Tracking 330 6-9 Word Error Probability Performance of a Suboptimum L-orthogonal Receiver with Noisy Reference Signals 333 Appendix A. A Series Solution for Average Error Probability, P E 333 7 DESIGN OF ONE-WAY AND TWO-WAY PHASE-COHERENT COMMUNICATION SYSTEMS 337 7-1 Introduction 337 7-2 Optimal Design of Single-Channel Systems 338 Basic System Model 338 Probability Density Functions for the System Phase Errors 341 Demodulator Output Statistics and System Performance 342 Design Characteristics 344 Suboptimum Design 354 System Performance as a Function of the Carrier-Tracking Loop Signal-To-Noise Ratio 356 An Application of the Single-Channel Theory to a Turn around Transponder Ranging System 357 7-3 Design of Two-Channel Systems 360 Basic System Model 360 Carrier-Tracking Loop Performance 362 Power Allocation and Selection of Modulation Factors for Two-Channel Systems (Data/Sync) 364 Determination of System Data Rate for a Given Bit Error Probability 366 Power Allocation and Selection of Modulation Factors for Two-Channel Systems (Data I/Data 2) 368 An Improved Modulation-Demodulation Technique for Certain Systems with Two Data Channels 370 xii CONTENTS 7-4 Design of Multichannel Systems 372 Basic System Model 372 Distribution of Transmitter Power Among the Various Modulation Terms 375 Choice of Parameters in the Design of Multichannel Satellite-to-Earth Links (L Large, M = 1) 378 The Case of Binary Signals 378 The Design of Block-Coded Systems 380 Choice of Parameters in the Design of a Deep Space­to-Earth, Block-Coded Communication System (L = 0, M = 1) 385 8 DESIGN AND PERFORMANCE OF PHASE-COHERENT SYSTEMS PRECEDED BY BAND-PASS LIMITERS 391 8-1 Introduction 391 8-2 The Noisy Reference Problem in Coherent Systems Preceded by a Band-Pass Limiter 391 8-3 Optimum Design of Single-Channel Systems Employing a Band-Pass Limiter 406 System Design Philosophies 407 System Model 408 Computation of Error Probability Performance 410 The Selection of an Optimum Modulation Factor 411 Optimization of Performance as a Function of Design Point 413 9 SYMBOL SYNCHRONIZATION AND ITS EFFECTS ON DATA DETECTION 418 9-1 Introduction 418 9-2 Symbol Synchronization from the Data-Bearing Signal 420 The Maximum a Posteriori (MAP) Estimator of Symbol Sync 420 Several Symbol Synchronizer Configurations Motivated by the MAP Estimation Approach 428 Open Loop Realizations 428 Closed Loop Realizations 430 The Effect of Signal Waveshape on the Design of Symbol Synchronizers 435 Minimization of the Area under the Tail of the Synchronization Error P.D.F. 436 Minimization of the kth Absolute Central Moment of the Synchronization Error P.D.F. 437 Maximization of the Synchronization Error P.D.F. at the Origin for a Unit Power Square-Wave Input Signal 439 The Digital Data Transition Tracking Loop (DTTL) 442 CONTENTS xiii The Early-Late Gate Symbol Synchronizer and a Comparison of Several Synchronizer Configurations 458 Absolute Value Type of Early-Late Gate Symbol Synchronizer (A VTS) 458 Difference of Squares Loop (DSL) 463 A Performance Comparison of Several Symbol Synchronizers 464 9-3 Symbol Synchronization over a Separate Channel 465 9-4 Error Probability Performance 466 Conditional Error Probability for a Fixed Symbol Sync Error 467 System Performance Due to Combined Noisy Reference and Symbol Sync Losses 473 Dependent Symbol and Subcarrier Synchronization References 474 Independent Symbol and Subcarrier Synchronization References 476 9-5 Conclusions 476 10 NONCOHERENT COMMUNICATION OVER THE GAUSSIAN CHANNEL 483 10-1 Introduction 483 10-2 Transmitter Characterization 484 10-3 Optimum Noncoherent Detection 486 Optimum Receiver Structures 487 Error Probability Performance of the Optimum Receiver 489 10-4 Suboptimum Noncoherent Detection 499 Techniques for Approximating the Evaluation of the Spectral Observations 499 Error Probability Performance in the Presence of Time Domain Truncation 500 10-5 Noncoherent Detection in the Presence of Short-Term Oscillator Instability 504 10-6 Time Synchronization of the Optimum Receiver 506 10-7 Error Probability Performance of the Optimum Receiver in the Presence of Timing Uncertainty 508 10-8 Frequency Synchronization of the Optimum Receiver 511 10-9 Error Probability Performance of the Optimum Receiver in the Presence of Frequency Uncertainty 513 10-10 Error Probability Performance of the Optimum Receiver in the Presence of Combined Time and Frequency Errors 513 10-11 Frequency Synchronization and Error Probability Performance of a Suboptimum Receiver 514 Appendix A. Derivation of the Maximum-Likelihood Estimator t 515 xiv CONTENTS 11 TRACKING LOOPS WITH IMPROVED PERFORMANCE 524 11-1 Introduction 524 11-2 The MAP Estimator of Phase for a Single-Channel System 525 11-3 Data-Aided Carrier-Tracking Loops 530 The Stochastic Integro-differential Equation of Operation 531 Nonlinear Analysis for Second-Order DALs with Identical Loop Filters 532 The Selection of the Upper and Lower Loop Gains 533 Tracking Performance for the Case of Perfect Ambiguity Resolution 535 Mean Time to First Slip or First Loss of Phase Synchronization 535 DAL and PLL Performance Comparisons (PSK Signals) 536 11-4 Hybrid Carrier-Tracking Loops 546 The Stochastic Integro-differential Equation of Operation 547 Nonlinear Analysis for Second-Order HTLs with Identical Loop Filters 548 The Selection of the Upper and Lower Loop Gains 549 HTL and PLL Performance Comparisons 553 11-5 Applications to Multichannel Systems 557 Appendix A. Derivation of the MAP Estimate of (J 561 INDEX 566