Your SlideShare is downloading. ×
(Kluwer) simulation of communication systems (2nd ed)
Upcoming SlideShare
Loading in...5
×

Thanks for flagging this SlideShare!

Oops! An error has occurred.

×

Saving this for later?

Get the SlideShare app to save on your phone or tablet. Read anywhere, anytime - even offline.

Text the download link to your phone

Standard text messaging rates apply

(Kluwer) simulation of communication systems (2nd ed)

3,199
views

Published on


0 Comments
3 Likes
Statistics
Notes
  • Be the first to comment

No Downloads
Views
Total Views
3,199
On Slideshare
0
From Embeds
0
Number of Embeds
0
Actions
Shares
0
Downloads
515
Comments
0
Likes
3
Embeds 0
No embeds

Report content
Flagged as inappropriate Flag as inappropriate
Flag as inappropriate

Select your reason for flagging this presentation as inappropriate.

Cancel
No notes for slide

Transcript

  • 1. Simulation ofCommunication Systems Second Edition
  • 2. Information Technology: Transmission, Processing, and StorageSeries Editor: Jack Keil Wolf University of California at San Diego La Jolla, CaliforniaEditorial Board: James E. Mazo Bell Laboratories, Lucent Technologies Murray Hill, New Jersey John Proakis Northeastern University Boston, Massachusetts William H. Tranter Virginia Polytechnic Institute and State University Blacksburg, VirginiaMulti-Carrier Digital Communications: Theory and Applications of OFDMAhmad R. S. Bahai and Burton R. SaltzbergPrinciples of Digital Transmission: With Wireless ApplicationsSergio Benedetto and Ezio BiglieriSimulation of Communication Systems, Second Edition: Methodology,Modeling, and TechniquesMichel C. Jeruchim, Philip Balaban, and K. Sam ShanmuganA Continuation Order Plan is available for this series. A continuation order will bring delivery of each new volumeimmediately upon publication. Volumes are billed only upon actual shipment. For further information please contactthe publisher.
  • 3. Simulation ofCommunication Systems Second EditionModeling, Methodology, and TechniquesMichel C. JeruchimLockheed Martin Management & Data SystemsValley Forge, PennsylvaniaPhilip BalabanAT&T LaboratoriesHolmdel, New JerseyK. Sam ShanmuganUniversity of KansasLawrence, KansasKLUWER ACADEMIC PUBLISHERSNEW YORK, BOSTON, DORDRECHT, LONDON, MOSCOW
  • 4. 971 5267 2
  • 5. ToJoan, Claude, and Kenny and to the memory of my parents, Sonia and Samuel —MCJAnna, to Victor and Nona and their families and to the memory of my parents, Shifra and Israel —PBRadha, Kannon, and Ravi and to the memory of my parents —KSS
  • 6. PrefaceSince the first edition of the book was published, the field of modeling and simulation ofcommunication systems has grown and matured in many ways, and the use of simulation as aday-to-day tool is now even more common practice. Many new modeling and simulationapproaches have been developed in the recent years, many more commercial simulationpackages are available, and the evolution of powerful general mathematical applicationspackages has provided still more options for computer-aided design and analysis. With thecurrent interest in digital mobile communications, a primary area of application of modelingand simulation is now to wireless systems of a different flavor than the traditional ones. Since the objective of modeling and simulation is to study and evaluate the behavior andperformance of systems of current interest, the practice of simulation has naturally evolvedalong with the types of systems that have emerged or are being designed for the future.Nevertheless, to the extent that simulation is an embodiment of fundamental principles ofseveral disciplines, communication theory in particular, the practice of modeling and simu-lation is still very much grounded in those basics. It is these principles, along with the manytricks of the trade that accompany their application, that still form the main focus of thissecond edition. This edition represents a substantial revision of the first, partly to accommodate the newapplications that have arisen. The text has been extensively reorganized and expanded. It nowcontains 13 chapters instead of the previous 7. Some of the former chapters have been dividedinto more logical units, edited for greater clarity where needed, and extended in coverage forselected topics. This division was made in part to facilitate the use of this book as a teachingtext. Two new chapters were added on material only lightly covered in the first edition. Onenew chapter, on modeling and simulation of nonlinear systems, provides a fairly extensivediscussion of “black-box” modeling of nonlinear systems with memory, and a comple-mentary section on related measurement techniques. As hinted above, perhaps the mostdramatic change in the communications/telecommunications industry since the first editionhas been the explosion of wireless services. In consequence, we have included a new chapteron channel modeling, the bulk of which deals with multipath and fading channels, the usualenvironment for wireless systems. As in the first edition, one chapter provides several casestudies as a means of illustrating different ways of approaching a problem and applyingspecific modeling and computational techniques from the arsenal of possibilities available tothe simulation practitioner. The first case study is a thoroughly reworked version of a previous vii
  • 7. viii Prefaceone, and three new case studies are given. A consolidated set of problems can be foundfollowing Chapter 12. By their nature, simulation and modeling embrace the whole of the fields to which theyare applied. To cover such a breadth of material, even larger now than in the first edition, wehave had again to rely on the generosity of friends and colleagues to provide us with adviceand material on various topics. First, we would like to reacknowledge the contributors to thefirst edition, whose contributions by and large still live in these pages. For the second edition, the list has grown longer. To our good friend and colleague atLockheed Martin M&DS, Dr. Robert J. Wolfe, mathematician and statistician par excellence,we extend our gratitude for innumerable pieces of advice, proofs, and inputs on coding,nonlinear differential equations, random number generation, and interpolation, among others.Dr Wolfe also reviewed several chapters and provided the basic material for the section onlarge-deviations theory (Section 11.2.5.3.2). Numerous contributions were also made by othermembers of the Communications Analysis and Simulation Group at Lockheed MartinM&DS. Aside from Bob Wolfe’s work just mentioned, Douglas Castor and Dr. GregoryMaskarinec kindly made available their previously published work on minimum-shift-keying,which was edited into Case Study III in Chapter 12. In addition, Doug generated all thefigures and carefully reviewed the final manuscript for that case study. We also benefited frommany discussions with Dr. Maskarinec about nonlinear modeling, based on his extensivesurvey of the literature; Greg also reviewed Chapter 5 and contributed the model in Section5.3.4.2. We appreciate the efforts of Gregory Sternberg, who used his expertise in Mathe-matica to compute Table 11.1 and to generate Figures 11.23 and 11.24. We thank PaulBeauvilliers for using his experience in simulating phase-locked loops to produce the materialfor Example 8.12.2 and the associated figures. We also express our appreciation to DanielMcGahey, who supplied the block diagram, its details, and the timing information that formthe basis for the discussion in Section 11.2.1. The team of Dr. Christopher Silva, Christopher Clark, Dr. Andrew Moulthrop, andMichael Muha at Aerospace Corporation were most generous in lending us the benefit of theirexperience and knowledge in nonlinear system modeling and measurement. The teamsupplied Section 5.5 on measurement techniques for nonlinear components. Dr. Silva wentbeyond the call of duty by providing the material on generalized Volterra models and poly-spectral models in Section 5.3.3, as well as the material in Section 5.2.4.3, supplying severalof the related problems, and thoroughly reviewing Chapter 5. Chris Clark is also to bethanked individually for writing Section 5.3.4.2 on nonlinear parametric discrete-timemodels. We have also benefited from numerous discussions with Harvey Berger of TRW onhis published and unpublished work in nonlinear amplifier modeling. Several individuals presently or formerly at AT&T Laboratories, or formerly with BellLaboratories, made contributions that we would like to acknowledge. Our appreciation isextended to Dr. William Turin, who codeveloped and coauthored Case Study IV in Chapter12; Bill also kindly reviewed sections of the book dealing with Markov models. We also thankDr. Don Li for his contributions as a codeveloper of the material in Case Study IV We aremost grateful to Dr. Thomas M. Willis III for contributing the material on shadow fading i nChapter 9. We also express our gratitude to Dr. Seong (Sam) Kim for providing the materialand the figures on indoor channel modeling in Chapter 9. We also acknowledge manydiscussions with Dr. Zoran Kostic on the workings of code division multiple-access (CDMA)systems; his advice helped shape Case Study IV We are indebted to Prof. Irving Kalet of the Technion, Haifa, Israel, for providing thematerial (and its iterations) on orthogonal frequency division multiplexing (OFDM) that
  • 8. Preface ixappears in Section 8.7.2.2. We much appreciate the efforts of Prof. J. Keith Townsend ofNorth Carolina State University for many discussions on importance sampling, for inputs intoSection 11.2.5.4 on stochastic importance sampling, and for the whole of Section 11.2.6 onimportance splitting. Keith also made other materials available that could not be accom-modated for space reasons. We thank Dr. Faroukh Abrishamkar of Qualcomm for his adviceon CDMA system modeling and for providing some of the reference channel models in theAppendix to Chapter 9. Professor Vasant Prabhu of the University of Texas at Arlington wasmost kind to provide us with several problems that he uses for his course in simulation, andlikewise we are pleased to acknowledge Prof. Brian Woerner of Virginia Polytechnic Institutefor providing us with a number of projects following Chapter 12. Finally, we renew our acknowledgment to our families for bearing with us—a secondtime—through this long process. Michel C. Jeruchim Philip Balaban K. Sam Shanmugan
  • 9. ContentsChapter 1. Introduction1.1. Methods of Performance Evaluation. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1 1.1.1. Introduction. ......................................... 1 1.1.2. Hierarchical View. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 21.2. Simulation Approach: Waveform-Level Simulation of Communication Systems. . . . . . 31.3. The Application of Simulation to the Design of Communication Systems . . . . . . . . . 51.4. Historical Perspective. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 61.5. Outline of the Book. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 8 References. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 12Chapter 2. Simulation and Modeling Methodology2.1. Some General Remarks on Methodology . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 142.2. Methodology of Problem Solving for Simulation . . . . . . . . . . . . . . . . . . . . . . . . 162.3. Basic Concepts of Modeling . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 17 2.3.1. System Modeling . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 21 2.3.2. Device Modeling ...................................... 21 2.3.3. Random Process Modeling ................................ 22 2.3.4. Modeling Hypothetical Systems . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 23 2.3.5. Simulation with Hardware in the Loop . . . . . . . . . . . . . . . . . . . . . . . . . 252.4. Performance Evaluation Techniques . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 262.5. Error Sources in Simulation. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 28 2.5.1. Errors in System Modeling . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 30 2.5.2. Errors in Device Modeling. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 31 2.5.3. Errors in Random Process Modeling. . . . . . . . . . . . . . . . . . . . . . . . . . . 32 2.5.4. Processing Errors . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 352.6. Validation. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 36 2.6.1. Validating Models of Devices or Subsystems . . . . . . . . . . . . . . . . . . . . . 37 2.6.2. Validating Random Process Models . . . . . . . . . . . . . . . . . . . . . . . . . . . 38 2.6.3. Validating the System Model . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 392.7. Simulation Environment and Software Issues . . . . . . . . . . . . . . . . . . . . . . . . . . 41 2.7.1. Features of the Software Environment. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 42 2.7.2. Components of the Software Environment . . . . . . . . . . . . . . . . . . . . . . . 43 2.7.3. Hardware Environment. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 45 2.7.4. Miscellaneous ........................................ 45 xi
  • 10. xii Contents2.8. The Role of Simulation in Communication System Engineering . . . . . . . . . . . . . . . 492.9. Summary. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 52 References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 54Chapter 3. Representation of Signals and Systems in Simulation: Analytic Fundamentals3.1. Introduction to Deterministic Signals and Systems . . . . . . . . . . . . . . . . . . . . . . . 56 3.1.1. Continuous Signals . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 56 3.1.2. Discrete-Time Signals . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 57 3.1.3. Systems. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 59 3.1.3.1. Properties of Systems. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 59 3.1.3.2. Block Diagram Representation of Systems . . . . . . . . . . . . . . . . . 603.2. Linear Time-Invariant Systems . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 61 3.2.1. Continuous Linear Time-Invariant Systems. . . . . . . . . . . . . . . . . . . . . . . . . . 62 3.2.1.1. The Impulse Response . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 62 3.2.1.2. The Convolution Integral, . . . . . . . . . . . . . . . . . . . . . . . . . . . 62 3.2.2. Discrete Linear Time-Invariant Systems. . . . . . . . . . . . . . . . . . . . . . . . . . . . . 62 3.2.2.1. The Impulse Response . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 62 3.2.2.2. Convolution Sum (Discrete Convolution) . . . . . . . . . . . . . . . . . . . . . . 633.3. Frequency-Domain Representation. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 63 3.3.1. The Fourier Transform . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 63 3.3.1.1. The Impulse Response . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 62 3.3.1.2. The Convolution Integral. . . . . . . . . . . . . . . . . . . . . . . . . . . . 62 3.3.2. Frequency-Domain Representation of Periodic Continuous Signals. . . . . . . . . 65 3.3.2.1. The Fourier Series . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 65 3.3.2.2. Parseval’s Theorem for Periodic Signals. . . . . . . . . . . . . . . . . . . . . . . 66 3.3.3. The Fourier Transform . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 66 3.3.3.1. Convergence ................................... 67 3.3.3.2. Properties of the Fourier Transform . . . . . . . . . . . . . . . . . . . . . 67 3.3.4. The Frequency Response . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 70 3.3.4.1. Interconnection of Systems in the Frequency Domain . . . . . . . . . . 70 3.3.4.2. Parseval’s Theorem for Continuous Signals. . . . . . . . . . . . . . . . . . . . 70 3.3.5. The Gibbs Phenomenon . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 71 3.3.6. Relationship between the Fourier Transform and the Fourier Series . . . . . . . . 72 3.3.6.1. Introduction. ................................... 72 3.3.6.2. Fourier Series Coefficients. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 72 3.3.7. The Fourier Transform of a Periodic Signal . . . . . . . . . . . . . . . . . . . . . . 72 3.3.7.1. Periodic Convolution . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 73 3.3.7.2. The Poisson Sum Formula. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 743.4. Lowpass-Equivalent Signals and Systems . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 74 3.4.1. The Hilbert Transform . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 75 3.4.2. Properties of the Hilbert Transform . . . . . . . . . . . . . . . . . . . . . . . . . . . 77 3.4.3. Lowpass-Equivalent Modulated Signals. . . . . . . . . . . . . . . . . . . . . . . . . . . . 78 3.4.4. Hilbert Transform in System Analysis. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 79 3.4.4.1. Introduction. ................................... 79 3.4.4.2. Lowpass Equivalent of a Bandpass Filter . . . . . . . . . . . . . . . . . . 79 3.4.5. Practical Considerations in Modeling of Lowpass Equivalents for Simulation. . . 82 3.4.5.1. Signals ....................................... 82 3.4.5.2. Filters ....................................... 833.5. Sampling and Interpolation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 83
  • 11. Contents xiii 3.5.1. Impulse Sampling. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 83 3.5.2. Sampling Theorem ....................................... 86 3.5.3. Multirate Sampling and Sampling Conversion . . . . . . . . . . . . . . . . . . . . . 87 3.5.4. Interpolation ......................................... 89 3.5.4.1. Introduction. ................................... 90 3.5.4.2. Interpolator Structures for Integer Upconversion. . . . . . . . . . . . . . . . . . . 93 3.5.4.3. Bandlimited and Windowed Bandlimited Interpolation . . . . . . . . . . 96 3.5.4.4. Linear Interpolation. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 98 3.5.4.5. Spline Interpolation. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1003.6. Characterization of Linear Time-Invariant Systems Using the Laplace Transform. . . . . 106 3.6.1. The Laplace Transform . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 106 3.6.1.1. Introduction. ................................... 106 3.6.1.2. Convergence and Stability. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 106 3.6.2. Inverse Laplace Transform. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 107 3.6.3. Properties of the Laplace Transform. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 107 3.6.4. Transfer or System Function. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 108 3.6.5. Interconnections of LTI Systems (Block Diagrams) . . . . . . . . . . . . . . . . . . . . . 108 3.6.6. Systems Characterized by Linear Constant-Coefficient Differential Equations. . . 110 3.6.6.1. Properties of the Transfer Function for Linear Constant-Coefficient Differential Equations. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 111 3.6.6.2. Realizations of Rational Transfer Functions Using Biquadratic Expansion. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 112 3.6.7. Frequency Response .................................... 1143.7. Representation of Continuous Systems by Discrete Transfer Functions . . . . . . . . . . . 115 3.7.1. The z-Transform. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 115 3.7.1.1. Convergence and Stability . . . . . . . . . . . . . . . . . . . . . . . . . . . 116 3.7.1.2. Table of Simple z-Transforms . . . . . . . . . . . . . . . . . . . . . . . . . 117 3.7.1.3. Properties of the z-Transform . . . . . . . . . . . . . . . . . . . . . . . . . 117 3.7.1.4. Discrete Transfer or System Function . . . . . . . . . . . . . . . . . . . . 1173.8. Fourier Analysis for Discrete-Time Systems . . . . . . . . . . . . . . . . . . . . . . . . . . . 118 3.8.1. Introduction. ......................................... 118 3.8.2. The Discrete Fourier Transform. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 119 3.8.3. The Fast Fourier Transform . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 120 3.8.4. Properties of the Discrete Fourier Transform. . . . . . . . . . . . . . . . . . . . . . . . . . . 121 3.8.4.1. Periodic or Circular Properties . . . . . . . . . . . . . . . . . . . . . . . . 121 3.8.4.2. The Periodic Time-Shift Property. . . . . . . . . . . . . . . . . . . . . . . 122 3.8.4.3. The Periodic or Circular Convolution . . . . . . . . . . . . . . . . . . . . 123 3.8.4.4. The Discrete Periodic Convolution Theorem . . . . . . . . . . . . . . . . 124 3.8.4.5. The Discrete Frequency Response . . . . . . . . . . . . . . . . . . . . . . 124 3.8.4.6. Relationship between the Bandwidth and the Duration of the Impulse Response. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 124 3.8.4.7. Relationship between the Discrete Fourier Transform and the z-Transform. ................................... 125 3.8.4.8. Increasing the Frequency Resolution of the Discrete Fourier Transform. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1253.9. Summary. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1263.10. Appendix: A Brief Summary of Some Transforms and Theorems Useful in Simulation. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 127 References. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 131
  • 12. xiv ContentsChapter 4. Modeling and Simulation of Linear Time-Invariant and Time-Varying Systems4.1. Modeling and Simulation of Linear Time-Invariant Systems . . . . . . . . . . . . . . . . . 133 4.1.1. LTI Filters: Description, Specification, and Approximation . . . . . . . . . . . . . 134 4.1.1.1. Filter Descriptions. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 135 4.1.1.2. Continuous Classical Filters . . . . . . . . . . . . . . . . . . . . . . . . . . 136 4.1.1.3. Frequency Transformations . . . . . . . . . . . . . . . . . . . . . . . . . . 141 4.1.1.4. Lowpass Equivalents of Bandpass Filters Represented by Rational Functions ..................................... 142 4.1.1.5. Filter Specifications. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 145 4.1.1.6. Approximating Continuous Structures in Discrete Time for Simulation .................................... 145 4.1.2. Simulation of Filtering with Finite Impulse Response Filters . . . . . . . . . . . . 149 4.1.2.1. Simulation of FIR Filtering in the Time Domain . . . . . . . . . . . . . 149 4.1.2.1.1. Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . 149 4.1.2.1.2. Windowing. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 150 4.1.2.2. Simulation of FIR Filtering in the Frequency Domain . . . . . . . . . . 152 4.1.2.2.1. Difference between Periodic and Linear Convolution.... 153 4.1.2.2.2. Linear Convolution for a Signal of Arbitrary Duration via the FFT. . . . . . . . . . . . . . . . . . . . . . . . . . . 154 4.1.2.2.3. The Overlap-and-Add (OA) Method. . . . . . . . . . . . . . . . . 155 4.1.2.2.4. The Overlap-and-Save (OS) Method. . . . . . . . . . . . . . . . . 156 4.1.2.2.5. Efficiency of the Linear Convolution via the FFT. . . . . . . . 158 4.1.2.2.6. Implications of Frequency-Domain FIR Filtering . . . . . . 158 4.1.2.3. Mapping of Continuous Filters into Discrete FIR Filters . . . . . . . . . 159 4.1.2.3.1. FIR Filters Defined in the Time Domain . . . . . . . . . . . 159 4.1.2.3.2. FIR Filters Defined in the Frequency Domain . . . . . . . . 159 4.1.2.4. Comparison of Time-Domain (Impulse Response) and Frequency-Domain (FFT) Implementations for FIR Filtering . . . . . . 162 4.1.3. Simulation of Filtering with IIR Filters . . . . . . . . . . . . . . . . . . . . . . . . . . 165 4.1.3.1. Systems Characterized by Linear Constant-Coefficient Difference Equations ..................................... 165 4.1.3.2. Structures of Recursive Discrete Filters Implemented in Simulation Models ...................................... 166 4.1.3.2.1. Direct-Form (Canonic) Realization. . . . . . . . . . . . . . . . . . . 166 4.1.3.2.2. The Cascade Interconnections of Biquadratic Canonic Sections. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 168 4.1.3.2.3. The Parallel Realization . . . . . . . . . . . . . . . . . . . . . 169 4.1.3.3. Transformations between Continuous-Time and Discrete-Time Systems Represented by Rational Functions . . . . . . . . . . . . . . . . . . . . . . . . . . . 169 4.1.3.3.1. Impulse-Invariant Transformation. . . . . . . . . . . . . . . . 170 4.1.3.3.2. The Bilinear Transformation. . . . . . . . . . . . . . . . . . . 173 4.1.3.3.3. Effect of Mapping on Lowpass-Equivalent Filters Represented by Rational Functions. . . . . . . . . . . . . . . 178 4.1.3.3.4. Guide for Mapping Recursive Filters Specified in Frequency Domain ........................ 178 4.1.4. Effects of Finite Word Length in Simulation of Digital Filters . . . . . . . . . . . 181 4.1.4.1. Roundoff Noise in Simulations of IIR Filters. . . . . . . . . . . . . . . . 181 4.1.4.2. Roundoff Noise in Simulations of FIR Filters . . . . . . . . . . . . . . . 182 4.1.4.3. Effects of Quantization in Computation of the Fast Fourier Transform. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 182
  • 13. Contents xv 4.1.5. Summary of the Process of Mapping Continuous Signals and Systems into Discrete Signals and Systems for Simulation . . . . . . . . . . . . . . . . . . . 182 4.1.5.1. Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 182 4.1.5.2. A Guide to the Selection of the Proper Method of Filter Simulation. . 1834.2. Time-Varying Linear Systems. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 184 4.2.1. Examples of Time-Varying Systems . . . . . . . . . . . . . . . . . . . . . . . . . . . 185 4.2.2. Time-Domain Description for Linear Time-Varying Systems . . . . . . . . . . . . 186 4.2.2.1. The Impulse Response . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 186 4.2.2.2. The Superposition Integral. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 187 4.2.3. Frequency-Domain Representations of Time-Varying Systems . . . . . . . . . . . 188 4.2.3.1. Two-Dimensional Frequency Response . . . . . . . . . . . . . . . . . . . 189 4.2.3.2. Bandwidth Relations in Time-Varying Systems . . . . . . . . . . . . . . 189 4.2.3.3. Sampling Rate . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 190 4.2.4. Properties of Linear Time-Varying Systems. . . . . . . . . . . . . . . . . . . . . . . 190 4.2.4.1. Introduction. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 190 4.2.4.2. Interconnections of Linear Time-Varying Systems. . . . . . . . . . . . . . . . 190 4.2.5. Models for LTV Systems . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 192 4.2.5.1. Linear Differential Equation with Time-Varying Coefficients . . . . . . 192 4.2.5.2. Separable Models ................................ 193 4.2.5.3. Tapped Delay-Line Channel Models . . . . . . . . . . . . . . . . . . . . . 1954.3. Summary. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1964.4. Appendix: Biquadratic Factors for Classical Filters . . . . . . . . . . . . . . . . . . . . . . . 198 References ............................................... 201Chapter 5. Modeling and Simulation of Nonlinear Systems5.1. Modeling Considerations for Nonlinear Systems . . . . . . . . . . . . . . . . . . . . . . . . 2045.2. Memoryless Nonlinearities. ..................................... 206 5.2.1. Memoryless Baseband Nonlinearities . . . . . . . . . . . . . . . . . . . . . . . . . . 206 5.2.2. Estimating the Sampling Rate for Nonlinear Systems. . . . . . . . . . . . . . . . . 207 5.2.3. Memoryless Bandpass Nonlinearities: Analytically Based Models . . . . . . . . . 209 5.2.3.1. The Limiter Family . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 212 5.2.3.2. Power Series Model. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 214 5.2.4. Memoryless Bandpass Amplifiers: Empirically Based Models . . . . . . . . . . . 215 5.2.4.1. Description and Interpretation of AM/AM and AM/PM Characteristics for Simulation. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 218 5.2.4.2. Lowpass Equivalent of a Bandpass Amplifier . . . . . . . . . . . . . . . 219 5.2.4.3. Alternative Approaches to Defining AM/AM and AM/PM Characteristics .................................. 220 5.2.4.4. Multiple Carriers and Intel-modulation Products . . . . . . . . . . . . . . 221 5.2.4.5. Setting the Operating Point of a Memoryless Nonlinearity. . . . . . . . 2235.3. Nonlinearities with Memory (NLWM). . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 224 5.3.1. NLWM Modeling I: Fitting Swept-Tone AM/AM and AM/PM Measurements ........................................ 227 5.3.1.1. The Poza–Sarokozy–Berger (PSB) Model. . . . . . . . . . . . . . . . . . 227 5.3.1.1.1. AM/AM Characteristics . . . . . . . . . . . . . . . . . . . . . 227 5.3.1.1.2. AM/PM Characteristics . . . . . . . . . . . . . . . . . . . . . 229 5.3.1.1.3. Combined Model . . . . . . . . . . . . . . . . . . . . . . . . . 229 5.3.1.2. The Saleh Model ................................ 229 5.3.1.3. The Abuelma’atti Model. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 232 5.3.2. NLWM Modeling II: Fitting Preset Structures . . . . . . . . . . . . . . . . . . . . . 234
  • 14. xvi Contents 5.3.2.1. One Filter–One Nonlinearity (Two-Box) Models. . . . . . . . . . . . . . 234 5.3.2.1.1. Filter–Nonlinearity with Least-Squares Fit . . . . . . . . . . 234 5.3.2.1.2. Filter–Nonlinearity ARMA Model. . . . . . . . . . . . . . . . . . 235 5.3.2.1.3. Filter–Nonlinearity with Small-Signal Transfer Function. . . 235 5.3.2.1.4. Nonlinearity–Filter with Least-Squares Fit . . . . . . . . . . 236 5.3.2.2. Filter–Nonlinearity–Filter (Three-Box) Models. . . . . . . . . . . . . . . 236 5.3.2.2.1. Three-Box Model with Least-Squares Fit . . . . . . . . . . . 236 5.3.2.2.2. Three-Box Model with Specified Characteristics. . . . . . . 237 5.3.3. NLWM Modeling III: Analytical Models . . . . . . . . . . . . . . . . . . . . . . . . 237 5.3.3.1. Volterra Series Modeling. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 237 5.3.3.2. Polyspectral Models. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 245 5.3.3.2.1. Nonlinearity–Filter Polyspectral Model . . . . . . . . . . . . 246 5.3.3.2.2. Filter–Nonlinearity Polyspectral Model . . . . . . . . . . . . 249 5.3.4. NLWM Modeling IV: Miscellaneous Models. . . . . . . . . . . . . . . . . . . . . . 252 5.3.4.1. Power-Dependent Transfer Function Model. . . . . . . . . . . . . . . . . . . . 252 5.3.4.2. Nonlinear Parametric Discrete-Time Models . . . . . . . . . . . . . . . . 253 5.3.4.3. Instantaneous Frequency Model. . . . . . . . . . . . . . . . . . . . . . . . 255 5.3.5. Setting the Operating Point for a Nonlinearity with Memory . . . . . . . . . . . . 2565.4. Nonlinear Differential Equations . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 257 5.4.1. Outline of Numerical Methods . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 257 5.4.2. Families of Numerical Methods. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 261 5.4.2.1. Solution Using Explicit Methods . . . . . . . . . . . . . . . . . . . . . . . 263 5.4.2.2. Solution Using Implicit Methods . . . . . . . . . . . . . . . . . . . . . . . 263 5.4.2.2.1. Iterated Predictor–Corrector Method. . . . . . . . . . . . . . . . . 263 5.4.2.2.2. Root Finding Using Newton–Raphson Method . . . . . . . 264 5.4.3. Properties of Numerical Methods: Accuracy and Stability . . . . . . . . . . . . . . 266 5.4.3.1. Order of a Method: Computation of Local or Truncation Error. . . . . . . 268 5.4.3.2. Absolute Stability . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 269 5.4.4. Computational Considerations: Methods of Quality Control . . . . . . . . . . . . . . . . 270 5.4.5. Application of Numerical Methods. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 271 5.4.5.1. Introduction. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 271 5.4.5.2. Stand-Alone Model for a Traveling-Wave Semiconductor Amplifier. . . 2725.5. Measurement Technique for Nonlinear Components . . . . . . . . . . . . . . . . . . . . . . 275 5.5.1. The Vector Network Analyzer Single-Tone Measurement . . . . . . . . . . . . . . 275 5.5.2. Dynamic AM/AM and AM/PM Measurement Techniques Using a Periodically Modulated Signal. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 277 5.5.3. Time-Domain Measurement Techniques. . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2805.6. Summary ................................................ 284 References ............................................... 285Chapter 6. Fundamentals of Random Variables and Random Processes for Simulation6.1. Introduction .............................................. 2896.2. Random Variables. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 291 6.2.1. Basic Concepts, Definitions, and Notations . . . . . . . . . . . . . . . . . . . . . . . . . . . 291 6.2.1.1. Introduction. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 291 6.2.1.2. Statistical Averages or Expected Values . . . . . . . . . . . . . . . . . . . 293 6.2.2. Multidimensional Random Variables (Random Vectors) . . . . . . . . . . . . . . . 294 6.2.3. Complex Random Variables . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2976.3. Univariate Models ........................................... 297
  • 15. Contents xvii 6.3.1. Univariate Models–Discrete . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 298 6.3.1.1. Uniform. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 298 6.3.1.2. Binomial. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 298 6.3.1.3. Negative Binomial. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 299 6.3.1.4. Poisson. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 299 6.3.2. Univariate Models—Continuous. . . . . . . . . . . . . . . . . . . . . . . . . . . . . 300 6.3.2.1. Uniform. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 300 6.3.2.2. Gaussian (Normal). . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 301 6.3.2.3. Exponential . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 301 6.3.2.4. Gamma. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 302 6.3.2.5. Rayleigh. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 302 6.3.2.6. Chi-Square. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 303 6.3.2.7. Student’s t. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 303 6.3.2.8. F Distribution. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 304 6.3.2.9. Generalized Exponential. . . . . . . . . . . . . . . . . . . . . . . . . . . . 3046.4. Multivariate Models. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 304 6.4.1. Multinomial. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 304 6.4.2. Multivariate Gaussian. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 305 6.4.2.1. Properties of the Multivariate Gaussian Distribution . . . . . . . . . . . 305 6.4.2.2. Moments of Multivariate Gaussian pdf. . . . . . . . . . . . . . . . . . . 3086.5. Transformations (Functions) of Random Variables. . . . . . . . . . . . . . . . . . . . . . . 308 6.5.1. Scalar-Valued Function of One Random Variable . . . . . . . . . . . . . . . . . . . 310 6.5.1.1. Discrete Case. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 310 6.5.1.2. Continuous Case. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 310 6.5.2. Functions of Several Random Variables. . . . . . . . . . . . . . . . . . . . . . . . . . . . . 313 6.5.2.1. Special Case—Linear Transformation. . . . . . . . . . . . . . . . . . . . 313 6.5.2.2. Sum of Random Variables. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 314 6.5.2.3. Order Statistics. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 315 6.5.3. Nonlinear Transformations. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 316 6.5.3.1. Moment-Based Techniques. . . . . . . . . . . . . . . . . . . . . . . . . . 316 6.5.3.2. Monte Carlo Simulation Techniques . . . . . . . . . . . . . . . . . . . . 3166.6. Bounds and Approximations. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 317 6.6.1. Chebyshev’s Inequality. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 317 6.6.2. Chernoff Bound. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 318 6.6.3. Union Bound. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 318 6.6.4. Central Limit Theorem. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 320 6.6.5. Approximate Computation of Expected Values. . . . . . . . . . . . . . . . . . . . . 321 6.6.5.1. Series Expansion Technique. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 321 6.6.5.2. Moments of Finite Sums of Random Variables. . . . . . . . . . . . . . . 322 6.6.5.3. Quadrature Approximations . . . . . . . . . . . . . . . . . . . . . . . . . . 3236.7. Random Processes. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 326 6.7.1. Basic Definitions and Notations. . . . . . . . . . . . . . . . . . . . . . . . . . . . . 326 6.7.2. Methods of Description. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 328 6.7.2.1. Joint Distribution. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 328 6.7.2.2. Analytical Description Using Random Variables . . . . . . . . . . . . . . . . . 328 6.7.2.3. Average Values. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 329 6.7.2.4. Two or More Random Processes. . . . . . . . . . . . . . . . . . . . . . . 330 6.7.3. Stationarity, Time Averaging, and Ergodicity. . . . . . . . . . . . . . . . . . . . . . . . . . 331 6.7.3.1. Time Averages. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 332 6.7.3.2. Ergodicity. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 333 6.7.4. Correlation and Power Spectral Density Function of Stationary Random Processes. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 334
  • 16. xviii Contents 6.7.4.1. Autocorrelation Function and Its Properties. . . . . . . . . . . . . . . . . 335 6.7.4.2. Cross-Correlation Function and Its Properties . . . . . . . . . . . . . . . 335 6.7.4.3. Power Spectral Density. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 336 6.7.4.4. Lowpass and Bandpass Processes. . . . . . . . . . . . . . . . . . . . . . . 337 6.7.4.5. Power and Bandwidth Calculations. . . . . . . . . . . . . . . . . . . . . . 338 6.7.5. Cross-Power Spectral Density Function and Its Properties . . . . . . . . . . . . . . 338 6.7.6. Power Spectral Density Functions of Random Sequences . . . . . . . . . . . . . . 3396.8. Random Process Models. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 340 6.8.1. Random Sequences . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 340 6.8.1.1. Independent Sequences. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 340 6.8.1.2. Markov Sequences (First Order) . . . . . . . . . . . . . . . . . . . . . . . 340 6.8.1.3. Autoregressive and Moving Average (ARMA) Sequences . . . . . . . . 342 6.8.2. M-ary Digital Waveforms ................................. 344 6.8.2.1. Introduction. ................................... 344 6.8.2.2. Random Binary Waveform. . . . . . . . . . . . . . . . . . . . . . . . . . . 345 6.8.3. Poisson Process ....................................... 346 6.8.4. Shot Noise and Impulsive Noise . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 346 6.8.4.1. Shot Noise .................................... 346 6.8.4.2. Impulsive Noise . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 348 6.8.5. Gaussian Process ...................................... 350 6.8.5.1. Definition of a Gaussian Process . . . . . . . . . . . . . . . . . . . . . . . 351 6.8.5.2. Models of White and Bandlimited White Noise . . . . . . . . . . . . . . 352 6.8.5.3. Quadrature Representation of Bandpass (Gaussian) Signals . . . . . . . 3546.9. Transformation of Random Processes . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 357 6.9.1. Response of Linear Time-Invariant Causal (LTIVC) System. . . . . . . . . . . . . 357 6.9.1.1. Stationarity .................................... 357 6.9.1.2. Probability Distribution. . . . . . . . . . . . . . . . . . . . . . . . . . . . . 357 6.9.1.3. Mean, Autocorrelation, and Power Spectral Density Functions . . . . . 357 6.9.2. Filtering. ........................................... 358 6.9.3. Integration .......................................... 360 6.9.4. Response of Nonlinear and Time-Varying Systems . . . . . . . . . . . . . . . . . . 361 6.9.4.1. Nonlinear Systems. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 361 6.9.4.2. Time-Varying Systems . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3626.10. Sampling of Stationary Random Processes . . . . . . . . . . . . . . . . . . . . . . . . . . . . 362 6.10.1. Sampling ........................................... 362 6.10.1.1. Sampling of Lowpass Random Processes . . . . . . . . . . . . . . . . . 362 6.10.1.2. Aliasing Effect. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 363 6.10.1.3. Sampling Rate for Simulations . . . . . . . . . . . . . . . . . . . . . . . 365 6.10.1.4. Sampling of Bandpass Random Process . . . . . . . . . . . . . . . . . . 365 6.10.2. Quantization ......................................... 366 6.10.2.1. Uniform Quantization. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 367 6.10.2.2. Nonuniform Quantizer . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3686.11. Summary ................................................ 369 References ............................................... 369Chapter 7. Monte Carlo Simulation and Generation of Random Numbers7.1. Principle of Monte Carlo Simulation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 371 7.1.1. Definition of Monte Carlo Simulation . . . . . . . . . . . . . . . . . . . . . . . . . . 371 7.1.2. Variations of Monte Carlo Simulation—Quasianalytical Monte Carlo Simulation .................................. 373
  • 17. Contents xix7.2. Random Number Generation .................................... 373 7.2.1. Generation of Uniform Random Numbers . . . . . . . . . . . . . . . . . . . . . . . 374 7.2.1.1. Wichman–Hill Algorithm ........................... 376 7.2.1.2. Marsaglia–Zaman Algorithm . . . . . . . . . . . . . . . . . . . . . . . . . 376 7.2.2. Methods of Generating Random Numbers from an Arbitrary pdf . . . . . . . . . . 377 7.2.2.1. Transform Method ( Analytical) . . . . . . . . . . . . . . . . . . . . . . . . . . . . 377 7.2.2.2. Transform Method (Empirical) . . . . . . . . . . . . . . . . . . . . . . . . 379 7.2.2.3. Transform Method for Discrete Random Variables . . . . . . . . . . . . 380 7.2.2.4. Acceptance/Rejection Method of Generating Random Numbers . . . . 381 7.2.3. Generating Gaussian Random Variables. . . . . . . . . . . . . . . . . . . . . . . . . . . . . 383 7.2.3.1. Sum-of-12 Method ............................... 383 7.2.3.2. Box Müller Method. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3837.3. Generating Independent Random Sequences . . . . . . . . . . . . . . . . . . . . . . . . . . . 384 7.3.1. White Gaussian Noise ................................... 384 7.3.2. Random Binary Sequences and Random Binary Waveforms . . . . . . . . . . . . 385 7.3.3. Pseudorandom Binary Sequences. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 386 7.3.4. M-ary Pseudo noise Sequences . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3897.4. Generation of Correlated Random Sequences . . . . . . . . . . . . . . . . . . . . . . . . . . 392 7.4.1. Correlated Gaussian Sequences: Scalar Case. . . . . . . . . . . . . . . . . . . . . . . . 393 7.4.1.1. Autoregressive Moving Average (ARMA) Models. . . . . . . . . . . . . 393 7.4.1.2. Spectral Factorization Method. ........................ 395 7.4.2. Correlated Gaussian Vector Sequences . . . . . . . . . . . . . . . . . . . . . . . . . 397 7.4.2.1. Special Case ................................... 397 7.4.2.2. General Case . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 398 7.4.3. Correlated Non-Gaussian Sequences. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3997.5. Testing of Random Number Generators . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 400 7.5.1. Stationarity and Uncorrelatedness . . . . . . . . . . . . . . . . . . . . . . . . . . . . 400 7.5.1.1. Introduction. ................................... 400 7.5.1.2. Durbin Watson Test for Correlation . . . . . . . . . . . . . . . . . . . . . 401 7.5.2. Goodness-of-Fit Tests. ................................... 4027.6. Summary. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 405 References ............................................... 406Chapter 8. Modeling of Communication Systems: Transmitter and Receiver Subsystems8.1. Introduction .............................................. 4078.2. Information Sources ......................................... 411 8.2.1. Analog Sources ....................................... 411 8.2.1.1. Single Test Tone. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 412 8.2.1.2. Multiple Test Tones. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 412 8.2.1.3. Filtered Random Processes. . . . . . . . . . . . . . . . . . . . . . . . . . . 413 8.2.1.4. Stored Experimental Data . . . . . . . . . . . . . . . . . . . . . . . . . . . 413 8.2.2. Digital Sources. ....................................... 4138.3. Formatting/Source Coding ..................................... 414 8.3.1. Analog-to-Digital (A/D) Conversion. . . . . . . . . . . . . . . . . . . . . . . . . . . 414 8.3.2. On Simulating the FSC Subsystem. . . . . . . . . . . . . . . . . . . . . . . . . . . . 4168.4. Digital Waveforms: Baseband Modulation (I) . . . . . . . . . . . . . . . . . . . . . . . . . . 4178.5. Line Coding: Baseband Modulation (II). . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 420 8.5.1. Logical-to-Logical Mapping I: Binary Differential Encoding . . . . . . . . . . . . 420
  • 18. xx Contents 8.5.2. Logical-to-Logical Mapping II: Correlative Coding . . . . . . . . . . . . . . . . . . 421 8.5.3. Logical-to-Logical Mapping III: Miller Code. . . . . . . . . . . . . . . . . . . . . . . . 421 8.5.4. Logical-to-Real Mapping I: Non-Return to Zero (NRZ) Binary Signaling . . . . 422 8.5.5. Logical-to-Real Mapping II: NRZ M-ary Signaling (PAM) . . . . . . . . . . . . . 423 8.5.6. Logical-to-Real Mapping III: Return-to-Zero (RZ) Binary Signaling. . . . . . . . 423 8.5.7. Logical-to-Real Mapping IV: Biphase Signaling or Manchester Code . . . . . . . 423 8.5.8. Logical-to-Real Mapping V: Miller Code or Delay Modulation. . . . . . . . . . . . . . . 423 8.5.9. Logical-to-Real Mapping VI: Partial Response Signaling . . . . . . . . . . . . . . 4258.6. Channel Coding. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 425 8.6.1. Computational Load for Block Coding/Decoding. . . . . . . . . . . . . . . . . . . . . . . . 428 8.6.2. Computational Load for Convolutional Coding/Decoding . . . . . . . . . . . . . . 4318.7. Radiofrequency and Optical Modulation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 433 8.7.1. Analog Modulation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 434 8.7.2. Digital Quadrature Modulation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 435 8.7.2.1. QPSK: Differential Quaternary Phase-Shift-Keying (DQSK). . . . 438 8.7.2.2. Multitone Modulation/OFDM. . . . . . . . . . . . . . . . . . . . . . . . . 439 8.7.3. Continuous Phase Modulation CPFSK, MSK, GMSK . . . . . . . . . . . . . . . . 443 8.7.3.1. Continuous Phase Modulation. . . . . . . . . . . . . . . . . . . . . . . . . 443 8.7.3.2. Continuous-Phase Frequency-Shift-Keying . . . . . . . . . . . . . . . . . 445 8.7.3.3. Minimum-Shift-Keying. . . . . . . . . . . . . . . . . . . . . . . . . . . . . 446 8.7.3.4. Gaussian Minimum-Shift-Keying. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 447 8.7.4. Coded Modulation. ..................................... 449 8.7.5. Modeling Considerations. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4518.8. Demodulation and Detection . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 455 8.8.1. Coherent Demodulation .................................. 457 8.8.2. Noncoherent Demodulation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 460 8.8.2.1. Amplitude Demodulation. . . . . . . . . . . . . . . . . . . . . . . . . . . . 460 8.8.2.2. Discriminator Detection of PM/FM Signals . . . . . . . . . . . . . . . . 461 8.8.2.3. PLL Demodulation of PM/FM Signals . . . . . . . . . . . . . . . . . . . 4658.9. Filtering ................................................. 467 8.9.1. Filters for Spectral Shaping . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 467 8.9.2. Filters for Pulse Shaping. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 468 8.9.3. Linear Minimum MSE Filters. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 470 8.9.4. Filters for Minimizing Noise and Distortion . . . . . . . . . . . . . . . . . . . . . . 471 8.9.5. Matched Filters ....................................... 472 8.9.6. Adaptive Filtering ( Equalization) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 474 8.9.6.1. Tap-Gain Adaptation for Minimizing MSE . . . . . . . . . . . . . . . . . 476 8.9.6.2. Covariance Matrix Inversion Method. . . . . . . . . . . . . . . . . . . . . 479 8.9.6.3. Simulation Considerations . . . . . . . . . . . . . . . . . . . . . . . . . . . 480 8.9.7. Filters Specified by Simple Functions in the Frequency Domain . . . . . . . . . . 481 8.9.8. Tabular Filter for Masks and Measurements . . . . . . . . . . . . . . . . . . . . . . 4838.10. Multiplexing/Multiple Access ................................... 484 8.10.1. Issues in the Simulation of Multiple-Access Methods. . . . . . . . . . . . . . . . . . . 484 8.10.1.1. SDMA and PDMA. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 484 8.10.1.2. FDMA ..................................... 486 8.10.1.3. TDMA ..................................... 487 8.10.1.4. CDMA (Spread Spectrum Techniques) . . . . . . . . . . . . . . . . . . 4898.11. Radiofrequency and Optical Carrier Sources. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 491 8.11.1. Radiofrequency Sources ................................. 491 8.11.2. Optical Sources . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4928.12. Synchronization ............................................ 495 8.12.1. Approaches to Including Synchronization in Simulation . . . . . . . . . . . . . . . 498
  • 19. Contents xxi 8.12.2. Hardwired Synchronization: Phase and Timing Bias . . . . . . . . . . . . . . . . . 500 8.12.3. Synchronization Using an Equivalent Random Process Model . . . . . . . . . . . 502 8.12.4. Carrier Recovery—BPSK . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 504 8.12.5. Timing Recovery—BPSK. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 506 8.12.6. Carrier Recovery—QPSK. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 510 8.12.7. Timing Recovery—QPSK. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 513 8.12.8. Simulation of Feedback Loops: Application to the Phase-Locked Loop, Phase-Locked Demodulator, and Costas Loop . . . . . . . . . . . . . . . . . . . . . 514 8.12.8.1. Modeling Considerations for the PLL . . . . . . . . . . . . . . . . . . . . 514 8.12.8.2. Stand-Alone PLL Model. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 515 8.12.8.3. Assembled PLL Model. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 522 8.12.8.4. The Phase-Locked Loop as a Phase Tracker . . . . . . . . . . . . . . . . 528 8.12.8.5. The Phase-Locked Loop as an FM Demodulator . . . . . . . . . . . . . 529 8.12.8.6. Effect of Delay on the Performance of the Assembled PLL Model. . . 5318.13. Calibration of Simulations. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 534 8.13.1. Introduction. ......................................... 534 8.13.2. Calibration of Signal-to-Noise Ratio or for Digital S i g n a l i n g . . . . . . . . 535 8.13.2.1. Signal Power Level . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 535 8.13.2.2. Noise Power Level . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 538 8.13.2.3. Calibrating Signal-to-Noise Ratio and ................ 5388.14. Summary. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 539 References ............................................... 540Chapter 9. Communication Channels and Models9.1. Fading and Multipath Channels. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 546 9.1.1. Introduction. ......................................... 546 9.1.2. Shadow Fading. ....................................... 547 9.1.3. Multipath Fading ...................................... 549 9.1.3.1. Lowpass-Equivalent Characterization of Multipath Channels . . . . . . 550 9.1.3.2. Statistical Characterization of Multipath Channels. . . . . . . . . . . . . . . . 551 9.1.3.3. Statistical Characterization of the Time-Variant Behavior. . . . . . . . . . . 551 9.1.3.4. Statistical Characterization: The WSSUS Model. . . . . . . . . . . . . . 553 9.1.3.4.1. The Delay Power Profile . . . . . . . . . . . . . . . . . . . . . . . . 554 9.1.3.4.2. The Spaced-Frequency Correlation Function. . . . . . . . . . . . 557 9.1.3.4.3. The Time-Varying Channel . . . . . . . . . . . . . . . . . . . 558 9.1.3.5. Structural Models for Multipath Fading Channels . . . . . . . . . . . . . 561 9.1.3.5.1. Diffuse Multipath Channel Model . . . . . . . . . . . . . . . 561 9.1.3.5.2. Statistical Tap-Gain Models. . . . . . . . . . . . . . . . . . . . . 572 9.1.3.5.3. Generation of Tap-Gain Processes . . . . . . . . . . . . . . . 575 9.1.3.6. Indoor Wireless Channels . . . . . . . . . . . . . . . . . . . . . . . . . . . 576 9.1.3.6.1. Factory and Open-Plan-Building Model. . . . . . . . . . . . 577 9.1.3.6.2. Office Building Model. . . . . . . . . . . . . . . . . . . . . . . . 578 9.1.3.6.3 Ray-Tracing Prediction Model. . . . . . . . . . . . . . . . . . . . 582 9.1.3.7. Radio-Relay Line-of-Sight (LOS) Discrete Multipath Fading Channel Model. ................................. 5839.2. The Almost Free-Space Channel. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 586 9.2.1. Clear-Air Atmospheric (Troposphenc) Channel . . . . . . . . . . . . . . . . . . . . 587 9.2.2. The Rainy-Atmospheric Channel. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .