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					APPLICATION OF THE FOUR VARIABLE MODEL
APPLICATION OF THE FOUR VARIABLE MODEL

     TO A CAD SYSTEM FOR MICROWAVE

         COMMUNICATIONS DEVICES




                           by

Yun Zou, B.Sc., M.Sc., (Wuhan University of Technology)

            M.Eng. (McMaster University)




                        A Thesis

      Submitted to the School of Graduate Studies

        in Partial Fulfillment of the Requirements

                     for the Degree

                 Master of Engineering




                 McMaster University



                            ii
MASTER OF ENGINEERING (2000)                                       McMaster University

(Computer Engineering)                                          Hamilton, Ontario




TITLE:               Application of the Four Variable Model to a CAD System for

                     Microwave Communications Devices



AUTHOR:              Yun Zou, B.Sc., M.Sc., M.Eng.

SUPERVISOR:          Dr. David L. Parnas, Professor of Computing and Software

NUMBER OF PAGES:x, 170




                                          iii
ABSTRACT



          The four variable model was successfully applied to the water level system, a simple

and practical real-time control system [van Schouwen90]. In this work, the application of the

four-variable model to the CAD system for microwave communications systems (CADMCS), a

complex non-real-time software package, has been studied. The documentation of the complete

system requirements for the CADMCS system has been presented.

          The four variable model has been reviewed in detail. Based on the characteristics of

CAD systems, the techniques to control the complexity using the well-known principles such as

information-hiding, separation of concerns or divide-and-conquer have been discussed. The use

of well-known mathematical concepts such as vectors, vector functions, as well as geometry

objects as the types of the monitored and controlled variables has been demonstrated. New

types of the variables are also introduced to abstract application domain objects and to serve as

the mechanism to support a hierarchical system structure.

        The recursive decomposition of the monitored and controlled variables has been

demonstrated in this work. Relational algebra has been applied to presenting and organizing the

REQ (requirements) relation in the CADMCS system. It has been shown how complex

relations can be described in terms of simpler sub-relations by the decomposition operator in

the relational algebra.




                                               iv
ACKNOWLEDGEMENT



        I would like to express my sincere thanks to Dr. David L. Parnas for his guidance,

insight and support throughout the preparation of this thesis.

        I would like to thank Dr. Chen Wu, Mr. Patrick Yau, Mr. Yan Zhang for the long

helpful discussions about the domain expertise involved in the CADMCS system and their

reviewing of the system requirements document as well as for their donations of the related

programs and document.

        I would also like to thank Dr. Tom Luo and Dr. Martin von Mohrenschildt for their

helpful comments and suggestions after reading the thesis. I would like to thank Dr. Anthony

Petric and Dr. Alex Zhang for voluntarily helping to improve the quality of the thesis from the

technical presentation point of view.

        My appreciation goes to the staff members Doris Burns and Cheryl Gies for their help

with administrative matters during my work on this thesis.

        Finally, I would like to acknowledge the financial support of the Natural Sciences and

Engineering Research Council of Canada, Bell Canada, The Telecommunications Research

Institute of Ontario (TRIO/CITO).




                                                 v
TABLE OF CONTENTS



ABSTRACT ………………………………………………………………………….                                      iii

ACKNOWLEDGEMENT          ………………………………………………………… iv

TABLE OF CONTENTS ………………………………………….………………...                                vi

CHAPTER 1 INTRODUCTION …………………………………………………….                                1

Section 1 Why a Software Requirements Document Is Needed………………………       1

Section 2 What Are Software Requirements? …………………………………………              3

Section 3 The Four-Variable Model …………………………………………………...                    4

 3.1. Introduction…………………………………………………….………………..                             4

 3.2. The Four Variables …………………………………………….………………..                         6

 3.3. The Relation NAT ……………………………………………….…………….                        10

 3.4. The Relation REQ …………………………………………………………….. 11

 3.5. The Relation IN ………………………………………………….…………….                        12

 3.6. The Relation OUT ……………………………………………….…………….. 12

 3.7. Contents of System Requirements Document …………………………………           13

 3.8. Contents of System Design Document ………………………………………...            13

 3.9. Software Behaviour Document ………………………………………………..                 14

Section 4 Why Apply the Four-Variable Model to a CAD System? …………………   15


                                    vi
 4.1. Real-Time vs. Non-Real-Time …………………………………………………                    15

 4.2. Is the Four-Variable Model Practical for a CAD System?….………………….. 19

 4.3. Why the CADMCS System? ………………….………………………………. 20

Section 5 The Scope of the Thesis …………………….……………………………...               21

CHAPTER 2 MATHEMATICS BACKGROUND ……………………………...                          23

Section 1 Why This Chapter Is Needed? …………………………………………….                23

Section 2 Relational Algebra ………………………………………………………...                   24

 2.1. Relations and Functions ………………………………………………………..                   24

 2.2. Relational Algebra ……………………………………………………………..                      27

 2.3. Graphical Notation ……………………………………………………………..                       34

Section 3 Review of Vector Analysis ………………………………………………...               39

Section 4 Geometry Review …………………………………………………………                        44

Section 5 Review of the Tabular Notation ……………..……………………………..           50

 5.1. Introduction ……………………………………………………………….…… 50

 5.2. Terminology in Tables .………………………………………………………..                    51

 5.3. Normal Tables ………………………………………………………………….                           52

 5.4. Vector Tables …………………………………………………………………..                          53

 5.5. Mixed Vector Tables …………………………………………………………... 53

CHAPTER 3 DISCUSSION OF THE APPLICATION OF THE FOUR VARIABLE

            MODEL TO A CAD SYSTEM ……………………………………                         55


                                     vii
Section 1 Description of the CADMCS System …………….……………………….                 55

Section 2 Conquering Complexity ……………………………………………………                         57

Section 3 The Monitored and Controlled Variables in the CADMCS System ……….. 58

Section 4 The Relation REQ ………………………………………………………….. 64

 4.1. System Mode and REQ Relation Partition ………..…………………………...             64

 4.2. REQ E Relation…………………………………………………………….……                                   66

 4.3. REQ I Relation ……….….……………………………………………….……..                               67

 4.4. REQ P Relation ….………………….…………………………………….…….                                67

Section 5 System Design Document ………………………………………………….                        69

CHAPTER 4 SUMMARY AND FUTURE WORK …..…………………………... 71

REFERENCES ………………………….………………………………………….. 74

APPENDIX A THE SYSTEM REQUIREMENTS OF A CAD SYSTEM FOR

               MICROWAVE COMMUNICATIONS DEVICES USING THE

               FOUR-VARIABLE MODEL ………….………………………… 78

Chapter A1 The Monitored Variables ….………………………………………….                       78

Section 1 Physical Variables (ME) ………….….……………………………………..                    78

 1.1. Known Actual Values (MK) ….………………………………………………..                        79

 1.2. Unknown Actual Value (MR) ……….…………………..……………………...                     91

Section 2 System Status Variables (MI) ………………….…….……………………..                 94

 2.1. Requesting Customizing Parameters …………….………..…………………...               94

                                       viii
 2.2. Status Except for Requesting Customizing Parameters………………………...   96

Section 3 Monitored Parameters (MP) ….…………………………..………………..                99

Chapter A2 The Controlled Variables …………….……………………………...                 103

Section 1 Computed Values (Cc) ……………………..…………………………….. 103

Section 2 Messages (C M) ……………………………………………………………                         106

 2.1. Customizing Parameters ………………...………………………………….                    106

 2.2. Status Messages Except for Customizing Parameters ……………………….      109

Section 3 Controlled Parameters (Cp) ………………………………………………                  110

Chapter A3 NAT and REQ Relation …….………………………………………                       114

Section 1 NAT Relation ……………………………………………………………..                         114

Section 2 System Mode and REQ Relation Partition …….………………………           114

 2.1. Mode Definitions ……………………………………………………………                           114

 2.2. Mode Transition Table ………………………………………………………                        115

 2.3. REQ Partition and Decomposition ……………….……………….……….…                115

Section 3 REQ E Relation ………………………………..……………………….….                      116

 3.1. REQ EI …………………………………………………..…………………….. 116

 3.2. REQ EO ………………………………………………………………..……….                               117

Section 4 REQ I Relation ………………………………………………………….                         124

Section 5 REQ P Relation …………………………………………………………...                       130

Chapter A4 MACROS, PREDICATES AND FUNCTIONS ……………………                     132
                                     ix
Section 1 Macro Definitions …..…………………………………………………….                                    132

Section 2 Predicate Definitions …………….……………………………………….                                  135

Section 3 Function Definitions …………………………………………………….. 138

CHAPTER A5 CONSTANT DEFINITIONS ……………………………………                                              139

Section 1 General Symbolic Definitions ……………….……………………………. 139

Section 2 Tolerance Constants ….………………………………………………….                                        142

CHAPTER A6 NEW VARIABLE TYPES DEFINITIONS ….…………………                                     144

Section 1 GAUSS Type ……..………………………………………………………                                              144

Section 2 MODGAUSS Type ………………………………………………………                                               146

Section 3 SYNTHETIC Type ……………………………………………………...                                            149

Section 4 SOUEXPRN Type ……………………………………………………….. 152

CHAPTER A7 FUNDAMENTAL ASSUMPTIONS …………………………... 155

Appendix B NOTATION AND PHYSICAL QUANTITIES ………………...…                                  156

Section 1 Notation ….………….…………………………………………………….                                             156

Section 2 Units, Standards and Symbols for Physical Quantities …………………...             158

APPENDIX C INDEX TO THE DEFINITIONS OF THE MONITORED,

CONTROLLED VARIABLES AND CONSTANTS……………………………..                                             162

Section 1. Index to the Definitions of the Monitored and Controlled Variables ..…..   162

Section 2. Index to the Definitions of the Constants ……...………………………..                  169




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