National Bureau of Standards Library, N.W. Bldg AUG 8 1962 ^ecltnical ^lote 100 REQUIRED SIGNAL-TO-NOISE RATIOS, RF SIGNAL POWER, AND BANDWIDTH FOR MULTICHANNEL RADIO COMMUNICATIONS SYSTEMS E. F. FLORMAN AND J. J. TARY U. S. DEPARTMENT OF COMMERCE NATIONAL BUREAU OF STANDARDS THE NATIONAL BUREAU OF STANDARDS Functions and Activities The functions of the National Bureau of Standards are set forth in the Act of Congress, March 3, 1901, as amended by Congress in Public Law 619, 1950. These include the development and maintenance of the na- tional standards of measurement and the provision of means and methods for making measurements consistent with these standards; the determination of physical constants and properties of materials; the development of methods and instruments for testing materials,- devices, and structures; advisory services to government agen- cies on scientific and technical problems; invention and development of devices to serve special needs of the Government; and the development of standard practices, codes, and specifications. The work includes basic and applied research, development, engineering, instrumentation, testing, evaluation, calibration services, and various consultation and information services. Research projects are also performed for other government agencies when the work relates to and supplements the basic program of the Bureau or when the Bureau's unique competence is required. The scope of activities is suggested by the listing of divisions and sections on the inside of the back cover. Publications The results of the Bureau's research are published either in the Bureau's own series of publications or in the journals of professional and scientific societies. The Bureau itself publishes three periodicals avail- able from the Government Printing Office: The Journal of Research, published in four separate sections, presents complete scientific and technical papers; the Technical News Bulletin presents summary and pre- liminary reports on work in progress; and Basic Radio Propagation Predictions provides data for determining the best frequencies to use for radio communications throughout the world. There are also five series of non- periodical publications: Monographs, Applied Mathematics Series, Handbooks, Miscellaneous Publications, and Technical Notes. A complete listing of the Bureau's publications can be found in National Bureau of Standards Circular 460, Publications of the National Bureau of Standards, 1901 to June 1947 ($1. 25), and the Supplement to Na- tional Bureau of Standards Circular 460, July 1947 to June 1957 (SI. 50), and Miscellaneous Publication 240, July 1957 to June 1960 (Includes Titles of Papers Published in Outside Journals 1950 to 1959) ($2. 25); avail- able from the Superintendent of Documents, Government Printing Office, Washington 25, D. C. NATIONAL BUREAU OF STANDARDS technical ^Kiote 100 JANUARY, 1962 ORIGINAL: JULY, 1960 REVISED: NOV., 1960; JUNE, 1961; AND NOV. 1961 REQUIRED SIGNAL-TO-NOISE RATIOS, RF SIGNAL POWER, AND BANDWIDTH FOR MULTICHANNEL RADIO COMMUNICATIONS SYSTEMS E.F. Florman and J.J. Tary NBS Boulder Laboratories NBS Technical Notes are designed to supplement the Bu- reau's regular publications program. They provide a means for making available scientific data that are of transient or limited interest. Technical Notes may be listed or referred to in the open literature. For sale by the Superintendent of Documents, U.S. Government Printing Office Washington 25, D.C. - Price $1.00 CONTENTS Page No. 1. INTRODUCTION 1 2. RADIO COMMUNICATION SYSTEM 4 2. 1 Performance of System 5 2.2 Design and Testing of Equipment and Systems ' 7 3. MODULATOR -TRANSMITTER PERFORMANCE 9 3. 1 Required Radio Frequency Signal-Spectrum 10 Bandwidth for Radio Communication Systems 3. 1. 1 Radio Frequency Bandwidth Required for 10 SSBSC-AM Systems 3. 1.2 Radio Frequency Bandwidth Required for 10 FM Systems 3. 1.2. 1 Required FM Radio Frequency 11 Bandwidth for a Single Sinsoidal Modulating Signal 3.1.2.2 Required FM Radio Frequency 15 Bandwidth for Various Types of Modulating Signals 3.1.2.3 Required FM Radio Frequency 16 Bandwidth for a "White Noise Modulating Signal 3.2 Radio -Frequency Signal Time -Amplitude 23 Characteristics for Radio Communication Systems 3.2.1 Radio-Frequency Signal Time -Amplitude 23 Characteristics for SSBSC-AM Systems 3.2.1.1 Radio-Frequency Signal Time- 23 Amplitude Characteristics of SSBSC-AM Systems for a Single Sinusoidal Modulating Signal 111 Page No. 3.2.1.2 Radio -Frequency Signal Time- 24 Amplitude Characteristics of SSBSC-AM Systems for a White- Noise Type of Modulating Signal 3. 2. 2 Radio-Frequency Signal Time -Amplitude 27 Characteristics for FM Systems 3. 3 Peak Power Requirements for SSBSC-AM Systems 27 RADIO RECEIVER -COMBINER PERFORMANCE 29 4. 1 Radio Frequency Signal Characteristics and 30 Power Levels in the Receiving System 4.2 Pre-Detection Noise-Power Levels in the Re- 33 ceiving System 4. 3 Post-Detection Noise-Power Levels in tne Re- 41 ceiving System 4. 3. 1 Post-Detection Noise Due to Pre-Detec- 43 tion Amplitude Noise 4. 3. 2 . Post-Detection Noise Due to Noise at the 43 Modulator Input 4.3.3 Equipment -Intermodulation Post-Detection 44 Noise 4.3.4 Post-Detection Path-Modulation Noise 47 4.3.5 Total Post-Detection Noise 49 4. 3. 6 Effect of Post-Detection Noise on 50 Receiver Characteristics and Methods of Correcting System -Design Curves 4.4 System Parameters which Affect the Message- 53 Channel Signal -to-Noise Ratio at the Radio Receiver Output 4.4.1 Dependence of Receiver-Output Signal-to- 54 Noise Ratio on the Modulating -Signal Power Level, Pm IV Page No. 4.4.2 Dependence of Receiver -Output 56 Message-Channel Signal-to-Noise Ratio, S /N , on the Message Channel Signal- oc oc / Power Loading Ratio, P /p , in the Modulating Baseband Signal. 4.5 Performance Characteristics of SSBSC-AM Radio 59 Receivers 4. 5. 1 Receiver -Input Radio Frequency Signal 6l Power Requirements for SSBSC-AM Systems Using Steady Received Signals 4. 5.2 Receiver -Input Radio Frequency Signal 66 Power Requirement for SSBSC-AM Systems Using a Rayleigh-Fading Type of Received Signal 4.6 Performance Characteristics of FM Radio Re- 67 ceiver s 4. 6. 1 FM Radio Receiver Characteristic Curves 68 4. 6. 1. 1 Linear Region of FM Receiver 69 Characteristic Curves 4.6.1.2 Threshold Region of FM Receiver 71 Characteristic Curves 4. 6. 2 FM Radio Receiver Input -Power and 73 Bandwidth Requirements for Steady Received Signals 4.6. 3 FM Radio Receiver Input-Power and Band- 77 width Requirements for a Rayleigh-Fading Type of Received Signal 4.6.4 Pre-Emphasis - - De-Emphasis Techniques 81 4. 6. 5 Bandwidth Compression in FM Receivers 83 Page No. PERFORMANCE CHARACTERISTICS OF MESSAGE- 88 SIGNAL DECODER UNIT RADIO COMMUNICATION SYSTEM DESIGN AND TEST 95 PROCEDURES 6. 1 Determination of the Basic System Parameters: 97 S /N , B , P /p , f , T and T for oc oc c m m m AA er Specified Average Message Error Rates, Number of Available Message Channels, and Specified Receiving -System Parameters. 6.2 Equipment Design Procedures, SSBSC-AM 101 Systems, for a Rayleigh-Fading Type of Received Signal, Dual Diversity, and Maximal -Ratio Combining 6. 3 Equipment Design Procedures, FM Systems, 103 for a Rayleigh-Fading Type of Received Signal, Dual Diversity, and Maximal -Ratio Combining 6.4 Test Procedures for SSBSC-AM and FM Systems 108 6. 5 System Performance Estimates for SSBSC-AM 108 and FM Systems REQUIRED TRANSMITTER-OUTPUT POWER 114 CONCLUSIONS 119 ACKNOWLEDGEMENTS 121 REFERENCES 122 LIST OF SYMBOLS 126 LIST OF FIGURES 132 VI Page No. APPENDICES A. PRE-DETECTION NOISE-POWER LEVELS IN THE RECEIVING SYSTEM 135 B. DERIVATION OF THE MESSAGE -CHANNEL SIGNAL -POWER LOADING RATIO P^/p , IN THE MODULATING BASEBAND SIGNAL 163 C. DERIVATION OF FM RECEIVER PERFORMANCE CHARACTERISTICS 167 D. METHOD OF ESTIMATING THE PERFORMANCE CHARACTERISTICS OF RADIO RECEIVERS AND MESSAGE -SIGNAL DECODING UNITS, FOR A TIME -VARYING SIGNAL 174 D. 1. Estimated Performance Characteristics of Radio Receivers 174 D. 1. 1 Estimated Performance of Radio Receivers with Diversity j 78 D. 2 Estimated Performance Characteristics of the Decoder Unit, for a Time -Varying Input Signal-to-Noise Ratio 1?9 vn ABSTRACT A method is outlined for determining the relationships between the grade of performance, or message error rate, of a radio communication system and the system parameters. Results are presented in the form of design equations and system-design curves The system parameters and variables considered are the following definable and measurable factors: signal-to-noise ratios, carrier- signal power level, message load, receiver noise figure, etc. These factors are used with the design curve scales as normalizing factors in order to yield quantitative results. vm REQUIRED SIGNAL-TO-NOISE RATIOS, RF SIGNAL POWER, AND BANDWIDTH FOR MULTICHANNEL RADIO COMMUNICATION SYSTEMS by E. F. Florman and J. J. Tary 1. INTRODUCTION The objective of this work is to obtain the basic relationships be- tween the grade of service, or the message error-rate, and the various system parameters, for radio communication systems. The results are presented in the form of design equations and sets of system-design curves, in which the system parameters are used as variables and as scale -normalizing factors. The design curves are basic and are general in form; however, they may easily be con- verted to families of curves which apply directly to specific cases, involving specified system parameters. This paper outlines a method for obtaining design equations and sets of design curves for radio communication systems, based pri- marily on the combined performance characteristics of the radio receiver, the diversity combiner, and the message-signal decoder unit. Results are obtained in terms of the important specified, defin- able, and measurable system parameters, such as message error rates, modulating -signal power levels, modulating baseband signal bandwidth, signal-to-noise ratio at the radio receiver output, radio receiver noise figure, order of diversity, number of available mes- sage channels, etc.