Communications receivers: principles and design, 4th edition ulrich l. rohde download pdf
Visit to download the full and correct content document: https://textbookfull.com/product/communications-receivers-principles-and-design-4thedition-ulrich-l-rohde/
More products digital (pdf, epub, mobi) instant download maybe you interests ...
The material in this eBook also appears in the print version of this title: ISBN: 978-0-07-184333-1, MHID: 0-07-184333-7
eBook conversion by codeMantra
Version 1.0
All trademarks are trademarks of their respective owners. Rather than put a trademark symbol after every occurrence of a trademarked name, we use names in an editorial fashion only, and to the benefit of the trademark owner, with no intention of infringement of the trademark. Where such designations appear in this book, they have been printed with initial caps
McGraw-Hill Education eBooks are available at special quantity discounts to use as premiums and sales promotions or for use in corporate training programs. To contact a representative, please visit the Contact Us page at www.mhprofessional.com.
Information contained in this work has been obtained by McGraw-Hill Education fromsources believed to be reliable. However, neither McGraw-Hill Education nor its authors guarantee the accuracy or completeness of any information published herein, and neither McGraw-Hill Education nor its authors shall be responsible for any errors, omissions, or damages arising out of use of this information. This work is published with the understanding that McGraw-Hill Education and its authors are supplying information but are not attempting to render engineering or other professional services. If such services are required, the assistance of an appropriate professional should be sought
TERMS OF USE
This is a copyrighted work and McGraw-Hill Education and its licensors reserve all rights in and to the work. Use of this work is subject to these terms. Except as permitted under the Copyright Act of 1976 and the right to store and retrieve one copy of the work, you may not decompile, disassemble, reverse engineer, reproduce, modify, create derivative works based upon, transmit, distribute, disseminate, sell, publish or sublicense the work or any part of it without McGraw-Hill Education’s prior consent You may use the work for your own noncommercial and personal use; any other use of the work is strictly prohibited. Your right to use the work may be terminated if you fail to comply with these terms.
THE WORK IS PROVIDED “AS IS.” McGRAW-HILLEDUCATION AND ITS LICENSORS MAKE NO GUARANTEES OR WARRANTIES AS TO THE ACCURACY, ADEQUACYOR COMPLETENESS OF OR RESULTS TO BE OBTAINED FROM USING THE WORK, INCLUDING ANYINFORMATION THAT CAN BE ACCESSED THROUGH THE WORK VIAHYPERLINK OR OTHERWISE, AND EXPRESSLYDISCLAIM ANYWARRANTY, EXPRESS OR IMPLIED, INCLUDING BUT NOT LIMITED TO IMPLIED WARRANTIES OF MERCHANTABILITYOR
FITNESS FOR APARTICULAR PURPOSE.
McGraw-Hill Education and its licensors do not warrant or guarantee that the functions contained in the work will meet your requirements or that its operation will be uninterrupted or error free. Neither McGraw-Hill Education nor its licensors shall be liable to you or anyone else for any inaccuracy, error or omission, regardless of cause, in the work or for any damages resulting therefrom. McGraw-Hill Education has no responsibility for the content of any information accessed through the work. Under no circumstances shall McGraw-Hill Education and/or its licensors be liable for any indirect, incidental, special, punitive, consequential or similar damages that result fromthe use of or inability to use the work, even if any of themhas been advised of the possibility of such damages. This limitation of liability shall apply to any claimor cause whatsoever whether such claimor cause arises in contract, tort or otherwise.
Preface
About the Authors
1 Basic Radio Considerations
1 1 Introduction
1.1.1 SDR, Defined
1.2 Radio SystemFrontiers
1.2.1 5G Fundamentals
1 2 2 Looking Ahead
1.3 Radio Communications Systems
1.3.1 Radio Transmission and Noise
1.4 Modulation
1 4 1 Analog Modulation
1.4.2 Modulation for Digital Signals
1.5 Digital Signal Processing
1.5.1 Analog-to-Digital (A/D) Conversion
1 5 2 Digital-to-Analog (D/A) Conversion
1.5.3 Converter Performance Criteria
1.5.4 Processing Signal Sequences
1.5.5 Digital Filters
1 5 6 Nonlinear Processes
1.5.7 Decimation and Interpolation
1.5.8 DSP Hardware and Development Tools
1.6 Radio Receiver Architectures
1 6 1 Super-Regenerative Receivers
1.7 Typical Radio Receivers
1.7.1 Analog Receiver Design
1.7.2 Mixed-Mode MFSK Communication System
1 7 3 PLLCAD Simulation
1.7.4 Software-Defined Radio Systems
1.7.5 Design Example: EB 500 Monitoring Receiver
1.8 References
1 9 Bibliography
1.10 Suggested Additional Reading
2 Radio Receiver Characteristics
2.1 Introduction
2.2 The Radio Channel
2 2 1 Channel Impulse Response
2.2.2 Doppler Effect
2.2.3 Transfer Function
2.2.4 Time Response of Channel Impulse Response and Transfer Function
2 3 Radio SystemImplementation
2.3.1 Input Characteristics
2.3.2 Gain, Sensitivity, and Noise Figure
2.4 Selectivity
2 5 Dynamic Range
2.5.1 Desensitization
2.5.2 AM Cross Modulation
2.5.3 IM
2 6 Reciprocal Mixing
2.6.1 Phase Errors
2.6.2 Error Vector Magnitude
2.7 Spurious Outputs
2 8 Gain Control
2.9 BFO
2.10 Output Characteristics
2.10.1 Baseband Response and Noise
2 10 2 Harmonic Distortion
2.10.3 IM Distortion
2.10.4 Transient Response
2.11 Frequency Accuracy and Stability
2 12 Frequency Settling Time
2.13 Electromagnetic Interference
2.14 Digital Receiver Characteristics
2.14.1 BER Testing
2 14 2 Transmission and Reception Quality
2.15 References
2.16 Bibliography
2.17 Suggested Additional Reading
3 Receiver SystemPlanning
3.1 The Receiver Level Plan
3.2 Calculation of NF
3.2.1 Noise Factor for Cascaded Circuits
3.3 Noise Correlation in Linear Two Ports Using Correlation Matrices
3.3.1 Noise Figure Test Equipment
3.3.2 How to Determine the Noise Parameters
3.4 Linearity
3.4.1 Dynamic Range, Compression, and IMO
3.4.2 Analysis
3.5 Calculation of IP
3 5 1 Example of NF and IP Calculation
3.6 Spurious Response Locations
3.6.1 D-H Traces
3.7 Selectivity
3 7 1 Single-Tuned Circuit
3.7.2 Coupled Resonant Pairs
3.8 Complex Filter Characteristics
3.8.1 Butterworth Selectivity
3 8 2 Chebyshev Selectivity
3.8.3 Thompson or Bessel Selectivity
3.8.4 Equiripple Linear Phase
3.8.5 Transitional Filters
3 8 6 Elliptic Filters
3.8.7 Special Designs and Phase Equalization
3.9 Filter Design Implementation
3.9.1 LC Filters
3 9 2 Electrical Resonators
3.9.3 Electromechanical Filters
3.9.4 Quartz Crystal Resonators
3.9.5 Monolithic Crystal Filters
3 9 6 Ceramic Filters
3.10 Time-Sampled Filters
3.10.1 Discrete Fourier and z Transforms
3.10.2 Discrete-Time-Sampled Filters
3 10 3 Analog-Sampled Filter Implementations
3.11 Digital Processing Filters
3.12 Frequency Tracking
3.13 IF and Image Frequency Rejection
3 14 Electronically Tuned Filter
3.14.1 Diode Performance
3.14.2 AVHF Example
3.15 References
3 16 Suggested Additional Reading
4 Receiver Implementation Considerations
4.1 Introduction
4.2 Digital Implementation of Receiver Functions
4.2.1 Digital Receiver Design Techniques
4.2.2 Noise Calculations
4.2.3 Noise Cancellation
4.2.4 Spectral Subtraction
4.3 Spread Spectrum
4.3.1 Basic Principles
4.3.2 Frequency Hopping
4 3 3 Direct Sequence
4.3.4 Performance
4.4 Simulation of SystemPerformance
4.4.1 SpectrumOccupancy
4 4 2 Network Response
4.4.3 MediumPrediction
4.4.4 SystemSimulation
4.4.5 HF MediumSimulation
4 4 6 Simple Simulations
4.4.7 Applications of Simulation
4.5 References
4.6 Bibliography
4 7 Suggested Additional Reading
5 Software-Defined Radio Principles and Technologies
5.1 Introduction
5.1.1 General Concept of a Software-Defined Radio
5.1.2 Components (Analog Elements, DSP, and FPGA)
5 1 3 About the DSP
5.2 RF Front-End Architectures
5.2.1 Heterodyne Receiver
5.2.2 Direct-Conversion Receiver
5 2 3 Digital IF Receiver Design
5.2.4 Direct-Sampling Receiver
5.2.5 Broadband Receiver Design
5.2.6 Multicarrier Receiver Design
5.3 RF Front-End Design Considerations
5.3.1 Receiver Link Budget
5.3.2 Analog-to-Digital Conversion
5.3.3 Dynamic Range
5.3.4 Image Rejection
5.3.5 RF Preselection
5.4 Digital Front-End Implementation
5.4.1 Digital Down Conversion
5.4.2 Numerically Controlled Oscillator
5.4.3 Decimation and Channel Filtering
5.4.4 Automatic Gain Control
5.4.5 IQ Mismatch Cancellation
5.5 Baseband Processing
5.5.1 Demodulation (AM/PM)
5.5.2 Synchronization Frequency Offset and Sampling Frequency Offset Correction
5.5.3 Automatic Gain Control for Audio Processing
5.5.4 Noise Blanker
5.5.5 The S-Meter
5 6 SDR Realization Example
5.7 References
5.8 Bibliography
5.9 Literature
5 10 Suggested Additional Reading
6 Transceiver SDR Considerations
6.1 Introduction
6.2 Architecture
6.2.1 I/Q Modulator
6 2 2 Adaptive Transmitter Predistortion
6.2.3 Power Enhancement Technique
6.3 Transceiver Device Implementation Examples
6.3.1 AD9364 RF Transceiver
6 3 2 Transceiver SystemImplementations
6.4 References
6.5 Suggested Additional Reading
7 Antennas and Antenna Systems
7.1 Introduction
7.1.1 Basic Principles
7.2 Antenna Coupling Network
7.3 Coupling Antennas to Tuned Circuits
7.4 Small Antennas
7.4.1 Whip Antennas
7.4.2 Loop Antennas
7.5 Multielement Antennas
7.5.1 Log-Periodic Antenna
7.5.2 Yagi-Uda Antenna
7.5.3 Reflector Antenna
7.5.4 Array Antenna
7.5.5 Phased Array Antenna Systems
7.6 Active Antennas
7.6.1 Application Considerations
7.7 Diversity Reception
7.8 Adaptive Receiver Processing
7.8.1 Adaptive Antenna Processing
7.8.2 Adaptive Equalization
7.8.3 Time-Gated Equalizer
7.8.4 Link-Quality Analysis
7.8.5 Automatic Link Establishment
7.9 References
7.10 Bibliography
7.11 Suggested Additional Reading
8 Mixers
8 1 Introduction
8.1.1 Key Terms
8.2 Passive Mixers
8.3 Active Mixers
8 4 Switching Mixers
8.5 IC-Based Mixers
8.5.1 Gilbert Cell Mixer
8.5.2 Gilbert Cell Performance Analysis
8 6 Wide Dynamic Range Converters
8.6.1 Process Gain
8.7 Mixer Design Considerations
8.7.1 Mixer Device Implementation Example
8 8 References
8.9 Suggested Additional Reading
8.10 Product Resources
9 Frequency Sources and Control
9.1 Introduction
9.1.1 Key Terms
9.2 Phase-Locked Loop Synthesizers
9.2.1 The Type 2, Second-Order Loop
9.2.2 Transient Behavior of Digital Loops Using Tri-State Phase Detectors
9.2.3 Practical PLLCircuits
9.2.4 Fractional-Division Synthesizers
9.2.5 Spur-Suppression Techniques
9.2.6 Noise in Synthesizers
9.2.7 Practical Discrete Component Examples
9.3 Noise and Performance Analysis of PLLSystems
9.3.1 Design Process
9.4 Multiloop Synthesizers
9.5 Direct Digital Synthesis
9.6 Monolithic PLLSystems
9.7 Digital WaveformSynthesizers
9.7.1 Systems Considerations
9.7.2 Modulation with the Phase Accumulator Synthesizer
9.7.3 RAM-Based Synthesis
9.7.4 Applications
9.7.5 Summary of Methods
9.7.6 Signal Quality
9.8 The Colpitts Oscillator
9.8.1 Linear Approach
9.8.2 Linear S-Parameters Approach
9 8 3 Time-Domain-Based Analysis of Transistor Nonlinearities
9.8.4 Selecting the Right Transistor
9.8.5 Design Example for a 350-MHz Fixed Frequency Colpitts Oscillator
9.8.6 Summary
9 9 Frequency Source Device Implementation Examples
This is an exciting time for the designers and users of communications receivers. The promise of software-defined radio (SDR) technologies has been fulfilled in a broad array of products. When the third edition of this book was published more than a decade ago, SDR was a well-developed technology, but one that was not widely fielded. Today, the situation is drastically different, with SDR at the core of modern communications systems.
The advancements in SDR, driven by improvements in components and techniques, have led to a new edition of Communications Receivers that reflects the many exciting changes that have occurred over the last 10 years
The authors of the third edition, Dr. Ulrich L. Rohde and Jerry C. Whitaker, are pleased to welcome a new coauthor, Hans Zahnd, an RF engineer by trade, who brings a wealth of experience with SDR systems to the fourth edition.
The many benefits of SDR-based systems are covered in detail in the following pages, along with key analog technologies that are still critically important for high-performance communications systems. SDR, like any technology, has certain limits, driven by the limitations of the state of component development, notably analog-to-digital converters (ADCs) and digital signal processing (DSP) devices While the performance of these devices continues to advance, they are not limitless in their capabilities. Likewise, the operating environment of a communications receiver may differ widely, depending on the application and location. Interfering signals, either natural or intentional, must be dealt with. These real-world operating constraints mean that for many applications, analog components still play an important role.
While front-end preselectors, filters, and other analog devices continue to be used in high-end applications, some traditional receiver stages are hardly recognizable compared to their analog predecessors. Nowhere is this more apparent than RF amplifiers, where “gain boxes” dominate, and demodulation, where DSP performs multiple functions that go far beyond just recovering the aural message
The ultimate manifestation of SDR is direct digital conversion (DDC), which involves digital downconversion, decimation of the channel rate, baseband I/Q generation, channel filtering, and offset cancellation. Until recently, commercially available ASICs (application-specific integrated circuits) have usually been applied, followed by DSP for demodulation, clock and carrier synchronization, decryption, audio processing, spectrumanalysis, etc The rapid advancement of FPGAs (field-programmable gate arrays) now allows designers to implement several receivers on the same chip. This trend is moving toward SoC (silicon on chip) devices, combining a large amount of very fast logic elements with powerful signal processing capabilities on the same device. This trend is extraordinarily important as it fundamentally changes the scope of what is possible in a communications receiver
Another by-product of SDR and DSP can be found in transceivers. The concept of the transmitter and receiver in the same physical box is nothing new, of course. Today, the difference is the level of integration between the transmit and receive functions. Adecade ago, technologies for reception and those for transmission were largely different disciplines. One operated at microvolts, and the other at tens of watts (and above) Although the two extreme ends of the transceiver the receiver front end and the
transmitter power amplifier remain distinctly different, the stages in between are beginning to merge around SDR and DSP technologies. It is for this reason that, in a departure fromprevious editions, we have included a chapter specifically discussing transceiver systems.
Communications Receivers, fourth edition, includes 11 chapters and an appendix:
• Chapter 5, Software-Defined Radio Principles and Technologies
• Chapter 6, Transceiver SDR Considerations
• Chapter 7, Antennas and Antenna Systems
• Chapter 8, Mixers
• Chapter 9, Frequency Sources and Control
• Chapter 10, Ancillary Receiver Circuits
• Chapter 11, Performance Measurement
• Appendix: Example Receiver Implementation
With the dramatic change fromall-analog designs to all-digital or hybrid (analog/digital) systems, the importance of covering certain analog technologies has diminished In the fourth edition, we have tried to strike the right balance between removing material fromthe previous edition that is no longer needed and providing the reader with a solid examination of fundamental principles and technologies. Aprinted book has a certain practical size, and so some tough decisions have been made with regard to “legacy” technologies. Page constraints have also made it necessary to treat some areas in less detail than we would prefer. However, throughout the book we have tried to provide references where more information can be found.
We would like to thank Prof. Dr.-Ing. Martin Buchholz, University of Applied Science, Saarbrücken (Hochschule fuer Technik und Wirtschaft des Saarlandes), for significant mathematical contributions to this book In addition, we want to thank other friends and colleagues, and many radio amateurs, all of whomprovided valuable advice and input, notably, Dr.-Ing. habil. Ajay Kumar Poddar (AC2KG). We also wish to acknowledge the considerable support of Rohde & Schwarz GmbH & Co., Munich, which made a number of resources available, including (but not limited to) various application notes and white papers on core receiver technologies and systemtesting.
This book has a long history, dating back to the 1980s As such, it enjoys a longevity that is unmatched in the field. The authors take this legacy very seriously. With each edition, we have tried to chronicle and explain the latest technologies that comprise the discipline of communications receivers. At the risk of broad generalizations, the first edition focused on implementations based on discrete semiconductors. In the second edition, the book expanded to include implementations based on integrated circuits (ICs) In the third edition, digital technologies became available and practical. Now, in the fourth edition, SDR is the driving force behind receiver development.
It is our sincere hope that Communications Receivers, fourth edition, will serve as a valuable reference for years to come.
Ulrich L. Rohde Jerry C. Whitaker
Hans Zahnd
About the Authors
Ulrich L. Rohde
Prof. Dr.-Ing. habil. Dr. h.c. mult. Ulrich L. Rohde, partner of Rohde & Schwarz GmbH & Co., KG, Munich, and chairman of Synergy Microwave Corp., Paterson, New Jersey, lives and works in Florida and New Jersey and in Munich.
After studying microwave and RF in Munich and Darmstadt (Germany) and New York (Columbia University Executive Programin Business Administration), he graduated fromthe TUBerlin with a Dr.Ing. and then fromthe BTUCottbus with a Dr.-Ing. habil. He was initially in charge of the Rohde & Schwarz office in the United States, and then was general manager of RCARadio Group for communications and radio intelligence, for the Department of Defense in the United States, with sales of around $3 billion and roughly 10,000 employees, until GE bought RCA. Dr. Rohde then founded several companies in the field of microwave CAD technology and for developing and manufacturing microwave components. His particular areas of interest are low-noise, highly linear microwave oscillators and amplifiers and active antennas. He has published six monographs and in excess of 100 peer-reviewed papers. He is the proprietor of roughly 50 patents. He has been presented with numerous international prizes.
In 2015 Dr. Rohde received the prestigious Isaak Rabi Award in the United States, “for intellectual leadership, selection and measurement of resonator structures for implementation in high performance frequency sources, essential to the determination of atomic resonance,” and in 2016 the IEEE MTT Microwave Application Award, “for his significant contributions to the development of low-noise oscillator performance The Microwave Application Award recognizes an individual, or a team, for an outstanding application of microwave theory and techniques, which has been reduced to practice nominally 10 years before the award.”
Also in 2016 Dr. Rohde was invited to deliver at IEEE Hyderabad the prestigious Sir J. C. Bose Memorial Lecture on “Next-Generation Networks: Software-Defined Radio Emerging Trends” (see http://www microwavejournal com/articles/27714-dr-ulrich-l-rohde-gives-the-6th-sir-j-c-bosememorial-lecture-at-ieee-hyderabad-section).
Since 1977 he has been professor of electrical engineering at the University of Florida, Gainesville,
and since 1982 he has been adjunct professor of electrical engineering at George Washington University, Washington, D.C. In addition to other academic commitments, Dr. Rohde is honorary professor at the University of Cottbus, honorary member of the Bavarian Academy of Sciences in Munich, and honorary senator at the Universität der Bundeswehr München (Federal Armed Forces University, Munich, Germany), and is a member of the Center of Excellence at this last university. He has been conferred with honorary doctorates fromthe Universities of Oradea and Klausenburg, and is a member of various scientific advisory boards and supervisory boards
His hobbies include amateur radio (DJ2LR and N1UL), sailing (U.S. Coast Guard License, U.S. Merchant Marine Officer, Master of Steamor Motor Vessels), and photography
Jerry C. Whitaker
Jerry C. Whitaker is Vice President for Standards Development at the Advanced Television Systems Committee, Washington, D C He supports the work of the various ATSC technology and specialist groups and assists in the development of ATSC standards and related documents. He currently serves as secretary of the Technology and Standards Group and secretary of the Technology Group on NextGeneration Broadcast Television. He is also closely involved in work relating to educational programs.
Mr. Whitaker joined ATSC in 2000 and has participated in all facets of the organization, from development of standards and recommended practices to representing ATSC at various organizations and venues.
Prior to joining ATSC, he headed the publishing company Technical Press, based in Morgan Hill, California. He is the author or editor of more than 35 books on technical topics, including SBE Broadcast Engineering Handbook; Standard Handbook of Video and Television Engineering, 4th ed.; NAB Engineering Handbook, 9th ed.; DTV Handbook, 3rd ed.; and The Electronics Handbook, 2nd ed.
Mr. Whitaker is a Fellow of the Society of Broadcast Engineers and a Fellow of the Society of Motion Picture and Television Engineers. He has served as a board member and vice president of the Society of Broadcast Engineers. He served as chair of the NAB Broadcast Engineering Conference Committee from 1993 until 2000, and as chair of the SMPTE Fall Technical Conference ProgramCommittee from2007 until 2013.
Mr. Whitaker was previously editor, editorial director, and associate publisher of Broadcast Engineering magazine and Video Systems magazine.
In a previous life, he was chief engineer for radio stations KRED-AM and KPDJ-FM in Eureka, California. He also worked in radio and television news in Sacramento, California, at KCRA-AM and KCRA-TV His first experience in broadcast engineering came at KERS-FM, the campus radio station at California State University, Sacramento.
Mr. Whitaker twice received the Jesse H. Neal Editorial Achievement Award fromthe Association of
Business Publishers (ABP). He was also named “Educator of the Year” by the Society of Broadcast Engineers in 2002.
His hobbies include building high-end vacuumtube audio amplifiers and attending his children’s numerous sporting events. He lives with his wife and daughters in Morgan Hill, California.
Hans Zahnd
Hans Zahnd is a pioneering developer of SDR-based communications receiver designs. He operates the company ADAT, which specializes in digital transceiver products.
After studying for a bachelor’s degree in electronic engineering in Switzerland, Mr. Zahnd began in 1968 as a development engineer in a microwave laboratory in Berne and was engaged with the development of microwave links for digital multichannel transmission. Starting in 1974, he led a paging systems development group, where he implemented the new low-voltage silicon gate CMOS technology as linear micropower function blocks in paging receivers. He then left the wireless domain and designed a bidirectional two-wire 64-kbit/s modem, which was presented as the first commercially available product at TelecomWorld Exhibition 1984 in Geneva. Later, he was a specialist in the design of “lastmile” transmission systems, such as ISDN and xDSL.
In 2005, Mr. Zahnd founded his own company for the design of niche products. This was also the start of the development of SDR radios. After a feasibility study with an SDR receiver, he began the design of the transceiver ADT-200A, which was first presented to hamradio operators in Germany in 2007. A series of 100 units was sold and many customers were amazed at the performance of the transceiver. Some of the results fromthis development are presented in this book.
Mr. Zahnd has been engaged as an expert on RF, SDR, and communications technologies at the University of Applied Science in Burgdorf, Switzerland.
His hobbies are playing clarinet in a harmonic band and a symphonic orchestra, and amateur radio. He has been licensed as HB9CBUsince 1980.
Additional Contributors
The task of researching, writing, editing, and reviewing a book the scope of the fourth edition of Communications Receivers requires the assistance, support, and ideas of many people. The authors are grateful for the help and guidance of many individuals too many to list here. One key group that we want to mention specifically is amateur radio operators In the early days of radio, hamoperators built their own gear and identified and then solved many difficult problems. They developed new ways of doing new things. As technology advances, new tools are available to design engineers that push the envelope of capability and performance. Invariably, however, the best tools are new ideas. It is fitting, then, that we include this photo of Ulrich L Rohde (DJ2LR) and his father Lothar A Rohde (DJ5LR), circa 1980 Countless new ideas froma hobby that stayed in the family.
CHAPTER 1
Basic Radio Considerations
1.1 Introduction
Within the period of time since the last edition of Communications Receivers was published, the pace of change has been astounding. When the third edition of this book was printed in 2001, software-defined radios (SDRs) were just entering the mainstreammarket Driven largely by fast, high-performance, application-specific integrated circuits, powerful microprocessors, and inexpensive memory, the promise of the SDR has now been realized. The communications receiver of today is a far cry fromwhat it used to be. Even inexpensive hobbyist radios are sophisticated by comparison with circa 2000 units, with a wide range of features made possible by advanced technologies and mass production
The focus of this book, of course, is not the hobbyist but rather professional users who require the best possible performance froma communications receiver. SDR is a key element of advanced radios today. Having said that, classic technologies still play an important part. For example, the noise figure for a basic SDR design is good, but usually not great. Overload can also be a problembecause of the relatively low signal overload point of many analog-to-digital (A/D) converters Including a preselector and tracking filter is one solution. The best combination for many applications is a preselector, tracking filter, galliumarsenide mixer, direct-digital synthesis local oscillator (LO), and a combination of analog plus digital filtering, followed by digital signal processing (DSP) functions. For operation above 100 MHz, analog filters are necessary for top performance today. In the future that may change as the maximum operating limits of digital technologies steadily move forward.
Current active devices of choice include advanced bipolar and heterojunction bipolar transistors. Junction field effect transistors are seldomused. Discrete transistors are best for performance and flexibility. To optimize a particular circuit, however, it is often necessary to use customtransistors.
An SDR is like a spectrumanalyzer in some respects. In fact, advanced monitoring receivers utilize spectrumanalyzer technologies and, in many cases, provide displays that mimic or go beyond those of a spectrumanalyzer
The origins of SDR go back at least three decades. Early applications were envisioned to serve military requirements, and although the concepts were firmly established, it would be many years before the SDR was practical for a wide range of applications and use cases. The computing power available in 1985 or even 1995 was very limited compared to current technologies. It is easy to forget that the original IBM PC had a clock speed of 4 77 MHz/s Today, a quad-core device running at 3 GHz with 8 MB of cache is commonplace.
For all of the advances that digital technology in general and SDR in particular have brought to communications receiver design, challenges still remain. Some are technical, others not so much. For better or worse, device production today is in large part being driven by consumer products such as smart phones, tablets, and laptop computers. The good news is that advancements in these very high
volume products provide countless spin-off benefits for other electronics products communications receivers included. The downside can be the difficulty in finding an optimized part for a specific application. Operating efficiency (battery drain) is a driving force in portable devices sometimes more so than performance Although it may seemcounter-intuitive, designers today may actually have less flexibility than in the past. While a number of things are technically possible, they are not always economically feasible.
Device availability over time can be a major challenge for complex products such as communications receivers. To achieve top performance, it is often necessary to use devices designed for a specific application or circuit Accurately predicting the number of units to produce in the foundry run is never an easy decision. And, usually, when the stock is gone, it’s gone. There may simply be no acceptable substitute.
Technical tradeoffs are nothing new to designers, of course. Each product is optimized for its intended application using all of the tools available. The common saying, “there is no such thing as a free lunch,” is certainly true when it comes to hardware design. You get what you pay for. Still, at the end of the day, technology moves forward.
Modern communications receivers are used in a wide range of challenging applications Perhaps the most extreme applications are shipboard service and other military uses, where the environment may include a host of interference sources (some natural, others intentional). The laws of physics do not allow a designer to build filters of infinitely small bandwidth at the frequency of interest, and therefore the single-conversion receiver has performance challenges Thus, there still exists the need to mix up to a higher IF, such as 45 MHz, where a filter of a few kilohertz bandwidth is practical. Fromthere the signal is usually mixed down to an IF chain and delivered to the DSP stage.
One of the great benefits of digital technology can be found in filter implementations. In the past, designers used L/C filters, which had certain performance limitations (e.g., ringing). Today, the state of the art is the composite filter, which utilizes a mathematical lookup table The designer can define the selectivity response, for example, from0 to 6 dB, 6 to 10 dB, etc., attenuation as a Bessel filter (no ringing), and after 10 dB attenuation followed by an elliptical filter with steep skirts. This could not be accomplished with discrete components. The advantage of the composite filter is the ability to make arbitrary-shaped filters and avoid ringing and other side effects. Such filters are, however, computationally intensive. Arelated tradeoff is delay, which is influenced by the processing capabilities of the receiver. The overall delay may be in the range of 100 to 300 ms, relative to a conventional analog design Despite the resource (computational power) requirements, composite filters are very attractive because, among other things, they are inherently stable and fully predictable. Digital systems, in general, do not age or drift. It is software. And once it is properly developed, it runs perfectly. Every time.
For lower operating frequencies, phase-locked loop (PLL) frequency sources as we currently know themare gradually being replaced by numerically controlled oscillators (NCO). An NCO is a derivative of a digital direct-frequency synthesizer It has the attribute of pushing the unwanted spurious elements outside the operating bandwidth. The phase noise performance is vastly superior to anything previously seen in analog designs (10 to 15 dB better), thanks to pure digital generation of the signal. The major advantage of the NCO is for frequencies up to about 80 MHz.
One basic architecture decision for a receiver designer is whether to do amplification at baseband or at RF. Gain in the IF section of a modern receiver is essentially the multiplication of two numbers. As mentioned previously, one of the benefits of digital processing is that it does not age or drift over time. The initial cost is in writing the code. Once the code has been developed, implementation is a minor consideration. Even if the architecture of the systemchanges, the mathematical code can often be used without significant modification
Apure SDR receiver, with all of its many benefits, will (for some time, anyway) not be as good as a comparable hybrid design with an analog input tracking filter, GaAs FET-based resistive mixer, and very low phase noise oscillator. Above 1 GHz, there is no way around it.
While certain stages of a modern hybrid receiver architecture still use analog technologies, some traditional analog stages have completely disappeared (or are at least unrecognizable). Amplifier stages were once built fromdiscrete components. Today designers utilize gain blocks optimized for the key operating points. Automatic gain control (AGC) functions are similarly performed by gain devices, rather than discrete components.
The revolution in design brought about by DSP is perhaps most visible in the demodulation stage, where analog techniques have largely disappeared. On the transmitter side, virtually any type of modulation scheme can be done in DSP
It should be no surprise that security is playing a larger role in communications technologies than ever before Encryption is a driving force in systemdevelopment In certain applications (e g , military) secure communication is a critical, fundamental user requirement.
It should also be no surprise that the RF noise environment is increasing worldwide, due to more intentional radiations and non-intentional radiations (e.g., certain types of industrial lighting systems, solar and wind inverters, non-licensed radio devices, and other sources). This problemcould be reduced through effective enforcement of interference limitations currently on the books within government regulatory authorities; however, enforcement in this area is often marginal (or in some cases nonexistent). Regardless of the causes, communications receivers are increasingly operating in a tough environment that requires creative and innovative designs. Fortunately, advanced digital technologies and time-proven analog techniques are ready for the challenge.
The evolution of electronic devices and systems tend to be marked by occasional technological leaps, followed by many incremental improvements over a long period of time. For communications receivers, the leap to SDR has been accomplished. Now, with each new generation of devices and products, the performance of communications receivers will continue to improve. The industry is in an exciting, and stable, position now It is no longer a question of whether to invest in an SDR-based solution; the question is, rather, which one?
1.1.1 SDR, Defined
The termsoftware-defined radio refers to a radio communication systemthat can be configured to receive a wide range of modulated signals across a large frequency spectrumby means of a programmable hardware/software platform[1.1]. That platformmay be based on a general-purpose processor, a special-purpose digital signal processor, a field-programmable-gate array, or some combination of these elements. In addition, an SDR platformincludes an air interface consisting of one or more radio frequency (RF) antenna(s) optionally reconfigurable and appropriate front end circuits.
The RF front end consists of a low-noise amplifier (LNA) with automatically controlled gain, and often a programmable RF to intermediate frequency (IF) functional block. It is important to have control over the bandwidth of the RF/IF signals in order to remove spurious elements and noise before conversion fromanalog to digital via an A/D converter (ADC).
For maximumflexibility, it is beneficial froma design standpoint to include the ADC stage as early in the systemas possible. Trade-offs include interference and filtering issues, as detailed previously. In a typical implementation, circuits after the ADC stage are highly configurable while those before the ADC stage are fixed or minimally configurable
Demodulation may be performed in a single step through direct-conversion of the RF signal to
baseband, or through the familiar superheterodyne process where down-conversion occurs through one or more IF stages.
Digital signal processing generally has the reputation of being more complicated than the analog circuits that it replaces [1.2]. In reality, since the analog signal has been converted into the digital domain, complicated functions can be implemented in software more easily than would be possible with analog components. Furthermore, there are many features that are straightforward with DSP that would be difficult or impractical to implement with analog circuitry. Replacing analog circuits with software algorithms eliminates a host of alignment and maintenance issues. However, as noted previously, analog still has a place in high-performance receivers, particularly those operating at high frequencies
1.2 Radio System Frontiers
The modern SDR-based communications receiver represents the state of the art. This book focuses on the technologies that comprise SDR and, of course, the fundamental physical principles and properties of receiver systemdesign and application. It is also instructive for readers to keep in mind the next leap in wireless communications technologies in the rapidly evolving smartphone/tablet market namely, “5G ” The sheer volume of product development aimed at wireless consumer devices requires designers to understand what is coming, and how it might impact their work. For these reasons, a brief overview of 5G is presented in the following section.
1.2.1 5G Fundamentals
Researchers all around the world are investigating possible concepts and technologies for the fifth generation of mobile networks, common known as “5G” [1.3]. Many use cases have been summarized in various white papers and reveal challenging requirements. The possible technologies and concepts under discussion to meet these requirements are quite diverse. Beyond doubt there is a need to improve the understanding of potential new air interfaces at frequencies above current cellular network technologies, from6 GHz right up to 100 GHz, as well as advanced antenna technologies such as massive MIMO (multiple-in multiple-out) and beamforming.
Mobile operators have commercialized LTE (Long-TermEvolution) and few of the features that make LTE a true 4G technology have made it into live networks. So why is industry already discussing 5G?
5G is indeed on the horizon and it clearly plays an important role in worldwide research and predevelopment. Constant user demands for higher data rates and faster connections require a lot more wireless network capacity, especially in dense areas. The industry is expecting demand for 100× higher data rate per user and 1000× more capacity and has defined these as targets for the fifth generation of mobile networks. One example is sporting events or concerts where huge numbers of spectators want to share their experiences instantly by sharing pictures or videos. The event itself might also offer spectators additional services, such as background information about the music being played or slow motion replays of sport sequences.
In addition to the never-ending “provide more” requirements i.e., higher peak data rate, more capacity, better cost efficiency, and above all the new buzzword Internet of Things (IoT) provide new challenges to be addressed. (See Figure 1.1.) It is anticipated that millions of devices will “talk” to each other, including machine-to-machine, vehicle-to-vehicle, or more general x-2-y use cases.
This will impose different requirements than those currently addressed by 4G systems, which were optimized to provide mobile broadband data access. But not only is the number of devices critical, high reliability, very long battery lifetimes (years instead of days), and very low response times (latency) call for another “G” in the future. Reduction of power consumption in cellular networks is another important requirement. This is particularly challenging since capacity and peak data rates need to be increased at the same time
Ongoing research work is revealing a number of technology components that aimto achieve these ambitious goals, including:
• Millimeter waves: Higher frequency ranges would allow the use of higher bandwidths, which would lead to higher peak data rates and systemcapacities.
• New air interfaces: The OFDM (orthogonal frequency-division multiplexing)–based LTE air interface will not be suitable for some use cases and therefore a number of new air interface candidates are under discussion.
• Massive MIMO/beamforming, active antennas: In particular at higher frequencies, the significantly increased propagation path loss must be compensated for by higher antenna gains. Additionally, adaptive beamforming algorithms even on a per user device basis are required and can be implemented using active antenna technology
• Device-to-device (D2D) communications: D2D is already an existing use case to satisfy public safety requirements using LTE Allowing D2D communications would also allow low latency for specific scenarios.
• Network virtualization (cloud-based network): The ultimate goal is to run today’s dedicated hardware as virtualized software functions on general-purpose hardware in the core network. This is extended to the radio network by separating base stations into radio units and baseband units (connected via, e.g., fiber), and pooling baseband units to handle a high number of radio units.
FIGURE 1.1 5G driving elements (Courtesy Rohde & Schwarz )
• Splitting the control and user planes and/or decoupling the downlink and uplink: The primary focus is on heterogeneous network deployments, making it possible to control all user devices on a macro layer, whereas user data is independently provided via a small cell.
• Light MAC (medium access control) and optimized RRM (radio resource management) strategies: Considering the high number of potentially very small cells, radio resource management needs to be optimized Scheduling strategies would potentially require lean protocol stacks, which could also be deployed in uncoordinated scenarios.
It is telling that the European 5G research programis called Horizon 2020. It gives an idea of the anticipated timeline for the deployment of this new technology. At this writing, research activities were being conducted by a number or organizations around the world.
5G has, thus, started globally and comprises countless projects at the research and pre-R&D level. It is obvious fromongoing studies that higher (> 6 GHz) frequencies will play a role, allowing higher bandwidths and enabling higher data rates. But 5G is not only high frequency and more bandwidth. Integration of potentially disruptive technologies with deployed LTE/LTE-Advanced and/or wireless LAN (WLAN) technologies will be the key, including offloading strategies. Satisfying D2D and IoT use cases will become essential, as well
One of the technology components discussed in 5G to address high capacity and high user data requirements is the adoption of significantly higher bandwidth modes Obviously this will only be possible at significantly higher carrier frequencies, compared with today’s cellular network implementations below 6 GHz. Since concrete systemspecifications are not yet available, the bandwidth requirements discussed range from500 MHz to 2 GHz.
Various research projects are already evaluating potential spectrumabove 6 GHz, however concrete spectrumagreements by the ITU(International Telecommunications Union) are not foreseen anytime soon (See Figure 1.2.) For the cellular industry, spectrumabove 6 GHz is a new area, and there is a need to understand the new ideas and concepts under discussion.
5G Waveform Candidates
OFDM is the access scheme that is used in today’s LTE/LTE-Advanced networks. Two separate
FIGURE 1.2 Potential frequency span of 5G wireless technologies (Courtesy Rohde & Schwarz )
waveforms are utilized to gain access to the network: OFDM access (OFDMA) in the downlink and single carrier frequency division multiple access (SC-FDMA) in the uplink. Both waveforms benefit from OFDM being a multicarrier transmission technique, but also share its disadvantages, such as high sensitivity to frequency and clock offsets, a high peak-to-average power ratio (PAPR), and less spectrum agility.
The sensitivity to frequency and clock offsets makes it necessary to periodically embed synchronization signals and reference signals into the overall emission, and requires the device and network to synchronize before communications (exchange of data) can take place. The limited spectrum agility in LTE depends on the transition between consecutive OFDM symbols The discontinuity (phase transition) between two OFDM symbols during signal generation causes spectral spikes in the frequency domain. This results in high out-of-band emissions and therefore a guard band is typically defined to prevent interference between neighboring channels. OFDM-based signals such as LTE also use a long symbol duration plus a cyclic prefix to avoid intersymbol interference (ISI) due to the expected delay spread of the radio channel. (See Figure 1.3.)
The limitations of OFDM-based waveforms were identified as research topics for future 5G waveforms. One aspect is the requirement for much shorter latency to enable new services and applications like autonomous driving that demands an ultralow latency and a highly resilient communication link. Another approach is to make the cyclic prefix optional and work with shorter symbol durations All this has led to several candidate waveforms, such as
FIGURE 1.3 Power spectrum of a 20-MHz LTE downlink signal with spectral spikes caused by the OFDM signal generation process. (Courtesy Rohde & Schwarz )
• Generalized frequency division multiplex (GFDM)
• Filter bank multicarrier (FBMC)
• Universal filtered multicarrier (UFMC)
• Filtered OFDM (f-OFDM)
The performance of these waveformcandidates is being analyzed and evaluated. At the same time, new multiple access schemes are also being researched, including sparse code multiple access (SCMA), nonorthogonal multiple access (NOMA), and resource spread multiple access (RSMA).1
Higher frequency bands in the millimeter-wave range place high demands on the components used in 5G communications devices and systems, such as filters, mixers, amplifiers, and antennas. Measurement systems for efficient and reliable characterization of these components need to address several challenges in order to ensure wide frequency coverage, high dynamic range, high output power, signal stability, and signal quality with as little distortion and harmonic content as possible
5G Channel Sounding
The need for higher bandwidth and thus higher data rates for 5G makes it necessary to adopt significantly higher carrier frequencies compared with today’s cellular network implementations below 6 GHz. As noted previously, the spectrumdiscussed in various research projects ranges from6 GHz to more than 60 GHz The entire industry needs to learn how signals in emerging high-frequency bands with very wide bandwidths propagate through the radio channel. Channel sounding is a process that allows a radio channel to be characterized by decomposing the radio propagation path into its individual multipath components This information is essential for developing robust modulation schemes to transmit data over the channel.
Currently, quite a few channel measurement studies address specific frequency bands and specific environments, but the industry is far frombeing able to define channel models at frequencies well above 6 GHz. Therefore, mobile network operators, research institutes, universities, and other industry players are conducting extensive channel measurement campaigns in order to define channel models for standardization bodies like 3GPP.
Channel characteristics at higher frequencies are expected to clearly differentiate fromthe characteristics at traditional frequencies up to 6 GHz, notably:
• The path loss is significantly higher so that highly directional beamforming will be required in the mm-wave domain.
• Oxygen and water absorption (e g , rain or humidity loss) needs to be taken into account for specific bands below 70 GHz and above 100 GHz, and above a range of 200 m. (See Figure 1.4.) The additional attenuation below 30 GHz is negligible.
1.4 Oxygen and water absorption at frequencies above 10 GHz. (Courtesy Rohde & Schwarz.)
• The time-selectivity of radio channels is much faster so that TDD (time-division duplex) technologies are preferable.
• The attenuation of most obstacles is stronger (e.g., even foliage loss), but reflections too. Astronger effect comes fromfog and rain, and more attenuation is caused by the windows and other part of buildings, and additional multipath effects.
• Line-of-sight (LOS) conditions cannot always be ensured, therefore, non-line-of-sight (NLOS) communications is essential (and possible).
1.2.2 Looking Ahead
The research into 5G technologies promises to push forward the operating frequencies and throughput of future devices of all types. The techniques and components that will spin-off fromthis work will no doubt impact a wide range of non-5G devices, communications receivers included.
1.3 Radio Communications Systems
The capability of radio waves to provide almost instantaneous distant communications without interconnecting wires was a major factor in the explosive growth of communications during the 20th century. Now in the 21st century, the future for communications systems seems limitless. The invention of the vacuumtube made radio a practical and affordable communications medium. The replacement of vacuumtubes by transistors and integrated circuits allowed the development of a wealth of complex communications systems, which have become an integral part of our society. The development of digital signal processing (DSP) has added a new dimension to communications, enabling sophisticated, secure
FIGURE
radio systems at affordable prices.
Figure 1 5 is a simplified block diagramof a communications systemthat allows the transfer of information between a source where information is generated and a destination that requires it. In the systems with which we are concerned, the transmission mediumis radio, which is used when alternative media, such as electrical cable, are not technically feasible or are uneconomical. Figure 1.5 represents the simplest kind of communications system, where a single source transmits to a single destination. Such a systemis often referred to as a simplex system. When two such links are used, the second sending information fromthe destination location to the source location, the systemis referred to as duplex. Such a systemmay be used for two-way communication or, in some cases, simply to provide information on the quality of received information to the source. If only one transmitter may transmit at a time, the systemis said to be half-duplex.
Figure 1.6 is a diagramrepresenting the simplex and duplex circuits, where a single block T represents all of the information functions at the source end of the link and a single block R represents those at the destination end of the link. In this simple diagram, we encounter one of the problems which arise in communications systems a definition of the boundaries between parts of the system. The blocks T and R, which might be thought of as transmitter and receiver, incorporate several functions that were portrayed separately in Figure 1.5.
FIGURE 1 5 Simplified block diagram of a communications link
FIGURE 1.6 Simplified portrayal of communications links: (a) simplex link, (b) duplex link
Another random document with no related content on Scribd:
thoroughly roused, and that he was by far the more incensed of the two.
“Lady Fairfax,” he said with emphatic distinctness, “permit me to delay you for one moment,” interposing himself between her and the door. “I quite enter into your wishes. The sooner we part the better. I will have no wife who suspects and despises me. A woman holding such views of my character I have no desire to see again. A wife who is ready to cast me off on the smallest and most unfounded suspicion—who does not even grant me a chance of proving my innocence—but tries, convicts, and condemns me unheard, is no wife for me except in name. I shall make all arrangements for your comfort, but I cannot bring myself to discuss them now. You can remain here till our future plans are arranged. Your father’s daughter occupies the same position beneath this roof as did my mother, although you may pretend to think otherwise. Had I been as wise a year ago as I am now, your father’s daughter would never have been my wife.”
Taking up the certificate and the ring, he turned and walked out of the room without another word.
On his way across the hall he was waylaid by Geoffrey, who sprang on him from the billiard-room and seized him by the arm, saying:
“Well, Rex, I suppose she has told you?”
“She has,” replied Reginald, shaking him off impatiently as he entered the library and threw himself into an armchair
“I don’t believe one word of it, mind you, Rex; and as for Alice, she is nothing but a silly girl, with a hot temper. It all blows over. I know her rages well,” he added consolingly.
“Don’t talk to me now, there’s a good fellow,” returned Sir Reginald, jumping up and pacing the room. “Run down and tell them to bring round ‘Dragon’ and the dog-cart, and to put in my portmanteau just as it came.”
“Why so, in the name of all that’s mad?”
“I’m off to London by the mail.”
“Are you in your sober senses, Reginald?” exclaimed Geoffrey, looking at him aghast.
“I scarcely know,” he returned, wearily passing his hand across his forehead; “but I am quite certain of one thing, and that is, that Alice and I have parted for ever.”
CHAPTER VII. WESSEX GARDENS.
It is needless to say that all this excitement upstairs had created no small stir in the lower regions. The servants held a court of inquiry on it over their meals, and discussed the subject in all its bearings and from every point of view. Susan Parker, lady’s-maid, examined and gave evidence that on Tuesday night she was called to her lady, who was in a dead faint in the drawing-room; that the two following days she had kept her room, refusing to eat or drink, save a very little toast, or tea; and that she sat all day long looking as if she was crazed, with her hands clasped idly before her, and that she, Susan, had surprised her more than once reading a letter and crying bitterly.
John Scott, groom, gave evidence that by order of Markham, the coachman, he had driven the dog-cart over to meet his master by the eight-o’clock down train. That Sir Reginald was never in better spirits in his life, asked him how they were all at home, talked of going to the meet at Copperley Gate next day, and drove along at his usual spanking pace, smoking a cheroot, as happy as you please.
That an hour after they got home, as he was at his supper in the servants’-hall, Mr. Geoffrey had come down and beckoned him out, and told him to be ready with the dog-cart in ten minutes, as Sir Reginald was going up by the mail. That when he was ready at the side door, his master had come out, shaken hands with Mr. Geoffrey, and driven away as if the Old Boy himself was after him.
They were just in time for the train, and Sir Reginald jumped out and tore off, leaving his portmanteau and rug behind him.
It was agreed on all hands that there had been an awful row between Sir Reginald and Lady Fairfax, but they were obliged to return a verdict of “Cause not known.”
The following morning Reginald called at the Mayhews’, and found them at breakfast.
“By Jove, my dear fellow, how seedy you look!” exclaimed the Honorable Mark. “I suppose you had it roughish in the Channel?”
“No; I arrived yesterday, and went straight to Looton.”
“Then you had it roughish there instead,” remarked Mr. Mayhew with a grin.
“Mark, I have come to speak to you about this,” said he, producing the certificate and handing it over to him. “You don’t believe it, do you? he asked anxiously.
“Not I; no more than if it were myself,” said Mr. Mayhew, pausing in the act of voraciously devouring a grill. “I stand by you, Rex.”
“And you, Helen?”
“And I also, Regy. Although appearances are against you, I believe in you firmly. You need not have asked,” she added, sipping her tea and speaking between every sip.
“I really wish you would sit down and have some breakfast instead of standing on the rug in that uncomfortable way. Have a cup of tea at any rate, and we’ll talk it over together.”
Her woman’s heart was touched by his haggard wan face. He looked as if he had not slept for nights, and although his “get-up” was as studiously correct as ever, there was a careless, reckless air about him that half frightened her. He looked like a man on the brink of a brain fever.
“Nothing for me, thank you. If I were to swallow a morsel it would choke me just now. I need not assure you, Mark and Helen, that the certificate is a most wicked forgery. I never heard of, much less married, Fanny Cole, nor anyone but Alice Saville. I must unwittingly have made some bitter enemy to bring down on myself such diabolical vengeance, uprooting my home and estranging my wife.”
“Alice believes it then?” they cried in one breath.
“Yes, so she has told me. She declares she is no longer my wife, and will never see me again. She means to leave Looton and live in remote retirement with Miss Fane, where, reversing the Elizabethan valediction, she will do her best to forgive and forget me.”
“Reginald!” said Helen with wide-open eyes, “you are joking.”
“Do you think this a subject for jests?” he said sternly.
“Did you not reason with her?” asked his cousin vehemently
“I did; I assured her of my innocence, on my word of honour. I reasoned with her as temperately as I could, till she nearly goaded me to madness. I could not trust myself to tell you what she said; but she concluded the interview by flinging me her wedding-ring. Here it is,” said he, taking it out of his waistcoat-pocket and laying it on the table between them.
At this tangible proof of the rupture they both stared in silent consternation. Presently Helen said:
“I need not tell you, Regy, how young and inexperienced she is— not yet eighteen. Make allowances for her, for she naturally received a great shock, and has been ill-advised by Miss Fane, whom, you know, I never could bear. Do not be hasty in taking Alice at her word; you know she is very fond of you.”
“If you had been present last night you would scarcely have said so,” returned Sir Reginald dryly; “but I have written to her this morning to say that, if she changes her mind, a line to the Club will find me for a week. She may have been carried away in the heat of passion to say more than she thought or meant. After a week it will be too late; I shall accept the liberty she offers me, and return to my profession. Fortunately my papers have not gone in yet. Now I must be going. You shall see me this day week.”
“Nonsense, man, you are coming to stay here.”
“No, Mark; many thanks to you. You would find me a restless, unbearable inmate. In a week’s time I shall have settled down and grown more accustomed to my fate—if fate it is to be. Meanwhile, I
shall spare neither time nor money to find out the author of this certificate, scoundrel that he is!”
“Reginald, I am sure a man never sent it,” said Helen. “I’m sorry to say it of my own sex, but it’s safe to be a woman.”
“My dear Helen, if you knew how very small my circle of lady acquaintances in India was you would not say so. I don’t think so badly of your sex. Good-bye.”
The allotted week having elapsed, Sir Reginald found himself once more in Wessex Gardens, this time to dinner. He was no longer the pale half-distracted man we had last seen him. He looked quiet and self-possessed, as if his fate had overtaken him, and he had submitted to it without a struggle. There had been no letter from Alice; his plans were fully formed, and he would unfold them after dinner—this much he imparted to Helen as he escorted her downstairs.
During dessert the children came in—Hilda, aged six, and Norman, eight—both delighted to see their special favourite, Uncle Regy. But Uncle Regy was very slow this evening—no stories, no paper boats, no rabbits on the wall. True, he took Hilda on his knee, gave her all his grapes, cracked walnuts for her, with the reckless profusion of a young man, not an experienced paterfamilias, and finally carried her up to bed. But even the children could see that something was amiss, and told their nurse that Uncle Regy never laughed nor showed his nice white teeth once, and they thought he must be sick, he looked so solemn.
“Now,” said Helen, as she poured out coffee, “let us have it all. What have you been doing, Regy?—and what are you going to do?”
“I have placed the certificate in the hands of a first-rate detective, for one thing; I have written to the chaplain at Cheetapore; and I have effected an exchange from the Fifth to the Seventeenth Hussars—now in India—and go out with drafts early in February.”
“Oh Regy, to India again so soon?” said Helen with tears in her eyes.
“Yes,” affecting not to observe them. “Is it not a good thing now I have the Service to fall back on? After all, India is not half a bad place for soldiering, and we are sure to have a row out there ere long.”
“But why leave this country? Why not stay at home?”
“Because it will the more effectually muzzle Mrs. Grundy. It will be less marked than if Alice and I both lived in England and kept up separate establishments.”
“But would you?” asked Helen in an awe-struck tone.
“Certainly. Alice has stood to her guns, and as ‘Trust me all in all, or not at all,’ is my motto, we should never get on. As a married couple our career is finished. I remember hearing a cynical old bachelor say that the marriage service, instead of being the prelude to happiness and harmony, was almost always the ceremony that inaugurated a long and arduous campaign, a series of skirmishes, varied with numerous pitched battles. Alice and I have had one desperate engagement, and both vacate the field. We live to fight another day, but not with each other! Our married life was a short one—barely four months—and I find myself once more a bachelor; for as Alice declares she is not my wife, and as I equally solemnly declare that the other is not my wife, I conclude I am single. What do you think, Helen?”
“I think you are talking a great deal of nonsense, my dear Regy, and though you rail at matrimony now, in your heart you know very well that the last four months were the happiest of your life. You need not deny it, and if you did it would be useless. Go on,” waving her fan imperiously, “go on; tell me what you are going to do about Alice.”
“Of course she must bear my name and live in my house, but that will be the only tie between us. Unfortunately I am her guardian, a post I would willingly relinquish; but it is out of the question to do so. However, my solicitor will manage to represent me as much as possible. I do not intend to be brought personally into contact with Alice, much less with Miss Fane, who has fanned the flame with all her might, Geoffrey tells me.”
“And how have you managed?”
“I have opened an account in Alice’s name at Drummond’s, and made her an allowance of five thousand a-year Her own money she cannot touch till she is one-and-twenty, excepting five hundred ayear, which her father very wisely thought ample for a girl in her teens.”
“Then why increase it?”
“My dear Helen, where is your common sense? Alice will have an establishment to keep up befitting her position as a married woman. I intend her to live at Monkswood, which has always been a kind of dower house. I shall shut up Looton, dismiss most of the servants, and send all the horses up to Tattersall’s on Saturday. I am going abroad for a month previous to returning to India, and start for Vienna the day after to-morrow. Now I think I have told you all my plans; have you any exception to take to them?” he inquired, drinking off his coffee and setting down his cup.
“I know you of old, Regy,” replied Mrs. Mayhew with a sigh. “Your asking me if I take exception to any of your arrangements is only a Chinese compliment; once you make up your mind nothing will alter it, so there is no use wasting words. I think you ought to stay at home instead of going to India. I think you ought to insist on bringing Alice to her senses; or suppose you allow me to take her in hand? Let her come here on a visit whilst you go out to Cheetapore and investigate this horrid business thoroughly.”
“No,” replied Reginald coldly; “Alice and I are strangers for the future. You will oblige me very much, Helen, by referring to her as seldom as possible. She thinks me a hypocrite, a deceiver, a thoroughly bad man. Such were her own words. She could not think worse of me if I were the greatest scoundrel that ever walked this earth.”
“Reginald, I am sure she does not,” pleaded Helen.
It was in vain she begged him to reconsider his decision. He listened to all she had to say with a kind of contemptuous tolerance.
“Very kind of you, Helen, to take her part in this way; very good of you to defend her; but, as you yourself remarked just now, it is only a waste of words.”
One has a good opportunity of studying Sir Reginald Fairfax as he stands on the rug looking down on Mrs. Mayhew, who, leaning back in the easiest of chairs, is slowly fanning herself.
Tall, slender, and graceful, his well-cut evening clothes fit him and suit him admirably. “Gentleman” is stamped on every line and lineament, and there is a leisurely ease and deliberation about everything he says or does; the repose that stamped the line of “Vere de Vere” is not wanting in the Fairfax family. His eyes are the most striking feature—so dark, so cool, so keen, they seem to read one’s thoughts like a book, to penetrate one through and through. His delicately-chiselled high-bred nose (to particularise each feature impartially) and proud sensitive nostrils he inherits from a long line of ancestors. Do not dozens of similar profiles adorn the walls of the gallery at Looton? There is a certain look about his well-cut lips— barely to be guessed at beneath his dark moustache—that to a close observer indicates a resolute, not to say imperious, disposition; and something altogether intangible in his bearing points out the soldier. A handsome, dark, daring face one could easily imagine leading the headlong hurricane of a cavalry charge.
CHAPTER VIII.
MRS. MAYHEW’S LITTLE SCHEME.
Mrs. Mayhew was most decidedly the clever woman of the family Not only had she brains, but an unusual allowance of common sense, and a kind heart to boot. She was dark and good-looking, like most of the Fairfaxes, and inherited no small share of their force of character and determination. Having no brother of her own, she had always appropriated her cousin Reginald as such, since he, at the ripe age of six, had made impassioned love to her, a grown-up young lady of seventeen. She absolutely ruled all the men of her family (husband included) with a mild and gracious sway, always with the notable exception of her cousin “Regy.” His head had never yet bent under her yoke, and he had the audacity to differ from her on many vital subjects, and held the heresy that “it was for man to command, woman to obey, all else confusion.” Nevertheless he possessed a place in Mrs. Mayhew’s heart second only to that occupied by her husband and children.
Mrs. Mayhew was never happier than when she was managing other people’s affairs, for which she had a singular aptitude. To do her justice, she meddled with the very best intentions, and her hands were always full. She was the confidante of lovers’ quarrels, of matrimonial differences untold: from the servant out of place to a girl jilted by her intended, all came to Mrs. Mayhew, and to them she lent a ready ear, her sympathy, and assistance. Her only serious trouble was her rapidly-increasing tendency to embonpoint, and she sighed when she ordered each new dress to be made with an increasing width of waist. Her weakness, her particular pet vanity, were her hands and feet; and certainly she had every reason to be proud of them.
“Tell Helen she has the prettiest foot in London, and she’ll ask you to stay for a month,” was one of Geoffrey’s impudent remarks; and
he also declared that knitting, to which she was much addicted, was merely a framework supplied by her vanity, in order to flourish about and show off her hands.
She was sitting at the fire one dripping February afternoon knitting the following thoughts into a stocking:
“This is the 8th. Let me see” (referring to a paper on her knees), “the Alligator sails on the 26th. Not much time to be lost. I must make one desperate effort to try to reunite this wretchedly headstrong young couple. I’ll take Norman down to Southsea next week for change of air for his cough, and once established in our old lodgings I can easily carry on operations.”
Here her husband entered, and she laid her plans before him.
“Go to Southsea, my dear, by all means, but whatever it may do for Norman’s cough, I don’t think it will be of much use as far as Alice and Reginald are concerned. There is no answer yet from the army chaplain. The detectives are no wiser than we are ourselves. Besides which, that old scorpion, Miss Fane, has Alice talked out of all her senses by this time, be sure.”
“But I anticipate a great deal from an unexpected meeting, nevertheless. I’ll get Alice over from Sandown to spend a few days, and ‘you shall see what you shall see.’ You know that she and Miss Fane are there, and have taken a house till April.”
“Please yourself and you please me; but I have a conviction that your little plot will be no go. Reginald’s temper is like what the Irish cook said of your own: ‘That you were a good Christian lady, but when you were riz, you was riz;’ and he is very much riz indeed.”
“Well, I can’t wonder at it, I must say. You would have been, to say the least of it, annoyed if I had, after being married to you a few months, called you a hypocrite and deceiver, and left you, after throwing you my wedding-ring; you knowing yourself to be entirely innocent of any blame all the time.”
“Yes, very true; but no such volcano as this certificate ever burst out in your home. Pray what would you have done, or say you would have done, in such a case?”
“I would have trusted you, Mark.”
“Humph.” What an extraordinary amount of unbelief a grunt can convey
“Ah well, perhaps you would. Such trust is, however, much easier in theory than in practice. Make some allowance for Alice, poor girl, although we all know she is in the wrong. It’s a bad business—a bad business.”
So saying, he opened his paper with an impressive rustle and buried himself in the news of the day.
A fortnight had passed. The Mayhews were domiciled at Southsea, and Alice had come over to stay with them for a few days after an immense amount of coaxing, and finally being “fetched.” She was as deaf as an adder to all Helen’s eloquent reasoning and remonstrances, and even Mark was out of patience with her at last. She had been primed by Miss Fane with answers to every argument, and had given her her most solemn promise never to yield an inch until the certificate was thoroughly disproved. There had been a letter from her husband to Helen, saying he was coming down on Monday to bid “Good-bye,” as he was to sail the following Thursday; and he mentioned that he wished to have an interview with his wife, so that her being on a visit at the Mayhews’ was most convenient. She was not told of his probable arrival, in case it should scare her away. She knew that he was shortly going to India, but where he was, or when he was going, she had no means of knowing, and was too proud to ask, and Helen was far too angry with her to offer any gratuitous information.
On Monday afternoon Helen and Alice were sitting in the drawingroom, the latter pouring out tea at a low gipsy table, and looking very fair, girlish, and lovely in a thick black damassé silk of most artistic cut, with lace ruffles at her throat and wrists. Helen, lounging opposite in a capacious armchair, was reading aloud tid-bits from The World, and occasionally glancing towards the door.
Norman and Hilda, with scrambling feet and buttered fingers, were making Alice’s life a burden to her; and she was by no means so tolerant of these young aggravations as her husband would have been.
“More sugar; more sugar, Alice!” cried Norman, passing a very sloppy cup recklessly towards her.
“No, my dear Norman; I gave you two lumps.”
“Give me another two, for I have fished them out and eaten them. Come, look sharp!”
“Norman!”
“If you don’t I’ll take that arrow out of your hair and pull it all down, and you’ll see how nice you’ll look if visitors come.”
“If you do——” began Alice indignantly. Just at this crisis the door opened and admitted Mark, Geoffrey, and Reginald.
The children made a violent charge towards the latter.
“Uncle Regy, Uncle Regy! where have you been all this long time? What have you brought us?” they cried, leaping and dancing expectantly round him.
Alice glanced up hastily. He was shaking hands with Helen. What was she to do? Would he shake hands with her? Yes; in another second she found her hand in his; and then he turned to the children.
“Give me a cup of tea, Alice,” said Geoffrey, drawing a chair close to the tea-table, and staring at her with a very unpleasant critical scrutiny.
Her hands trembled so violently she could hardly hold the teapot; the colour sank from her cheeks, and her heart beat so fast it seemed as if it would choke her; but she made a brave struggle for self-command, and endeavoured to converse easily and indifferently with Geoffrey whilst her husband was talking to Helen. Presently she stole a look at him; he was standing on his favourite place—the rug —and she met point-blank the steady glance of his keen dark eyes, fixed on herself—a look full of interest, yet grave and stern.
She felt her face becoming crimson, and dived under the table for her handkerchief, glad of an opportunity of composing her countenance. Dare she take another look? No, she dare not.
At this moment visitors were announced, and the bustle consequent on their arrival was the greatest relief.
Enter two fashionable ladies with a cavalier in tow. Reginald evidently found favour in the eyes of one of them; he had the unmistakable air of a man of birth and distinction. She therefore proceeded to make herself most agreeable, and put him through a series of animated questions, giving him a pretty good benefit of her eyes all the time. Alice, looking on, felt indignation burn within her; and yet, why should she mind? he was nothing to her! He had destroyed her life, as far as her happiness went. All she valued was gone. Bravely indeed did she try to sustain a share of conversation, and to keep up appearances to the best of her ability. She knew she was answering the strange young man’s remarks at random, but she could not help it. He was looking intensely puzzled, as well he might, when she told him that “she was staying in India, but had come over to Southsea for two or three days.” Oh, if she could only get out of the room! No sooner thought than done. She was gliding quietly towards the door, when her husband with two steps confronted her.
“Alice,” said he, “I wish to speak to you particularly. Can you come out with me and take a turn on the pier?”
Alice bowed her head in assent, and passed on. When she came down in her walking things—close-fitting velvet paletôt trimmed with superb sable, and cap to match—she found him waiting in the hall. Having ceremoniously opened the door for her, they set out, and walked on rapidly, exchanging the veriest commonplaces. The pier was evidently to be the scene of action, so Alice braced up all her nerve for the encounter, and firmly determined to abide by Miss Fane’s advice, and not yield an inch till the certificate was utterly refuted.
No one meeting them would have guessed at the storm that was raging in their hearts. They did not look like married people, nor
lovers certainly “A young fellow taking his very pretty sister for a walk, most likely,” would have been the verdict of a passer-by.
Arrived at the pier, Alice summoned up all her courage, and taking a good long breath and a firm grasp of her umbrella, said, with apparent composure: “Now what have you to say to me?”
“Several things as your husband, and a few as your guardian,” he replied, leaning against the railing and looking at her intently.
“Say nothing to me as my husband, but whatever you have to say as my guardian I will perhaps attend to.”
“Then you still entertain the monstrous notion—that I am not your husband?”
To this question Alice made no reply, and he proceeded. “Well, I am, all the same. But I see it would be a waste of time and temper to endeavour to persuade you otherwise. I have every reason to believe that within the next two months all will be satisfactorily cleared up. May I ask what you will do in that case?”
“I will return to you as your wife, of course,” she replied calmly.
“And do you suppose that I will receive you then? Return to me now—show, even at the eleventh hour, that you can trust me—I will send in my papers and stay at home. I have interest, and it is not yet too late. I will freely forgive and forget all you thought, all you said. It shall be as though it had never been spoken.” He paused, and looked at her eagerly. “I told you,” he proceeded still more earnestly, “that I had done with you, that I had no desire to see you again, but I found, on cool reflection, that I loved you far too dearly to give you up without an effort at reconciliation. I have made two—once in London and once now—but this, I declare to you solemnly, will be the last. Come back to me, and trust me, my dearest,” he said, laying his hand entreatingly on her arm. “Trust me only for a little time; all will, all must come right. You will never again in all your life have such an opportunity of showing your love, your confidence in me. Do you think I would not stand by you in a similar case? You know I would,” he added emphatically. “Come back to me, Alice,” he urged.
“No, I will not,” she replied doggedly leaning both elbows on the railing of the pier and staring steadily out to sea.
“You will not?” he repeated, in a tone of bitter disappointment. “You cannot mean it.” After an inward struggle with himself he continued as before: “Think of what you are doing, Alice. You have broken up our home and turned me adrift—taken your freedom and your own way. You are sending me back to India, and God knows if I shall ever return.”
“You need not go,” she replied in a low voice, still looking out to sea, as if addressing the ocean.
“Of course I must go!” he cried emphatically; “unless you wish to have the open mouth of scandal busy with our names. If the world knows that I am engaged in my country’s service it may leave you alone. But I warn you that society looks coldly on a young and pretty woman living apart from her husband, and rightly or wrongly, they almost always throw the blame of the separation on her shoulders. I know you have been influenced by Miss Fane; I know you have. It was not my generous, true-hearted Alice that spoke to me that night at Looton. You don’t know how you pained me, how you nearly maddened me by some of the things she put into your mouth— things my pure-minded girl-wife would never have thought of herself. You could not seriously think that I had another wife living, and that I had dared, nevertheless, to marry you—an orphan, as you justly remarked, committed to my care! Think of the shameful crime it would be! Look me full in the face, and tell me candidly, truthfully, and of your own free will, whether you imagine that I, Reginald Fairfax, could be guilty of such a thing?”
Alice turned round at once and confronted him—his face pale with emotion. His dark, miserable eyes haunted her painfully afterwards for many and many a day.
“Clear yourself first,” she exclaimed, “then I will listen to you. As long as that certificate is unexplained I will never return to you as your wife; I will never, never see you again, as far as I can help it, until the whole affair is refuted. I am amazed that you should expect it.”
Sir Reginald gazed incredulously at his wife for a moment, as if he thought that his ears must have deceived him.
“Is this your last word?” he said in a voice husky with passion.
She nodded emphatically.
Exasperated beyond endurance, he left her side and walked to the other end of the pier alone. Presently he returned with firm rapid strides, and confronted her with a compression of the lips and a flash in his eyes she had never seen before. Coming to a stop, and standing directly before her, he said:
“That was your last word; now hear mine. I most solemnly take God to witness”—raising his hat as he spoke—“that I will never receive you back as my wife until you have made the most humble, abject apology that ever came from woman’s lips. You shall abase yourself to the very dust for the shameful injustice you have done me.”
“Shall I, indeed?” she exclaimed passionately “You will never see a Saville abased to the dust. I will never apologise and never beg your pardon. Pray do not offer your forgiveness before it is required.”
“Very well,” he replied coldly, “there is no more to be said, as you declare that you will never apologise, and I have sworn to yield to no other terms. We shall live for the future as strangers, excepting that I shall exercise over you—even though at a distance—the authority of your guardian till you are twenty-five.”
“I shall not submit to your authority!” she interrupted hotly.
“Oh yes, you will,” he returned in a cool unmoved tone. “You have as yet to learn that I too have a will—that I am your master—no longer your slave. I am aware I cannot flatter myself that you either love or honour me,” with ironical emphasis, “but you will certainly obey me.”
“I shall not!” she cried indignantly.
“Oh yes, I am quite sure you will,” he replied in the easy authoritative tone with which one talks to a naughty child. “You will live at Monkswood,” he proceeded tranquilly. “It is smaller than
Looton, but I hope you will find it as comfortable. Horses, carriages, and servants will precede you there, and I hope all will be ready for your reception in a fortnight’s time. In the meanwhile I must beg you will remain with Helen, as I do not wish you to return to Miss Fane. I forbid you to see her or to correspond with her.” He paused to see the effect of his words, then continued: “Your own aunt, Miss Saville, has been good enough to promise to reside with you permanently, as it would be out of the question for you to live alone.”
During the above long speech Alice had been gazing at her husband with amazed indignant eyes. Drawing herself up as he concluded, she said:
“And supposing I decline to leave Miss Fane and to go to Monkswood, what are to be the dire consequences?”
“You have no other alternative,” he replied with freezing politeness. “Unfortunately for your independent spirit, all your money is in my hands.”
“What a shame!” she cried passionately.
“Yes, is it not?” he answered with a satirical smile. “A young lady with an empty purse, and utterly cut off from her friends, would find herself rather embarrassed, to say the least of it.”
“Miss Fane will allow me to live with her as before,” she returned confidently.
“When she finds that you are absolutely penniless, I think you will discover that her interest in you has ceased,” he replied significantly.
“Must I go to Monkswood? Must I?” she asked passionately.
A bow was her reply.
“I suppose I am completely in your power?”
“I am afraid so,” he answered composedly.
“Oh, if anyone else were only my guardian! If your father had lived, or if he had chosen Mr. Mayhew.”
“I sincerely echo both your wishes, but I hope you will be able to reconcile yourself to circumstances. You will go to Monkswood, I am sure.”
“I suppose I must—for a time at least,” looking at him defiantly.
“Very well,” he replied, ignoring her look, “we will consider the matter settled. Mark Mayhew and my solicitors will look after your interests. Personally, I will have no communication with you. This is our last interview; from to-day we are strangers.” After a pause he went on: “You will hear from Helen whether I am dead or alive; if the former, you will be freed from every tie—you will be your own mistress, an exceedingly rich widow, with no one to control you in any way. Should you marry again, as no doubt you will, I sincerely hope your second venture in matrimony will be more fortunate than your first.”
“Reginald!” she exclaimed indignantly.
“He will have to be a different sort of fellow to me,” he continued, without noticing the interruption; “to have a pretty thick skin; to give you your own way completely; and to have no self-respect whatever. Of course that will be a sine qua non. He must not mind your changeful moods, nor be offended, if after telling him he is dearer to you than words can express, and making an utter fool of him, you turn on him at the first breath of suspicion and call him a hypocrite, a deceiver, a ruffian of the deepest dye, and altogether a most infernal scoundrel.”
“Reginald, I never used such expressions. How dare you speak to me in such a way! How dare you treat me so!” she exclaimed, raising her voice, much to the amusement of two sailors, the only other people on the pier, who were lolling over the railings close by, and had been watching the scene with unaffected delight.
“She’s giving it to him. By Jove, Bill, that chap has his hands full!” said one of them, turning his quid. “If he is going to venture out on the sea of matrimony with that craft, he’ll happen to have heavy weather frequent and squalls every day.”
“What do you mean by bringing me here to ridicule and insult me?” repeated Alice in a towering rage. “The marriage certificate is still unexplained, and you talk to me as if you were the injured person— you!”
“I am glad to see that you have grasped my meaning,” he replied coolly. “I am the injured person; suspected by you, who should be the last to doubt me—homeless, wifeless, nevertheless innocent. I am leaving my native land, this time a voluntary exile. You have destroyed my faith in womankind: a woman’s word—a woman’s love —a woman’s generosity are to me now merely so many names for delusions believed in by children and fools. I brought you here to tell you of various arrangements I had made. I preferred a personal interview to letter-writing; besides which, I am sure you will be amused to hear that I had a lingering hope you would have believed me and trusted me, even at the eleventh hour—a hope I now see,” looking at her steadily, “that I was mad to entertain.”
“You were indeed insane to think it,” exclaimed Alice very emphatically. “Prove the certificate to be a forgery, and then I will believe you,” she said abruptly, turning to leave the pier, with a scarlet flush on either cheek and a general air of outraged dignity.
They walked homewards, that cold, dusky February evening, in solemn silence. Alice’s conscience was clamouring loudly as she stepped briskly along, endeavouring to keep up with her husband’s rapid strides. He seemed totally unconscious of her presence. Buried deep in his own thoughts, he did not vouchsafe a single remark between the pier and the Mayhews’ house.
“God forgive you if you have wronged him,” said Alice’s inward monitor. “He is going away to the other end of the world, and you may never see him again.”
“But the certificate—the clergyman’s signature so far undenied and unrefuted,” argued Pride and Propriety.
Helen, who had been expecting great things from this interview, met her cousins in the hall on their return. One glance at Alice was sufficient to dash her hopes to the ground—she looked the very
