Digital Signal Processing in Communication Systems Digital Signal Processing in Communication Systems

DIGITAL SIGNAL PROCESSING IN COMMUNICATION SYSTEMS DIGITAL SIGNAL PROCESSING IN COMMUNICATION SYSTEMS

Marvin E. Frerking

SPRINGER SCIENCE+BUSINESS" MEDIA, LLC Library of Congress Cataloging-in-Publication Data

Frerking, Marvin E. Digital signal processing in communication systems / Marvin E. Frerking. p. em. Includes index. ISBN 978-1-4419-4740-6 ISBN 978-1-4757-4990-8 (eBook) DOI 10.1007/978-1-4757-4990-8 1. Signal processing--Digital techniques. 2. Digital communications. I. Title. TK5102.9.F74 1993 93-25299 621.382'2--dc20 eIP

All rights reserved. No part of this publication may be reproduced, stored in a retrlevaJ system or transmitted in any form or by any means, mechanical, photo-copying, recording, or otherwise, without the prior written permission of the publisher, Springer Science+ Business Media, LLC.

This book is published with the understanding that it is providing information only and not rendering engineering services. Information was used from sources believed to be reliable, but neither the author nor publisher guarantees the accuracy of the information, and neither shall be held responsible for any damages resulting from the use of this information. Neither the author nor publisher assume liability for patent infringements, nor is any patent license implied.

Printed on acid-free paper. Dedication

This book is dedicated to my wife, Shirley, who encouraged and sup• ported the work and generously gave of her time to type the manu• script. The author would also like to thank Linda Frerking for the many hours she spent drawing illustrations. Contents

Preface ..••.....•.•.•.....••...... •.....••.....•.•.xi Acknowledgment . . . • • . . • ...... • . . • . • • . • ...... • . . . . .• xiii

Symbols and Abbreviations ..••...•...... •.•...... •. xv

1. Introduction ...... •.....••..•...•..... 1 2. Digital Signal Processing Concepts ..•...•....•...•...•...... • 6 Signal Representations ...... 6 Fourier Series ...... II Fourier Transforms ...... 16 Discrete Fourier Transforms ...... 27 Inverse Discrete Fourier Transforms ...... 32 Fast Fourier Transforms ...... 33 Radix Four FFTs ...... 38 Sliding Discrete Fourier Transforms ...... 42 Z-Transforms ...... 43 Digital Approximations of Analog Transfer Functions ...... 57 Impulse Invarient Method ...... 58 Bilinear Transforms ...... 61 Sample Rate Changes ...... 65 Problems ...... 67

3. Analog-to-Digital Conversion ...... •...... •..... 72 Quantization Noise ...... 73

vii viii Digital Signal Processing in Communication Systems

Intermodulation Distortion ...... 81 Sampling Time Related Distortions ...... 82 Distortions Unique to Flash AID Converters ...... 84 Successive Approximation AID Converters ...... 86 Sample-and-Hold Circuits ...... 87 Digital-to-Analog Converter Distortions ...... 90 Linearity Correction in AID Converters ...... 93 Two-Stage AID Converters ...... 94 Sigma-Delta Modulators ...... 96 Charge Redistribution AID Converters ...... 98 Performance Measurement ...... 103 Sampling Narrowband Signals ...... 107 Problems ...... 111

4. Processing Complex Signals .•.•.•...•••.•...•....•••.•..••... 113 Positive and Negative Frequencies ...... 113 Complex Signals ...... 118 Frequency Translation ...... 124 Hilbert Transformers ...... 138 Problems ...... 148

5. Digital Filters ...... •...•....•.•...... •.•••.....••...•• 152 Finite Impulse-Response Filters ...... 153 Complex FIR Filters ...... 170 Frequency Translation in FIR Filters ...... 171 Polyphase Filters ...... 174 Infinite Impulse-Response (IIR) Filters ...... 182 Butterworth Filters ...... 183 Chebyshev Filters ...... 184 Elliptic Filters ...... 186 Filter Design ...... 187 Boxcar Filters ...... 193 Cascaded Integrator Comb Filters ...... 199 Fast Convolution Filters ...... 202 Problems ...... 209

6. Digital Algorithms for Communication Systems •••••...••...... • 212 Digital Frequency Sources ...... 212 Modulation ...... 227 Amplitude Modulation Algorithms ...... 229 Frequency Modulation ...... 243 FM Detection ...... 249 Threshold Extension Techniques-Phase Locked Loop ...... 257 Contents ix

Single-Sideband Systems ...... 262 Audio Compressors ...... 286 Automatic Gain Control ...... 292 Squelch Circuits ...... 297 Problems ...... 299

7. Digital Receiver/Exciter Design ...... 305 Receiver Design Example ...... 307 Narrowband Receivers with High-Speed ND Converters ...... 342 Harmonic Sampling Receiver ...... 353 Direct Sampling Receiver ...... 364 Radio Transmitters ...... 371 Detailed Exciter Design ...... 374 High-Efficiency Power Amplifiers ...... 384 Problems ...... 389

8. Data Transmission ...... 392 Introduction ...... 392 Matched Filters ...... 398 Frequency Shift Keying ...... 410 Phase Shift Keying ...... 430 PSK Demodulation ...... 433 Quadrature Amplitude Modulation ...... 459 Equalizers ...... 464 Problems ...... 485

9. Speech Processing ...... 490 Pulse Code Modulation ...... 492 Differential Pulse Code Modulation ...... 494 Delta Modulation ...... 495 Continuously Variable Slope Delta Modulation ...... 497 Linear Predictive Coding ...... 498 Performance Evaluation ...... 526 Government Standard Algorithm: LPC-lO ...... 527 Very Low Data Rate Speech Coding ...... 532 Code Excited Linear Prediction (CELP) ...... 539 Problems ...... 545

10. DSP Hardware ...... 548 Digital Signal Processors ...... 549 Fast Fourier Transform Hardware ...... 552 Interprocessor Communications ...... 554 Multiplier Accumulators ...... 556 x Digital Signal Processing in Communication Systems

Other DSP Chips ...... 559 Data Flow Structures ...... 560 Standard Bus Characteristics ...... 562 Very High-Speed Parallel Buses ...... 569 High-Speed Serial Data Exchange ...... 571 Simulation and Testing ...... 572 Software Design ...... 574

Appendix A-Derivation of Aperture Jitter Effects ...... 577

Appendix B-Derivation of Constants for IIR Oscillator ...... 581

Appendix C-Derivation of Equations for Function Table ...... 585

Appendix D-Error Rate for Differentially Encoded Phase Shift Keying ...... 592

Appendix E-Derivation of Error Rate for Incoherent FSK Data Transmission ...... 597

Appendix F-Cordic Algorithm ...... 600

Appendix G-Noise in a Sigma-Delta Modulator ...... 604

References ...... 613

Index ...... 618 Preface

This book was written with the intent of developing the concepts of digital signal processing (DSP) that are particularly useful and often applied in the design of communications equipment. Both professional engineers who wish to upgrade their skills in digital signal processing and students who wish to gain additional knowledge in the area of communications should find it useful. The author has been privileged to work in the design of communications equip• ment during the period when rapidly expanding hardware capability made it prac• tical and economical to apply many of the techniques of digital signal processing to real-world problems in communications. As a result, the algorithms and con• cepts chosen for development in the book tend to be those that are likely to find applications in the design of radio receivers, transmitters, modems, and so forth. Many engineers working in the communications field are well experienced in the design of analog equipment but have limited experience with digital signal processing techniques. The book is particularly designed to assist engineers in this category by first reviewing some of the basic concepts of digital signal processing, and then proceeding with the algorithms and techniques used in communications. Students who have already taken a basic digital signal processing course can use these chapters as a quick review to ensure that they thoroughly understand the fun• damentals that will be required later to develop the techniques used in communi• cations equipment design. The author believes that a thorough understanding of the fundamentals often leads to greater insight in identifying when a particular concept or idea can be applied in an equipment design. The availability of low-cost digital signal processing hardware during the late 1970s, as well as a near explosion in LSI technology and analog-to-digital con• verter capability, has paved the way for digital signal processing applications. Consequently, digital signal processing techniques are replacing many functions

xi xii Digital Signal Processing in Communication Systems

that were previously designed using analog circuits. The advantages of digital sig• nal processing are very great in many areas, and equipments are being designed with features not previously practical or economical to implement with analog cir• cuits (e.g., radio receivers and transmitters with embedded modems). DSP is par• ticularly attractive in equipment that must provide many modes of operation or different bandwidths. The equipment can also be made flexible to accommodate new requirements as they arise, or can be tailored to specific customer needs. These advantages, along with the continuing advancements in hardware capa• bility, virtually ensure the continued application of digital signal processing in the foreseeable future. It is, therefore, most useful for the engineer or student to master the fundamental concepts used in digital signal processing as applied to commu• nications problems. After a brief introduction (Chapter 1), the book continues with a review of sig• nal representations and sampling (Chapter 2), along with a review of such impor• tant concepts as convolution and z-transforms. Chapter 3 discusses analog-to• digital conversion, with a particular emphasis on the noise and distortion perfor• mance. Chapter 4 sets the stage for many ofthe specialized operations required in radio transmitter and receiver design and deals with the processing of complex signals. A great deal of the power of digital signal processing stems from the abil• ity to manipulate complex signals. A thorough understanding of the concepts of positive and negative frequencies is therefore of great value and is clearly ex• plained, along with the importance of Hilbert transformers. Chapter 5 presents a review of digital filters that may be useful for engineers who have had limited experience in this area. The chapter may be omitted by stu• dents who have recently taken a course in digital filtering. Chapter 6 is dedicated to the development of many of the algorithms that are used in digital signal processing for communications, such as digital oscillators, detectors, modulators, automatic gain control circuits, and the like. The theory and algorithms developed in previous chapters are brought together in Chapter 7, which deals with radio receiver and transmitter design. Chapter 8 then treats the important subject of data transmission and emphasizes digital tech• niques for data transmission. Chapter 9 is included for readers who wish to learn more about the subject of speech processing, particularly of digitizing speech at low to modest data rates. The concepts of linear predictive coding (LPC) and code excited linear predictive coding (CELP) are sufficiently developed to give the reader a good general under• standing of these techniques, as well as some insight into the special processing required. Finally, Chapter 10 deals with various hardware considerations, such as multi• plier accumulators, fast Fourier transform processors, digital signal processors, and data flow techniques in an equipment. Simulation and testing also are dis• cussed briefly. Acknowledgment

The author would like to acknowledge the support of Rockwell International Cor• poration for publication of this work and to thank my fellow employees who pro• vided comments on the manuscript. The author would also like to thank Robert Craiglow, with whom discussions were held, leading to a deeper understanding of the fundamental concepts discussed in this book.

xiii Symbols and Abbreviations

Aa = filter stopband attenuation in dB App = peak-to-peak filter passband ripple in dB AID = analog-to-digital (converter) b = number of bits in a digital word BPF = bandpass filter CIC = cascade integrator comb D/A = digital-to-analog (converter) DEMUX = demultiplexer DFT = discrete Fourier transform e = natural constant 2.718281828 Eb = energy per bit f = frequency in Hz, kHz, or MHz fs = sample rate liT fT = digital filter transition bandwidth FFT = fast Fourier transform FSK = frequency shift keying G(f) = power spectral density h = filter coefficient or impulse response value HPF = highpass filter IF = intermediate frequency k = Boltzmann's Constant 1.38 x 10-23 Ilk

xv xvi Digital Signal Processing in Communication Systems

LPF = lowpass filter LSP = line spectrum pair MSK = minimum shift keying n = sample number N = total number of taps in a filter, length of FFT No = one-sided noise density Noq = one-sided quantization noise density PSK = phase shift keying r = symbol rate for data transmission rb = bit rate of transmission R = sample rate decimation or interpolation value, or resistance SNR = signal-to-noise ratio t = continuous time T = sample time in seconds T s = symbol time TTY = teletype w(n) = window function values x(n) = discrete time function evaluated at instant nT X(k) = frequency spectrum point ofx(n) obtained by DFT

~ = derivation ratio O"a = RMS value of AID converter aperture jitter 't = time delay <0 = angular frequency <0 = 21tf