# Book

Wireless Communications From the Ground Up

An SDR Perspective

“As to methods there may be a million and then some, but principles are few. The man who grasps principles can successfully select his own methods. The man who tries methods, ignoring principles, is sure to have trouble.”. – Emerson

There are three different angles from which this book contributes to the understanding of wireless communication systems from the perspective of a Software Defined Radio (SDR).

1. Visualization: In my opinion, any language, including that of mathematics, is an unnatural mode of communication. For example, I can write the words darwaza, porte, puerta, umnyango, ovi and only certain people will understand what I mean. However, if I show you an image of a door, almost every single person on the planet will immediately get the concept. A figure imprints a massive amount of parallel information in our brains that is much easier to process and recall later. Since a human mind handles images very well, I try to visualize equations through beautiful figures which you will encounter throughout the text with logical and intuitive explanations.
2. Mathematics:

If you are not a pure wireless communications academic, you would have found that the mainstream textbooks on this topic are filled with heavy mathematical details which makes this field an exclusive membership club for those who can understand several types of frequency variables and their corresponding Fourier transforms, probability and random processes and detection and estimation theories. While this is true for becoming a master, the Software Defined Radio (SDR) revolution and subsequent projects like GNU Radio have made it possible for anyone to sit down and construct their own unique radio by writing code. For this purpose, I have only relied on school level mathematics to explain all the concepts. You will not find any $e$ or $j$ of complex numbers here, nor will you encounter any integrals, probability theory and detection or estimation theory. The only things to know are a sine, cosine and a summation as well as a derivative (which I have occasionally used).

“When you understand something, then you can find the math to express that understanding. The math doesn’t provide the understanding.” – Leslie Lamport

Please note that this is not a mathematics-free guide to SDRs. Instead, it relies on mathematics of simpler operations to explain how radio algorithms work.

3. Why: The best books written on implementing digital communication systems using Digital Signal Processing (DSP) algorithms are by fred harris (Multirate signal processing for communication systems) and Michael Rice (Digital communications – A discrete-time approach). As often happens with the grandmasters, they walk on a trail without exactly clarifying it for others. After reading their books, I started to feel that fred harris has mainly focused on how of communication systems in an unprecedented detail while Michael Rice has mainly covered what of communication systems in his simple and beautiful style. In this process, there were many why generated in my mind for which I had to find satisfactory answers. This book is a collection of those simple answers.
1.

Bonus: An extra little bonus is a one page summary of the crux of Rx algorithms, clarifying the role of particular parameters in the signal waveform. Most of the algorithm design can be understood by just grasping the concepts on this one page.

A common theme in this text is that some concepts seem easier in time domain and some others are simpler in frequency domain, while their mathematical derivations reinforce the idea. It is fun to grasp a concept covering all three sides. Finally, using this same approach of time and frequency domains as well as mathematics, the book explains the logic behind the functionality of some GNU Radio blocks (e.g., Costas loop, band edge FLL, polyphase clock sync, MM clock recovery).

## Product Details

Paperback: 827 pages
Publisher: CreateSpace (November 29, 2018)
Language: English
ISBN-10: 1729732232
ISBN-13: 978-1729732236
Product Dimensions: 7 x 1.9 x 10 inches

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Buy now for $69.90 Here are the table of contents or see the pdf file here. Preface ix 1 Introduction to Signals 1 1.1 Basic Signals . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4 1.2 Transforming a Signal . . . . . . . . . . . . . . . . . . . . . . . . . . . . 9 1.3 Dealing with Complex Numbers . . . . . . . . . . . . . . . . . . . . . . . 16 1.4 The Concept of Frequency . . . . . . . . . . . . . . . . . . . . . . . . . 23 1.5 Sampling a Continuous-Time Signal . . . . . . . . . . . . . . . . . . . . 33 1.6 Correlation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 37 1.7 Discrete Frequency . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 42 1.8 The Discrete Fourier Transform (DFT) . . . . . . . . . . . . . . . . . . . 51 1.9 Effect of Time Shift in Frequency Domain . . . . . . . . . . . . . . . . . 59 1.10 DFT Examples . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 65 1.10.1 A Rectangular Signal . . . . . . . . . . . . . . . . . . . . . . . . 65 1.10.2 A General Sinusoid . . . . . . . . . . . . . . . . . . . . . . . . . 74 1.10.3 The Unit Impulse . . . . . . . . . . . . . . . . . . . . . . . . . . . 77 1.10.4 The Sampling Sequence . . . . . . . . . . . . . . . . . . . . . . 78 1.11 A Digital Signal . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 80 2 Introduction to Systems 83 2.1 Linear Systems . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 86 2.2 Time-Invariant Systems . . . . . . . . . . . . . . . . . . . . . . . . . . . 88 2.3 System Characterization . . . . . . . . . . . . . . . . . . . . . . . . . . . 89 2.4 Convolution . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 91 2.4.1 Regular Convolution . . . . . . . . . . . . . . . . . . . . . . . . . 91 2.4.2 Complex Sinusoids and the Grand Scheme of Things . . . . . . 101 2.4.3 Circular Convolution . . . . . . . . . . . . . . . . . . . . . . . . . 103 2.5 Finite Impulse Response (FIR) Filters . . . . . . . . . . . . . . . . . . . 110 2.6 Some Useful FIR Filters . . . . . . . . . . . . . . . . . . . . . . . . . . . 117 2.7 Sample Rate Conversion . . . . . . . . . . . . . . . . . . . . . . . . . . 123 2.7.1 Downsampling . . . . . . . . . . . . . . . . . . . . . . . . . . . . 124 2.7.2 Upsampling . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 130 2.8 Additive White Gaussian Noise (AWGN) . . . . . . . . . . . . . . . . . . 137 2.9 Some DFT Properties . . . . . . . . . . . . . . . . . . . . . . . . . . . . 140 3 Digital Communication with Linear Modulations 145 3.1 A Simple Communication System . . . . . . . . . . . . . . . . . . . . . . 147 3.2 Packing More Bits in One Symbol . . . . . . . . . . . . . . . . . . . . . . 149 3.3 Modulation: From Numbers to Signals . . . . . . . . . . . . . . . . . . . 151 3.4 Demodulation: From Signals Back to Numbers . . . . . . . . . . . . . . 153 3.4.1 Matched Filter in Time Domain . . . . . . . . . . . . . . . . . . . 156 3.4.2 Matched Filter in Frequency Domain . . . . . . . . . . . . . . . . 158 3.5 Pulse Amplitude Modulation (PAM) . . . . . . . . . . . . . . . . . . . . . 163 3.6 Pulse Shaping Filter . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 172 3.7 Quadrature Amplitude Modulation (QAM) . . . . . . . . . . . . . . . . . 202 3.8 Stethoscopes for a Communication System . . . . . . . . . . . . . . . . 217 3.9 Modulation Bandwidths . . . . . . . . . . . . . . . . . . . . . . . . . . . 224 3.10 Computing Error Rates . . . . . . . . . . . . . . . . . . . . . . . . . . . 225 3.11 Spectral Efﬁciency . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 233 4 Phase Locked Loop 237 4.1 What is Synchronization? . . . . . . . . . . . . . . . . . . . . . . . . . . 239 4.2 Basic Components of a PLL . . . . . . . . . . . . . . . . . . . . . . . . . 243 4.3 Phase Error Detector . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 245 4.4 Proportional + Integrator (PI) Loop Filter . . . . . . . . . . . . . . . . . . 247 4.5 Numerically Controlled Oscillator (NCO) . . . . . . . . . . . . . . . . . . 249 4.6 Designing a PLL . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 251 4.7 Comments on Locking and Acquisition . . . . . . . . . . . . . . . . . . . 266 5 Carrier Phase Synchronization 269 5.1 Effect of Carrier Phase Mismatch . . . . . . . . . . . . . . . . . . . . . . 272 5.2 The Fundamental Problem of Synchronization . . . . . . . . . . . . . . 280 5.3 The Big Picture . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 283 5.4 Enter the Correlation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 285 5.5 Data-Aided/Decision-Directed Techniques . . . . . . . . . . . . . . . . . 290 5.5.1 Feedforward: Conjugate Product Estimator . . . . . . . . . . . . 290 5.5.2 General Approach to Feedforward Synchronization . . . . . . . . 297 5.5.3 Feedback: Phase Difference Phase Error Detector . . . . . . . . 297 5.5.4 General Approach to Feedback Synchronization . . . . . . . . . 310 5.5.5 Feedback: Cross Product Phase Error Detector . . . . . . . . . . 311 5.5.6 A Comparison of Phase Error Detectors . . . . . . . . . . . . . . 327 5.6 Non-Data-Aided Techniques . . . . . . . . . . . . . . . . . . . . . . . . . 328 5.6.1 Feedforward: Mth-Power Estimator . . . . . . . . . . . . . . . . . 329 5.6.2 Feedback: Mth-Power Phase Error Detector . . . . . . . . . . . 331 5.6.3 The Costas Loop: A Classic Solution . . . . . . . . . . . . . . . . 333 5.7 Detection Aids . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 339 5.7.1 Carrier Lock Detector . . . . . . . . . . . . . . . . . . . . . . . . 339 5.7.2 Resolving Phase Ambiguity . . . . . . . . . . . . . . . . . . . . . 340 5.7.3 Cycle Slips, Hangup and the Role of AGC . . . . . . . . . . . . . 344 5.8 The Small Picture . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 345 6 Carrier Frequency Synchronization 347 6.1 Effect of Carrier Frequency Mismatch . . . . . . . . . . . . . . . . . . . 349 6.2 The Big Picture . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 356 6.3 Timing-Aided Techniques . . . . . . . . . . . . . . . . . . . . . . . . . . 358 6.3.1 Enter the Correlation . . . . . . . . . . . . . . . . . . . . . . . . . 359 6.3.2 Feedforward: Brute Force Estimator . . . . . . . . . . . . . . . . 362 6.3.3 Feedforward: The DFT Estimator . . . . . . . . . . . . . . . . . . 364 6.3.4 Feedforward: Multiple Correlations Estimators . . . . . . . . . . 369 6.3.5 A Frequency Locked Loop (FLL) . . . . . . . . . . . . . . . . . . 373 6.3.6 Feedback: Phase Based Frequency Error Detector . . . . . . . . 374 6.4 Non-Timing-Aided Techniques . . . . . . . . . . . . . . . . . . . . . . . 382 6.4.1 Feedforward: Delay and Multiply Technique . . . . . . . . . . . . 382 6.4.2 Feedback: Derivative Frequency Error Detector . . . . . . . . . . 385 6.4.3 Feedback: Band Edge FLL . . . . . . . . . . . . . . . . . . . . . 402 6.5 The Small Picture . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 415 6.6 Appendix . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 416 7 Timing or Clock Synchronization 419 7.1 Effect of Symbol Timing Mismatch . . . . . . . . . . . . . . . . . . . . . 422 7.2 The Big Picture . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 432 7.3 Enter the Correlation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 435 7.3.1 Feedforward: Brute Force Estimator . . . . . . . . . . . . . . . . 437 7.4 Why Squaring is Fundamental to Timing Synchronization . . . . . . . . 439 7.4.1 The Sinusoid Perspective . . . . . . . . . . . . . . . . . . . . . . 439 7.4.2 Role of Excess Bandwidth . . . . . . . . . . . . . . . . . . . . . . 450 7.4.3 Clock Recovery in Analog Modems . . . . . . . . . . . . . . . . . 452 7.4.4 Feedforward: Digital Filter and Square Estimator . . . . . . . . . 454 7.5 A Timing Locked Loop (TLL) . . . . . . . . . . . . . . . . . . . . . . . . 457 7.6 Symbol Centric Timing Error Detectors . . . . . . . . . . . . . . . . . . . 460 7.6.1 Feedback: Derivative Timing Error Detector . . . . . . . . . . . . 461 7.6.2 Feedback: Early-Late Timing Error Detector . . . . . . . . . . . . 475 7.6.3 Why Symbol Centric? . . . . . . . . . . . . . . . . . . . . . . . . 481 7.7 Feedback: Zero Crossing (Gardner) Timing Error Detector . . . . . . . . 484 7.8 Interpolation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 496 7.8.1 Piecewise Polynomial Interpolation . . . . . . . . . . . . . . . . . 497 7.8.2 Farrow Structure . . . . . . . . . . . . . . . . . . . . . . . . . . . 503 7.9 Interpolator Control . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 507 7.9.1 Modulo-1 Counter . . . . . . . . . . . . . . . . . . . . . . . . . . 508 7.9.2 Computing Basepoint Indices and Fractional Intervals . . . . . . 511 7.10 Sampling Clock Offset . . . . . . . . . . . . . . . . . . . . . . . . . . . . 514 7.11 Feedback: Mueller and Muller (M&M) Timing Error Detector . . . . . . . 515 7.12 Feedback: Band Edge Timing Error Detector . . . . . . . . . . . . . . . 523 7.13 Polyphase Clock Synchronization . . . . . . . . . . . . . . . . . . . . . . 535 7.14 The Small Picture . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 555 8 Wireless Channel and Equalization 559 8.1 A Wireless Channel . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 562 8.1.1 Multipath Distortion Assuming No Carrier Wave . . . . . . . . . . 563 8.1.2 What Happens When a Carrier Wave Enters the Picture . . . . . 567 8.1.3 Frequency Flat and Frequency Selective Fading . . . . . . . . . 581 8.1.4 Doppler Shift: A Deceptive Villain . . . . . . . . . . . . . . . . . . 586 8.1.5 What Happens When Motion Enters the Picture . . . . . . . . . 595 8.1.6 Time Flat (Slow) and Time Selective (Fast) Fading . . . . . . . . 600 8.1.7 From Channel Paths to Channel Taps . . . . . . . . . . . . . . . 603 8.1.8 Dealing with a Time-Varying Channel . . . . . . . . . . . . . . . 610 8.1.9 Effect of Channel on Rx Constellation . . . . . . . . . . . . . . . 612 8.2 Channel Estimation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 614 8.3 Equalization . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 617 8.3.1 The Big Picture . . . . . . . . . . . . . . . . . . . . . . . . . . . . 617 8.3.2 Brute Force Equalization: ML Sequence Estimation . . . . . . . 621 8.3.3 Linear Equalizers . . . . . . . . . . . . . . . . . . . . . . . . . . . 625 8.3.4 Least Mean Square (LMS) Equalizer . . . . . . . . . . . . . . . . 637 8.3.5 Decision Feedback Equalization . . . . . . . . . . . . . . . . . . 648 8.3.6 Blind Equalization: Constant Modulus Algorithm (CMA) . . . . . 654 8.3.7 From Time to Frequency Domain Equalization . . . . . . . . . . 657 8.3.8 Single-Carrier Frequency Domain Equalization . . . . . . . . . . 659 9 Orthogonal Frequency Division Multiplexing (OFDM) 675 9.1 The Big Picture . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 678 9.2 How OFDM Works . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 680 9.2.1 From the Printer Port . . . . . . . . . . . . . . . . . . . . . . . . . 680 9.2.2 To a Sliced Bread . . . . . . . . . . . . . . . . . . . . . . . . . . 698 9.3 An OFDM Transceiver . . . . . . . . . . . . . . . . . . . . . . . . . . . . 706 9.4 Timing Synchronization . . . . . . . . . . . . . . . . . . . . . . . . . . . 715 9.5 Carrier Frequency Synchronization . . . . . . . . . . . . . . . . . . . . . 734 9.6 Sampling Clock Synchronization . . . . . . . . . . . . . . . . . . . . . . 741 9.7 Channel Estimation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 747 10 The Chapter with No Title 755 10.1 Tx Architecture . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 758 10.1.1 Polyphase Filterbank Implementation . . . . . . . . . . . . . . . 759 10.2 Rx Architectures . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 771 10.2.1 Tuned Radio Frequency (TRF) Rx . . . . . . . . . . . . . . . . . 772 10.2.2 Heterodyne Rx . . . . . . . . . . . . . . . . . . . . . . . . . . . . 773 10.2.3 Zero-IF (Direct Conversion) Rx . . . . . . . . . . . . . . . . . . . 779 10.2.4 Low-IF and Digital-IF Rx . . . . . . . . . . . . . . . . . . . . . . . 785 10.2.5 Polyphase Filterbank Implementation . . . . . . . . . . . . . . . 788 10.3 The Small Picture . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 806 One Page Summary for Rx Algorithms 808 Bibliography 811 Index 814 You can buy the book from Amazon below. 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### Frequently Asked Questions

Q. Are Wireless Communications from the Ground Up – Fundamentals of Digital Communication Systems and Wireless Communications from the Ground Up – An SDR Perspective two different books?

A. The former is the first edition and basically just constitutes the first three chapters of the initial manuscript while the latter is the second edition.

Q. Is it a guide to build an SDR?

A. No and yes. The focus is not on RF electronics but instead on the DSP part. Using concepts from time and frequency domains as well as mathematics, you will come to know how to produce IQ samples on the Tx side that are fed into the SDR hardware. On the Rx side, once the RF signal is converted into IQ samples through SDR hardware, you will understand the physical layer (PHY) algorithms leading to the detection of bits.

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