# 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. Easy 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 simpler operations to explain how radio algorithms work. I have also reduced the font size for some unavoidable derivations or moved them to their respective appendices where possible. The reader can skip the content with a smaller font if desired.

## 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.

## + 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.

## And More

– 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 (in addition to being extremely useful) to grasp a concept covering all three sides.

– Using this same approach of time and frequency domains as well as mathematics, the book explains the logic behind the functionality of several GNU Radio blocks (e.g., Costas Loop, Band Edge FLL, Polyphase Clock Sync, MM Clock Recovery and timing error detectors in Symbol Sync). This is important because most books on digital and wireless communications do not contain an in-depth discussion on the topics of timing and carrier synchronization or equalization from an implementation viewpoint. Interestingly, these are the exact challenges the designer of a digital modem or radio needs to overcome for a working product.

There are 26 letters in English language and countless rules. The language of signal processing is simpler.

- It has only 1 letter: a sample at time 0. From there, we can build any discrete-time signal on which our 1s and 0s can be mapped.

- It has one major rule which is repeatedly employed for demapping the received signal to bits.

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