## A Real-Imaginative Guide to Complex Numbers

June 18, 2020 A PDF of this guide is available for printing and offline reading as an e-Booklet. Buy it here (or see a preview). On a cold morning in August 2015, I narrowly missed a train to my office…

## A Beginner’s Guide to OFDM

In the recent past, high data rate wireless communications is often considered synonymous to an Orthogonal Frequency Division Multiplexing (OFDM) system. OFDM is a special case of multi-carrier communication as opposed to a conventional single-carrier system.  The concepts on which…

## Minimum Shift Keying (MSK) – A Tutorial

Minimum Shift Keying (MSK) is one of the most spectrally efficient modulation schemes available. Due to its constant envelope, it is resilient to non-linear distortion and was therefore chosen as the modulation technique for the GSM cell phone standard. MSK…

## Convolution and Fourier Transform

One question I am frequently asked is regarding the definition of Fourier Transform. A continuous-time Fourier Transform for time domain signal $x(t)$ is defined as $X(\Omega) = \int _{-\infty} ^{\infty} x(t) e^{-j\Omega t} dt$ where $\Omega$ is the…

## Understanding Space-Time Codes: Alamouti Scheme

In major cellular and wireless networks today, space diversity is employed with the help of multiple Tx antennas and/or multiple Rx antennas giving rise to Multiple Input Multiple Output (MIMO) systems. There are three different modes in which multiple antennas…

## How Errors Lead to New Discoveries

In the book "Where Good Ideas Come From", the author Steven Johnson mentions some stories on how errors lead to new scientific breakthroughs which I think would be interesting for radio/wireless enthusiasts. The first among them is what laid the…

## On the Link Between Gardner Timing Error Detector and Early-Late Timing Error Detector

This post is written on an advanced topic mainly for practitioners and researchers in the design of wireless communication systems. For learning about wireless communication systems and an SDR implementation, I recommend you have a look at my book. F….

## CDMA or OFDM

Reading about interference cancellation techniques today, I recalled an interesting article by Sridhar Vembu titled Two Philosophies in CDMA: A Stroll Down Memory Lane. Vembu is the founder and CEO of Zoho Corporation, a venture which has turned him into…

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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