How to Add Noise to Set a Digital Communications Signal to a Given Es/N0

When you are designing a modem, you’ll typically make heavy use of simulations. Much of the design work is concentrated on the algorithmic part of the device, especially in these days of Software-Defined Radio (SDR), where the actual electronics might…

Tom Sun, 08/23/2020 - 19:43
Mapping Bits to a Constellation

Figure 2. Bit mapping for QPSK.

Before information can be transmitted using a digital modulation scheme, the information bits have to be mapped to the constellation. Each point in the constellation is known as a symbol, making the full collection of symbols a kind of alphabet of the modulation scheme. For most digital modulation schemes…

Tom Mon, 05/06/2019 - 09:57
What is a Constellation Diagram?

Figure 1. QPSK constellation.

A constellation diagram is a diagram that shows how the information in a digital modulation scheme such as phase shift keying (PSK) is represented in a modulated carrier. This article is a bit of an experiment; instead of introducing the constellation diagram by simply presenting it…

Tom Mon, 03/25/2019 - 12:54
What is an Analytic Signal?

Figure 1. Spectra of cosine (left) and complex exponential (right).

An analytic signal is a signal without negative frequency components. This might seem a strange concept if you’re not used to it, but analytic signals are used in signal processing, for example in modems for telecommunications. Let’s start from…

Tom Mon, 02/25/2019 - 09:56

I’m working on a series of articles on modems. It’ll be a loose collection of posts, and not a true multi-part article such as the one on tomography. Modem technology is not widely known and/or understood, even by a technical audience. However…

Tom Wed, 02/13/2019 - 10:52
How Does Phase-Shift Keying Modulation Work?

Figure 3. BPSK-modulated carrier.

After explaining how amplitude modulation and frequency modulation work, which are both analog modulation schemes, I’d now like to give an example of a digital modulation techique. A basic, but very relevant, example of a digital modulation scheme is…

Tom Sat, 01/12/2019 - 16:07
Why is Eb/N0 the Natural Figure of Merit in Digital Communications?

In digital communications, the measure of the signal to noise ratio of a signal is Eb/N0. Why is that? To figure it out, let’s start from the classical SNR, which is the ratio of the average signal power S to the average noise power N, given by…

Tom Wed, 06/29/2016 - 18:54