Digital Modulation

A digital source produces a sequence of bits in the form of $0$s and $1$s. The question is how to send these bits from point A to point B. For this purpose, an electromagnetic wave acts as a carrier of information.

Remember that the signal produced by an unmodulated electromagnetic wave is a sinusoid given as:

$$x(t) = A \cos \left(2\pi ft + \theta\right)$$

There are three tunable parameters, which are listed below:

• Amplitude $A$
• Frequency $f$
• Phase $\theta$

Information can be conveyed by altering any of these parameters.

Let’s explore them below.

Amplitude shift keying

The process starts with converting the bits of $0$s and $1$s into voltage levels known as symbols, for example:

$$\begin{align*} 0 \quad &\longrightarrow \quad 1 \\ 1 \quad &\longrightarrow \quad 2 \end{align*}$$

This is called binary modulation. To keep the contents simple, we will focus on binary modulations only. Otherwise, multiple bits can also be assigned to a symbol. For instance, a quaternary modulation can represent the sets of $2$ bits as:

$$\begin{align*} 00 \quad &\longrightarrow \quad -3 \\ 01 \quad &\longrightarrow \quad -1 \\ 10 \quad &\longrightarrow \quad +1 \\ 11 \quad &\longrightarrow \quad +3 \end{align*}$$

The serial-to-parallel converter we saw in the OFDM block diagram represents this aggregation of bits ($2$ in this case) for subsequent mapping to a signal level.

Let’s investigate how a sinusoidal wave can be modulated in amplitude.