# Symbols

## What are symbols in digital communications?

We do not want to confuse the reader but let us start by defining that a digital signal is nothing else than a special analog signal.

The reason is that an electric signal is a signal and whether analog or digital. The physics of both signals are the same.

Comparison

Consider the amplitude characteristics of an analog signal. The analog signal’s amplitude can take unending instantaneous values between the minimum (negative amplitude) and maximum (positive amplitude).

The digital signal is just an analog signal with only 2 instantaneous values.
When an analog signal can only have two instantaneous values, as is amplitude, we call it a digital signal.

Modulation

Modulation techniques make use of this because transmitting always uses analog signals. The (digital) modulation on the carrier happens by switching (keying) between two amplitudes, frequencies, or phases.

However, there is a solution to increase the bitrate in digital transmissions by choosing more than 2 instantaneous values of a signal.

• When using   4 instantaneous values, we would be able to transmit 2 bits at once
• When using   8 instantaneous values, we would be able to transmit 3 bits at once
• When using 16 instantaneous values, we would be able to transmit 4 bits at once
• Etc.

Table – number of analog states and the number of bits per symbol.

0 -> 00
1 -> 01
2 -> 10
3 -> 11

0 -> 000
1 -> 001
2 -> 010
3 -> 011
4 -> 100
5 -> 101
6 -> 110
7 -> 111

0 -> 0000
1 -> 0001
2 -> 0010
3 -> 0011
4 -> 0100
5 -> 0101
6 -> 0110
7 -> 0111
8 -> 1000
9 -> 1001
10 -> 1010
11 -> 1011
12 -> 1100
13 -> 1101
14 -> 1110
15 -> 1111

We call symbols (similar to the unit Bauds) the number of bits we can send at once. The above example shows symbols of 2, 3, and 4 bits.

It is important because these techniques of sending multiple bits in one signal apply to all digital modulations.

The disadvantage of increasing the number of bits per symbol is that the number of values increases. When talking about amplitudes, the discrete amplitude values will be closer and more difficult to detect correctly. Their detection tolerance becomes smaller.

Remember that noise added to a signal will make the parameters wobble in their tolerance area.

The rule to detect the values precisely is that the more bits a symbol contains, the higher the signal-to-noise ratio should be. There will be an SNR threshold to detect a signal based on symbols correctly.

The parameters of the electric signal can be amplitude, frequency, and phase.

DAB/DAB+

In DAB(+) the symbols contain 2 bits. The 1536 carriers in DAB Mode-I can carry 3072 bits in one modulation cycle.

The modulation used is DPQSK. The parameter of the carrier that changes is the Phase.

The Q means quadrature or 4 phases and. The 4 values indicate that the symbol contains 2 bits. “SK” means Shift Keying between the 4  values.

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