# Demodulation of amplitude modulated digital signals

#### Bacab

Joined Dec 21, 2021
4
Hi,

When explaining the demodulation process of an amplitude modulated digital signal, I haven't find any article about how a receiver retrieves the "correct" levels for decoding the signal without error. In a binary (On/off) modulation it is not an issue however if there are more than two amplitude values then how the receiver knows that the signal it's receiving is a '01' and not a '11' that was attenuated by distance (assuming a purely amplitude modulated digital signal) ?
I can see several ways of doing it but I didn't find how it's done in a real system :
- the transmission of a synchronization word that will be recognised as such by the receiver and used as a reference;
- the use of an AGC that will amplify the received signal to a normalized level (but then how the AGC work ?);

Thank you in advance for your answer. I apologise if the question is either not in the correct subsection of the forum or if it was answered before (and I didn't find the information).

#### Irving

Joined Jan 30, 2016
3,813

#### Bacab

Joined Dec 21, 2021
4
Thank you for your answer. Unfortunately the author only deals with a simple modulation : either there is a signal and it can only be a '1' or there is nothing and it's a '0'.
Therefore you can't really mistake a level for another assuming there is enough signal in the receiver to detect the presence of the signal. My issue is : if you have a multiple levels amplitude modulated digital signal how do you know you are receiving one symbol or another.
If I take a real life modulation like a 16 state QAM : how do the receiver locates the received signal on the amplitude axis ?

#### Irving

Joined Jan 30, 2016
3,813
My understanding is that QAM works by assuming the amplitude changes at the bit level are modulation and the overall amplitude (ie received power) is essentially constant - AGC is therefore used to maintain a base amplitude. Additionally bit stuffing is used to ensure long trains of similar bits don't impact on the overall envelope. Finally error correcting CRC is used to correct 1 bit errors or force packet retry on 2 or more bit errors.

#### Irving

Joined Jan 30, 2016
3,813

#### ApacheKid

Joined Jan 12, 2015
1,471
If I understand this article correctly the amplitude questions is answered by understanding that there are two signals (out of phase by 90 ° ).

Therefore it is likely the relative amplitudes of the two carriers that is used to decide the binary significance. That article has this diagram:

But this does beg the question - how can this system distinguish 1010 from 1111 when the relative amplitudes are the same in each case and the phase difference...

I think my understanding is not quite right though...

#### ApacheKid

Joined Jan 12, 2015
1,471
see:

This is where the amplitude modulation makes its first real appearance in the QAM scheme. Rotating through the first quadrant, the first four points are at 18.4°, 45°, 45° and 71.6°. Because there are two points at 45°, they are differentiated by their amplitude; that is, their distance from the origin.
From here.

#### ApacheKid

Joined Jan 12, 2015
1,471

#### Bacab

Joined Dec 21, 2021
4
@ApacheKid & @Irving
@ApacheKid : You have gone through the exact same thinking process I have. I have red the article you found (I found them yesterday while searching for this issue). None of them give an answer to this particular issue.
@Irving : this last pdf is the closest thing to an answer I have found yesterday but it's a bit lacking in explanations.

#### drjohsmith

Joined Dec 13, 2021
850
QAM is interesting to decode
in reality, each of the "dots" is a probability density.

One of the problem,
if say the stream transmitted a constant 1111
then decoding would be "interesting"

The part of QAM in relaity is the stream of data is encrypted / scrabbled,
such that the average number of 1 and 0 is "constant"

This if you "AC couple" , wither in the electrical or the digital computer side,
then you will receive signals that go between all the extremities of the constellation,

I.e. if you put the I and Q signals onto a scopes X/Y , you will see the above constellation
and if the SNR is ok, then its relatively easy to set up a "grid" of "detection"