# Calculate symbol rate for QAM modulation

Not sure if this is the right place to ask, feel free to move it if any other site suits this better.
Anyway I am referring to QAM modulation used in US Cable TV. I know it comes under Annex B which is related to FEC.
I know that 64 QAM has a symbol rate ~= 5057000 Symbols/s and 256 QAM 5360000Symbols/s I would like to know how this is calculated, also what symbol rate will, say 128 QAM have for example?

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In the absence of units on these numbers 5360000 etc, this question cannot be answered. – Dilip Sarwate May 3 '12 at 12:24

There is no inherent symbol rate for any modulation type. 64 QAM symbols transmit 6 bits per symbol, and 256 QAM symbols transmit 8 bits per symbol. If the bit rate were to stay constant, then the 256 QAM symbol rate would be 6/8 of the 64 QAM symbol rate, but it appears that that is not the case (assuming your numbers are correct). That may be because they are using more forward error correction (FEC) to mitigate the higher power requirements of 256 QAM.

Given that the bit rates are not the same, we can't guess what the 128 QAM symbol rate would be.

The general equation for a given modulation type and its symbol rate is: $symbols/s = \frac{bits/s}{bits/symbol}$

Determining the bits per symbol is usually pretty easy. It's log2 of the number of possible symbol points. Thus, the bits per symbol of 256QAM (which has 256 possible points) is 8.

The trick is finding the bits per second. Wireless transmitters often have the following blocks:

Data source => Compression => Scrambling => FEC Encoding => Pulse Shaping => Modulation

To know the final bit rate you need to know the bit rate of the data source, how much the compression reduces the data rate (if there is compression), and how much the FEC encoding increases the data rate.

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This is more a broadcast question than a DSP one. The figures I quoted are the standard values used when configuring a tuner. I was curious how these value were calculated. Is there a formula connecting symbol rate, QAM mode, FEC etc? – jogabonito May 3 '12 at 12:54
@jogabonito I have edited my answer to respond to your question. – Jim Clay May 3 '12 at 13:45

For anyone interested in the figures used to obtain the values I mentioned, Annex A of the SCTE Cable Specification is a good reference. The basic formula is the same as in @Jim's answer. So I have accepted his answer, and leaving this as a reference point for any RF engineeers out there :-)

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The specific symbol rate numbers you cited are the Annex B standard values for 64 QAM and 256 QAM, which are specific profiles with set parameters including fixed symbol rates and bitrates. Annex A is more flexible.

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