Article in M-QAM symbol error

Its been a nice week for me, wherein I guest posted an article in πŸ™‚

The article derives the theoretical symbol error rate for M-QAM modulation. The theoretical results are further supplemented by Matlab/Octave simulation scripts.

Those who are familiar with derivation of symbol error rate for 16-QAM modulation will find the equations easy to interpret. As we did for 16-QAM,

(a) We identify the three different types of symbols – corner, inside, neither inside nor corner.

(b) Then we find the symbol error probability for each of the three types of symbols

(c) Total error probability is found assuming that all the symbols are equally likely.

Click here to read the article published in

The same article is cross-posted also in

For those who are not interested in the full article, the probability of error for M-QAM modulation is,

. πŸ™‚

21 thoughts on “Article in M-QAM symbol error

  1. Here is how one can establish a relationship between BER and SER. A symbol will be in error when at least one bit (one or more bits) in the symbol is in error. In otherwords,
    SER = 1-prob(all bits are correct). Let there be ‘M’ bits for a symbol.
    Thus SER = 1 – (1-BER)^N. This is the exact equation connecting SER and BER.
    Conversely, BER = 1 – (1 – SER)^(1/N). This can be expanded as an infinite series of powers of SER.
    Since 0 <= SER <= 1, we can approximate (1 – SER)^(1/N) to 1 – SER/N and therefore BER = SER/N.
    This approximation is valid irrespective of the number of bits in error in the symbol.

  2. Hi Krishna,
    Thanks but M-ary is different than MQAM! M-ary means you can send e.g. 100 modulated signal, which every modulated signal can be 64-QAM or M-QAM. Don’t mix M in M-ary with M in MQAM.
    May be I should say MCM or multy carrier modulation.
    So my question is how can we implement MCM (M-ary) for 64QAM to estimate BER for that?

          1. Hi Krishna,
            Sorry, I mix the M-ary with MCM, I am very sorry!!!
            But my problem still exist. I will simulate BER for a MCM system for a M-ary or 64-QAM. Now I have code for 64-QAM, but if I will use it for MCM what I should do?
            Definition of MCM is still same, sending e.g 100 of 64QAM simultaneously.
            Thank you for your answer and your time and consideration.
            I will waiting for your answer.

  3. Hi…
    Thank you for this article…

    I want to ask something about relation between SER and BER. To compute BER, i can use the formula :

    BER = number of bit error / total bit

    how about to compute SER? Is it similar formula like BER in simple way?
    like :
    SER = number of symbols error / total symbols

    or another to compute SER ?

    Thank you…

  4. slam krishna
    do u have bit error or symbol error simulations in nakagami_m channel.or related simulations with nakagami_m channel.
    if u have plz email me.and plz email me ebook of bit error probability in awgn channel


  5. Hi,

    Thanks for the dsplog, it really helps a lot.

    I was wondering how this SER formula can be turned into BER vs EbNo formula, take 64-QAM for instance, i would use k = 1/sqrt(42), M = 64, and EsNo = 6*EbNo and then divide the whole formula by 6

    Am I right?


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