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Its been a nice week for me, wherein I guest posted an article in DSPDesignLine.com. 
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 DSPDesignLine.com
The same article is cross-posted also in Embedded.com
For those who are not interested in the full article, the probability of error for M-QAM modulation is,
.
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Related posts
- Comparing BPSK, QPSK, 4PAM, 16QAM, 16PSK, 64QAM and 32PSK
- Symbol Error Rate (SER) for 16-QAM
- Comparing 16PSK vs 16QAM for symbol error rate
- Symbol Error Rate (SER) for QPSK (4-QAM) modulation
- Bit error rate for 16PSK modulation using Gray mapping
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{ 10 comments… read them below or add one }
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?
thanks…
@neon: Thats correct. To be preceise, to divide the whole formula by 6, one needs to assume that each symbol error corresponds to only one bit error. For that to be true, one needs to assume Gray coded mapping. Which is a reasonable assumption.
You may look at the BER computation for 16-QAM with Gray mapping as an example:
http://www.dsplog.com/2008/06/05/16qam-bit-error-gray-mapping/
Hope this helps.
yes it helps, thanks
Could you help me find matlab script for M-QAM that is used on OFDM?
Thank You
@ananta: If the channel is AWGN, the symbol error rate equation holds good for OFDM too. I have not posted code for M-QAM in OFDM case.
@ananta: You may find the M-QAM symbol error rate in AWGN simulation model @
http://www.dsplog.com/db-install/wp-content/uploads/2008/04/script_m_qam_ser.m
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
thanks
@farrakh: Sorry, I have not discussed Nakagami fading in any posts till date.
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…
@Aditya: Your equation for symbol error rate is correct.