I was performing a simulation of the BER of an experimental communication system while transmitting QPSK symbols. In the model I have been following, I have to introduce a random matrix (normal distributed) that represents an error. The BER obtained is sometimes close to the theoretical one and sometimes it's really bad (more or less constant at 0.5). I realized that this is caused by the randomness introduced by the error matrix. Now, I'm performing simulations computing the mean BER for different realizations of the error matrix and the result obtained is still so random. How can I mitigate more this effect?
Thanks in advance
The theoretical BER is obtained by averaging the results over numerous simulations runs (theoretically an infinite number). The difference that you got may be due to the insufficient number of simulations runs and/or to the low size of the matrix you consider. The randomness that you can observe in your result is indeed induced by the random nature of your random matrix: the average of random variables is still a random variable (with non-zero variance) unless you perform the average over a very large number of samples.
Note that in practice, if you want to get a relevant BER of 10^-n, you should simulate at least 10^(n+2) bits.
Note that there is difference between calculating bit error rate and calculating symbol error rate. That means that if you use QPSK (i.e 2 bits for each symbol), the required number of simulations is divided by two. So, the equation Vincent has mentioned is OK for a 1-bit symbol, which isn't your case. For m-bits symbol, the mentioned equation should be divided by m.
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