Bit error rate (BER) and confidence interval of Monte Carlo simulation
[ber,interval] = berconfint(nerrs,ntrials)
[ber,interval] = berconfint(nerrs,ntrials,level)
[ber,interval] = berconfint(nerrs,ntrials) returns
the error probability estimate ber and the 95%
confidence interval interval for a Monte Carlo
simulation of ntrials trials with nerrs errors. interval is
a two-element vector that lists the endpoints of the interval. If
the errors and trials are measured in bits, the error probability
is the bit error rate (BER); if the errors and trials are measured
in symbols, the error probability is the symbol error rate (SER).
[ber,interval] = berconfint(nerrs,ntrials,level) specifies
the confidence level as a real number between 0 and 1.
If a simulation of a communication system results in 100 bit errors in 106 trials, the BER (bit error rate) for that simulation is the quotient 10-4. The command below finds the 95% confidence interval for the BER of the system.
nerrs = 100; % Number of bit errors in simulation ntrials = 10^6; % Number of trials in simulation level = 0.95; % Confidence level [ber,interval] = berconfint(nerrs,ntrials,level)
The output below shows that, with 95% confidence, the BER for the system is between 0.0000814 and 0.0001216.
ber =
1.0000e-004
interval =
1.0e-003 *
0.0814 0.1216
For an example that uses the output of berconfint to
plot error bars on a BER plot, see Curve Fitting An Error Rate Plot
[1] Jeruchim, Michel C., Philip Balaban, and K. Sam Shanmugan, Simulation of Communication Systems, Second Edition, New York, Kluwer Academic/Plenum, 2000.