berconfint

Error probability estimate and confidence interval of Monte Carlo simulation

Syntax

[errprobest,interval] = berconfint(nerrs,ntrials)

[errprobest,interval] = berconfint(nerrs,ntrials,level)

Description

[errprobest,interval] = berconfint(nerrs,ntrials) returns the error probability estimate and 95% confidence interval for a Monte Carlo simulation of ntrials trials with nerrs errors.

[errprobest,interval] = berconfint(nerrs,ntrials,level) specifies the confidence level.

Examples

Compute BER Confidence Interval for Simulation Results

Compute the confidence interval for the simulation of a communication system that has 100 bit errors in 106 trials. The bit error rate (BER) for that simulation is ${10}^{-4}$.

Compute the 90% confidence interval for the BER of the system. The output shows that, with 90% confidence level, the BER for the system is between 0.0000841 and 0.0001181.

nerrs = 100;    % Number of bit errors in simulation
ntrials = 10^6; % Number of trials in simulation
level = 0.90;   % Confidence level
[ber,interval] = berconfint(nerrs,ntrials,level)

ber = 
1.0000e-04

interval = 1×2
10-3 ×

    0.0841    0.1181

For an example that uses the output of the berconfint function to plot error bars on a BER plot, see Use Curve Fitting on Error Rate Plot.

Input Arguments

nerrs — Number of errors

scalar

Number of errors from Monte Carlo simulation results, specified as a scalar.

Data Types: single | double

ntrials — Number of trials

scalar

Number of trials from Monte Carlo simulation results, specified as a scalar.

Data Types: single | double

level — Confidence level

scalar in the range [0, 1]

Confidence level for a Monte Carlo simulation, specified as a scalar in the range [0, 1].

Data Types: single | double

Output Arguments

errprobest — Error probability estimate

scalar

Error probability estimate for a Monte Carlo simulation, returned as a scalar.

• 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).

interval — Confidence interval

two-element column vector

Confidence interval for a Monte Carlo simulation, returned as a two-element column vector that lists the endpoints of the confidence interval for the confidence level specified by the input level.

References

[1] Jeruchim, Michel C., Philip Balaban, and K. Sam Shanmugan. Simulation of Communication Systems. Second Edition. New York: Kluwer Academic/Plenum, 2000.

Version History

Introduced before R2006a