The bit error rate (BER) is a wellunderstood metric for measuring communications system performance. When a system is not amenable to analytical performance analysis, a Monte Carlo simulation is often used to determine the performance. In such simulations, it is necessary to compute a 95% (or other percent) confidence interval to establish the statistical significance of the simulation run, or to determine how long to run a simulation to achieve the desired accuracy.
There are standard techniques to compute the confidence interval, including for the BER, but these assume that bit errors are statistically independent events. This is not the case at all in a coded communications system, where bit errors occur in bursts within frames in error.
Using analytical methods, a new method to compute the confidence interval for the BER of a coded communications system was developed. When a simulation of coded frames is conducted, instead of just storing a count of the bits in error, B1, an additional quantity, a count of the square of the number of bits in error per frame, B2, is stored. A confidence interval for the BER can be computed from B1 and B2. A numerical example demonstrates that previous methods to compute confidence intervals for the BER of a coded system fail if they rely on standard techniques that assume error events are independent. The new method provides a robust, rigorous confidence interval that is a foundation on which communications performance and system risk may be determined.
The novel aspect of this work is a derivation of the confidence interval of the BER that relies on the variance of the number of bits-in-error in each frame simulated. Prior work considered only the number of bits-in-error in all frames, but not the uncertainty in the number of bits-in-error within frames that contained errors. This enabled a framework to be derived that resulted in a statistically accurate confidence interval.
Systems engineers associate uncertainty, or variance, with each item in the communications link budgets they maintain. This new work enables a systems engineer to properly account for the variance of the communications system from its nominal, simulated performance. This is a critical aspect of designing a system that has an overall risk that is well understood.