Bit Error Rate Comparison Statistics and Hypothesis Tests for Inverse Sampling (Negative Binomial) Experiments

摘要

Inverse, or negative binomial, sampling is often used when the observation of interest occurs extremely infrequently. As this is the case in bit error rate (BER) simulations, especially in high signal-to-noise ratio cases, negative binomial sampling can be advantageously employed in a computationally economic fashion to compare bit error rates between different systems. When the results of two negative binomial sampling tests are compared, point estimates and interval estimates quantify the performance relationship between the results of the tests. This paper derives a new, optimal, logarithmically symmetric confidence interval estimator for the ratio of BER estimates derived from two negative binomial tests. In addition, a three-sided hypothesis test with a single significance level is derived to quantify the confidence of the relationship between the two systems. Low-BER approximations for the confidence interval and decision thresholds are derived based on the F-distribution. The approximation is shown to work with BERs as high as . An example inspired by bit interleaved coded modulation shows how the technique can be used to reduce simulation time by an order of magnitude and facilitate straightforward interpretation and comparison between different systems. Negative binomial sampling is recommended for comparison experiments where BER is the key metric.