14)
As N approaches infinity, ?†P
0 will converge to the true value of P0.
Let us take a moment to evaluate the estimator, given a finite value of N. Recall one such property
of the estimator is the confidence interval and is given below for (y, y).
(8.15)
Next we summarize the detailed steps carried out in [1] and [3]. It is known that ?†P
0 is binomially distributed
and it converges to either a Poisson or Normal distribution, depending on the imposed constraints.
A common practice is to use the Normal approximations due to insight and mathematical
tractability. The end result is provided below, assuming the estimated error rate of and an
estimation window size of .
(8.16)
where d is chosen so that the following holds true:
(8.17)
The confidence interval is plotted in Fig. 8.4 for 90% and 99% values, assuming a hypothetical BER
of 10v, where v has been set equal to 2.
What we can extract from this graph is, for a fixed 90% confidence interval and an observation
length of 10v2 bits, a variation of approximately 0.9 ?†P
0??“1.1 ?†P
0 is observed. In other words, giving the
bit error event 100 opportunities to make itself public results in a small spread (approximately
10%)
around the expected BER value.
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