Rohde & Schwarz CMU-K20, Operating Manual

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Signalling: Receiver Quality Measurements
CMU-K20/K21/K22/K23/K24
1115.6088.12 4.126 E-12
In the figure below the lower confidence level is the sum of all probabilities p(n
e
, n
s
,
BER
low
) up to the measured number of bit errors. The upper confidence level is the
sum of all probabilities p(n
e
, n
s
, BER
high
) above the measured number of bit errors.
n
e
p(
n
e
)
Measured number of bit errors
Confidence Interval
p(n
e
, BER
low
)
p(n
e
, BER
high
)
Example:
Assume that 20 bit errors were measured after 1000 received
bits (n
e
= 20, n
s
= 1000, preliminary BER = n
e
/n
s
= 2 %). The
probability of the exact BER to be smaller than 1.1 % is 1 %
(lower confidence level: 99 %). The probability of the exact BER
to be larger than 3.3 % is 1 % (upper confidence level: 99 %).
If the specified upper BER limit is 1 %, then the measurement
can be stopped and the receiver can be failed with a risk of less
than 1 % that the exact BER is below the specified limit.
Confidence Fail,
Confidence
Pass,
Bad DUT Factor
In analogy to the calculation in the example above it is possible to calculate
confidence intervals [a(BER
limit
), b(BER
limit
)
]
for the measured preliminary BER
around the specified limit:
•
At a given confidence level, any measured preliminary BER below a(BER
limit
)
means that the exact BER of the receiver is below BER
limit
so that the receiver
should pass the test (early pass decision, test stopped).
•
At a given confidence level, any measured preliminary BER above b(BER
limit
)
means that the exact BER of the receiver is above BER
limit
so that the receiver
should fail the BER test (early fail decision, test stopped). b(BER
limit
) is termed
the early fail limit; the confidence level for b(BER
limit
) can be set as
Confidence
fail
value.
•
If a preliminary BER inside the confidence interval [a(BER
limit
), b(BER
limit
)
]
is
measured, no decision is possible so that the measurement must be continued.
The calculation can be performed for arbitrary BER
limit
values and confidence
levels. Increasing BER
limit
by multiplication with a factor M > 1 also shifts the
confidence interval and increases the number of early pass decisions, causing a
further reduction of test times. In practice, a factor M = 1.5 has been proved to
provide a reasonable compromise between test time and accuracy requirements.
•
At a given confidence level, any measured preliminary BER below the lower
interval border a(M*BER
limit
) means that the exact BER of the receiver is below
M*BER
limit
so that the receiver should pass the test (early pass decision, test
stopped). a(M*BER
limit
) is termed the early pass limit; the confidence level for
a(M*BER
limit
) can be set as
Confidence pass
value. The factor M itself is fixed to
the value 1.5 and termed the
Bad DUT Factor.
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