DOC#8545-0017-01
AXONN, L.L.C.
Packet Error Rate to Bit Error Rate Relationship
By
Eric Blanchard
Technical Memorandum
June 13, 2006
1. Introduction
This document explains some of the mathematics behind relating a measured
packet error rate value to an immeasurable bit error rate. In certain cases, it can be
assumed that when an erroneous packet is received, there was only one bit that caused the
error. However, for large packet sizes and/or error rates, the effects of multiple errors per
packet must be taken into account. Three different methods of computing BER from
PER will be examined and compared.
2. Test Program Parameters
For the Stamp error and sensitivity testing, the packet size used in Ronnie’s test
program is 128 bits per packet. The probability of 1 error occurring within that packet is
128*BER. There are 8128 combinations of having 2 errors in a packet and 341376
combos of 3 errors per packet. Since these combinations will be multiplied by their
probability of occurring (BER^2 or BER^3), the lower the BER, the less of an impact
those multiple error combos will have on the measured PER.
3. One Bit Error per Packet Assumption
In the MMT throughput tests with the 2.4 GHz transceiver, there were packet
success rates of 98.5%-99.1% at a distance of 200 feet out in the open. That means the
PER was between 9.0*10-3 and 1.5*10-2. By assuming 1 bit error per packet, the
resulting BER range is 7.0*10-5 to 1.172*10-4.
4. Effect of Adding One, Two, Three, and Four Bit Errors per Packet
I decided to test the impact of including the possibilities of up to 4 errors per
packet using the high end of the measured PER range (1.5*10-2). By setting the
following equation equal to a PER of 1.5*10-2 and solving for BER, I found that a more
accurate BER approximation is 1.162*10-4.
PER=128*BER+8128*BER2+341376*BER3+10668000*BER4
This compares quite closely with the 1 error per packet assumption which yielded BER of
1.172*10-4.
5. Standard PER and BER relationship
There is also a somewhat standard approximation formula in some journal
publications and lecture notes that says PER=1-(1-BER)n where n is the packet size.
Using that formula yields a BER range of 7.06*10-5 to 1.181*10-4. This seems to
overestimate the BER slightly, but still within a reasonable amount.
6. Conclusion
Although assuming 1 bit error per packet proved satisfactory for the given PER
measurements and resulting BER approximations above, at a significantly higher bit error
rate, say 0.1%, the probability of having 1 error in a packet of 128 bits is 0.128. If the
possibility of 2 and 3 errors per packet is included, that raises the PER to:
0.128+8128*0.001^2+341376*0.001^3=0.1365
This is a fairly significant increase; so unless the packet size is decreased, care must be
taken when deriving BER values from PER measurements near the sensitivity threshold
of 0.1% BER at -90dBm.
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