ERROR CONTROL SCHEMES FOR BLUETOOTH TECHNOLOGY:ANALYSIS AND PERFORMANCE - Computer Science Research and Technology - page 63

E = H × n [ n + n × 0 75 ] × p

ham 2 pac bits bits h 2

where H can be evaluated H=3 , n bits is the number of bits of the HAM2 packet and p h2 is the
probability that the AUX2 packet arrives correctly at the receiver after the second hop
(because the packet will be discarded if the CRC detects errors):

( ) 2 p = 1 − PER

h 2 f

The total energy consumed by DH1 packet is

[ ] E = H × n × N × n + n × 0 . 75 × p

dh 1 pac bits bits h 5

where H is the number of the remaining hops of the network, n bits is the number of bits of the
DH1 packet and p h5 is the probability that the HAM2 packet arrives correctly at the receiver
after the fifth hop, given by:

( )

3

p = 1 − PER × p

h 5 f h 2

The number of transmitted packets with error is the sum of errors occurred in the
transmissions of the AUX2 and HAM2 packets, as the DH1 packet will always be
retransmitted until it is correctly received:

n = n + n

error error _ aux 2 error _ ham 2

The number of errors of the AUX2 packet is the product of the total number of
transmitted packets n pac and the probability of error of the AUX2 packet in two hops:

2

n = [ − ( − PER ) ] × n

error _ aux 2 f pac

The number of errors of the HAM2 packet has the same form, but the number of errors
occurred in the first and second hops using the AUX2 packet have to be subtracted from the
total number of transmitted packets n pac :

3

n = [ − ( − PER ) ] × ( n − n )

error _ ham 2 f pac error _ aux 2

Then the reliability and the energy efficiency can be evaluated. For the ADP2 scheme,
the energy efficiency may be evaluated using the same equations of ADP1 scheme, replacing
the HAM2 packet by the BCH2 packet.