Packet Error Rate Distribution Between Random Bluetooth Piconet Pairs

The packet error rate between two piconets depends on the temporal alignment of their packets and the spectral alignment of the intervals from which the frequencies in their hop sequence are chosen. The relationship between two randomly paired piconets is one of over 828 billion possible relationships. We define these relationships and derive an expression for determining the packet error rate for a specific pair of piconets using single-slot packets. We derive the probability mass function for the packet error rate and extend it to provide the possible packet error rates for an arbitrary number of neighboring piconets. We also derive a probability mass function for the goodput of a piconet with a neighboring piconet. The probability mass functions for the packet error rate is bimodal, meaning the expected value of the goodput or packet error rate is not a good choice for piconet performance analysis. Brian S. Peterson is Chief of the Advanced MASINT Research and Requirements Branch at the National Air and Space Intelligence Center, Wright-Patterson AFB, Ohio. He received the B.S.E.E degree in 1991 from the United States Air Force Academy, an M.S. degree in Systems Engineering in 1995 from, and an M.S.E.E. degree from Florida State University in 1998. He received his Ph.D. degree in Electrical Engineering in 2005 from the Air Force Institute of Technology. Dr. Peterson's research interests include computer communication protocols and wireless networking. Dr. Peterson is a member of the IEEE. Rusty O. Baldwin is an Associate Professor of Computer Engineering in the Department of Electrical and Computer Engineering at the Air Force Institute of Technology, Wright-Patterson AFB, Ohio. He received the B.S.E.E degree (with honors) in 1987 from the New Mexico State University and the M.S. degree in Computer Engineering in 1992 from AFIT. He received his Ph.D. degree in Electrical Engineering in 1999 from Virginia Polytechnic Institute and State University. Dr. Baldwin's research interests include computer communication protocols, information warfare, and wireless networking. Dr. Baldwin is a Senior member of the IEEE. Richard A. Raines is an Associate Professor of Electrical Engineering in the Department of Electrical and Computer Engineering at the Air Force Institute of Technology (AFIT), Wright-Patterson AFB, Ohio. He received the B.S.E.E degree (with honors) in 1985 from the Florida State University and the M.S. degree in Computer Engineering in 1987 from AFIT. He received his Ph.D. degree in Electrical Engineering in 1994 from Virginia Polytechnic Institute and State University. Dr. Raines' research interests include computer communication protocols, information security, and wireless networking. Dr. Raines is a Senior member of the IEEE.