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Department of Information Engineering University of Padova, ITALY

Department of Information Engineering University of Padova, ITALY. Special Interest Group on NEtworking & Telecommunications. Mathematical Analysis of Bluetooth Energy Efficiency. Andrea Zanella, Daniele Miorandi, Silvano Pupolin.

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Department of Information Engineering University of Padova, ITALY

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  1. Department of Information EngineeringUniversity of Padova, ITALY Special Interest Group on NEtworking & Telecommunications Mathematical Analysis of Bluetooth Energy Efficiency Andrea Zanella, Daniele Miorandi, Silvano Pupolin {andrea.zanella, daniele.miorandi, silvano.pupolin}@dei.unipd.it WPMC 2003, 21-22 October 2003 Yokosuka, Kanagawa (Japan) 21-22 October 2003

  2. Outline of the contents • Motivations & Purposes • Bluetooth reception mechanism • System Model • Results • Conclusions Yokosuka, Kanagawa (Japan) 21-22 October 2003

  3. What & Why… Motivations & Purposes Yokosuka, Kanagawa (Japan) 21-22 October 2003

  4. Motivations • Bluetooth was designed to be integrated in portable battery driven electronic devices  Energy Saving is a key issue! • Bluetooth Baseband aims to achieve high energy efficiency: • Units periodically scan radio channel for valid packets • Scanning takes just the time for a valid packet to be recognized • Units that are not addressed by any valid packet are active for less than 10%of the time Yokosuka, Kanagawa (Japan) 21-22 October 2003

  5. Aims of the work • Although reception mechanism is well defined, many aspects still need to be investigated: • What’s the energy efficiency achieved by multi-slot packets? • What’s the role plaid by the receiver-correlator margin parameter? • What’s the amount of energy drained by Master and Slave units? • Our aim is to provide answers to such questions! How? • Capture system dynamic by means of a FSMC • Define appropriate reward functions (Data, Energy, Time) • Resort to renewal reward analysis to compute system performance Yokosuka, Kanagawa (Japan) 21-22 October 2003

  6. What standard says… Bluetooth reception mechanism Yokosuka, Kanagawa (Japan) 21-22 October 2003

  7. 54 72 0-2745 AC HEAD CRC access code packet header payload Access Code field • Access Code (AC) • AC field is used for synchronization and piconet identification • All packet exchanged in a piconet have same AC • Bluetooth receiver correlates the incoming bit stream against the expected synchronization word: • AC is recognized if correlator output exceeds a given threshold • AC does check HEAD is received • AC doesNOT checkreception stops and pck is immediately discarded PAYL Yokosuka, Kanagawa (Japan) 21-22 October 2003

  8. Receiver-Correlator Margin • S: Receiver–correlator margin • Determines the selectivityof the receiver with respect to packets containing errors • Low Sstrong selectivity • risk of dropping packets that could be successfully recovered • High Sweak selectivity • risk of receiving an entire packet that contains unrecoverable errors Yokosuka, Kanagawa (Japan) 21-22 October 2003

  9. 54 72 0-2745 AC HEAD CRC accesscode packet header payload Packet HEADer field • Packet Header (HEAD) • Contains: • Destination address • Packet type • ARQN flags: used for piggy-backing ACK information • Header checksum field (HEC): used to check HEAD integrity • HEC does check PAYL is received • HEC doesNOT check reception stops and pck is immediately discarded PAYL Yokosuka, Kanagawa (Japan) 21-22 October 2003

  10. 54 72 0-2745 AC HEAD CRC accesscode packet header payload Packet PAYLoad field • Payload (PAYL) • DH: High capacity unprotected packet types • DM: Medium capacity FEC protected packet types • (15,10) Hamming code • CRC field is used to check PAYL integrity: • CRCdoescheck positive acknowledgedis return (piggy-back) • CRC doesNOTcheck negative acknowledgedis return (piggy-back) PAYL Yokosuka, Kanagawa (Japan) 21-22 October 2003

  11. Conditioned probabilities DHn: Unprotected DMn: (15,10) Hamming FEC 2-time bit rep. (1/3 FEC) Receiver- Correlator Margin (S) AC HEAD PAYLOAD CRC 54 bits 72 bits h=2202745 bits 0: BER Yokosuka, Kanagawa (Japan) 21-22 October 2003

  12. A B B B B B H G F H Retransmissions NAK MASTER • Automatic Retransmission Query (ARQ): • Each data packet is transmitted and retransmitted until positive acknowledge is returned by the destination • Negative acknowledgement is implicitly assumed! • Errors on return packet determine transmission of duplicate packets (DUPCK) • Slave filters out duplicate packets by checking their sequence number • Slave does never transmit DUPCKs! • Slave can transmit when it receives a Master packet • Master packet piggy-backs the ACK/NACK for previous Slave transmission • Slave retransmits only when needed! ACK SLAVE X A DPCK B X DPCK Yokosuka, Kanagawa (Japan) 21-22 October 2003

  13. Mathematical Analysis System Model Yokosuka, Kanagawa (Japan) 21-22 October 2003

  14. Hypothesis • Single slave piconet • Saturated links • Master and slave have always packets waiting for transmission • Unlimited retransmission attempts • Packets are transmitted over and over again until positive acknowledgement • Static Segmentation & Reassembly policy • Unique packet type per connection • Sensing capability • Nodes can to sense the channel to identify the end of ongoing transmissions • Nodes always wait for idle channel before attempting new transmissions Yokosuka, Kanagawa (Japan) 21-22 October 2003

  15. Packet error probabilities • Let us define the following basic packet reception events • ACer: AC does not check • Packet is not recognized • HECer: AC does check & HEAD does not • Packet is not recognized • CRCer: AC & HEAD do check, PAYL does not • Packet is recognized but PAYL contains unrecoverable errors • PRok: AC & HEAD & PAYL do check • Packet is successfully received • Packets experiment independent error events Yokosuka, Kanagawa (Japan) 21-22 October 2003

  16. Reception events Downlink pck reception events Reception Event Index Uplink pck reception events • 0: both downlink and uplink packet are correctly received • 1: downlink packet is correctly received, uplink packet is received but with errors in the PAYL field • 2U3: downlink packet is correctly received but uplink packet is not recognized by the master unit • Master will transmit DUPCKs • 49: downlink and uplink packets are not correctly received • Master will retransmit useful packets Yokosuka, Kanagawa (Japan) 21-22 October 2003

  17. Mathematical Model • Normal State (N) • Master transmits packets that have never been correctly received by the slave • Duplicate State (D) • Master transmits duplicate packets (DUPCKs) • Since error events are disjoint, the state transition probabilities are given by • The steady-state probabilities are, then, Yokosuka, Kanagawa (Japan) 21-22 October 2003

  18. Reward Functions • For each state j we define the following reward functions • Tj= Average amount of time spent in state j • Dj(x)= Average amount of data delivered by unit x{M,S} • Wj(x)= Average amount of energy consumed by unit x{M,S} • The average amount of reward earned in state j is given by • Performance indexes • Energy Efficiency:  • Goodput: G Yokosuka, Kanagawa (Japan) 21-22 October 2003

  19. Notations • Let us introduce some notation: • Dxn (Dym) downlink (uplink) packet type, n=1,3,5 • L(Dxn) = PAYL length (bit) for Dxn packet type • wTX(X) /wRX(X)/wss(X)= amount of power consumed by transmitting/ receiving/ sensing the packet field X • pj = Pr(j) Yokosuka, Kanagawa (Japan) 21-22 October 2003

  20. Transmission Time reward ( T ) Reception/Sensing MASTER SLAVE n+m MASTER SLAVE n+1 Yokosuka, Kanagawa (Japan) 21-22 October 2003

  21. Data reward ( D ) • Master gains Data reward when • System is in state N • Slave perfectly receives the master packet • Slave gains Data reward when • Slave recognizes the master polling • Master perfectly receives the slave packet Yokosuka, Kanagawa (Japan) 21-22 October 2003

  22. Master energy reward ( W ) Receives entire uplink packet Receives only AC field Receives till the first uncorrected field and senses till the end of the packet Always transmits a downlink packet Yokosuka, Kanagawa (Japan) 21-22 October 2003

  23. Slave energy reward ( W ) • Slave’ energy reward resembles mater’ one except that, in D state, Slave does not listen for the PAYL field of recognized downlink packet since it has been already correctly received! Yokosuka, Kanagawa (Japan) 21-22 October 2003

  24. Performance Analysis Results Yokosuka, Kanagawa (Japan) 21-22 October 2003

  25. Energy Efficiency • Downlink traffic only (M>S) and S=0 • Energy efficiency gets worse in Rayleigh channels • DH5 outperform other packet formats for almost every SNR value • For SNRdB=1418, DMn outperforms DHn Yokosuka, Kanagawa (Japan) 21-22 October 2003

  26. Master Slave swapping • Swapping Master and Slave role: • DM5 & DM3 energy efficiency increases up to 15 % for SNR20dB • Unprotected pck types show slightly reduced performance gain • Performance gain drastically reduces for increasing values of the Rice factor K • For AWGN channels, master slave swapping does not lead to any significant performance improvement Yokosuka, Kanagawa (Japan) 21-22 October 2003

  27. Master Slave swapping • Swapping Master and Slave role: • DM5 & DM3 energy efficiency increases up to 15 % for SNR20dB • Unprotected pck types show slightly reduced performance gain • Performance gain drastically reduces for increasing values of the Rice factor K • For AWGN channels, master slave swapping does not lead to any significant performance improvement Yokosuka, Kanagawa (Japan) 21-22 October 2003

  28. Impact of parameter S AWGN Rayleigh • The receiver correlator margin S has strong impact on system performance • AWGN:  improves with S, in particular for low SNR values • Rayleigh:  gets worse with S, except for low SNR values • Relaxing AC selectivity is convenient, since G gain is much higher than  loss • Impact of S, however, rapidly reduces for SNRdB>15 Yokosuka, Kanagawa (Japan) 21-22 October 2003

  29. Conclusions • Main Contribution • mathematical framework for performance evaluation of Bluetooth piconets • Results • In case of asymmetric connections, Slave to Master configuration yields better performance in terms of both Goodput and Energy Efficiency • Slave never transmits DUPCK • Parameter S may significantly impact on performance • Short and Protected packet types improve performance with S • Long and Unprotected packet types show less dependence on this parameter • Results may be exploited to design energy–efficient scheduling algorithms for Bluetooth piconets Yokosuka, Kanagawa (Japan) 21-22 October 2003

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