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Mathematical Analysis of Bluetooth Energy Efficiency

Department of Information Engineering University of Padova, Italy. Mathematical Analysis of Bluetooth Energy Efficiency. Andrea Zanella, Silvano Pupolin. {zanella, pupolin}@dei.unipd.it. COST273 Barcelona, 15-17 January 2003. Outline of the contents. Motivations & Purposes

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Mathematical Analysis of Bluetooth Energy Efficiency

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  1. Department of Information Engineering University of Padova, Italy Mathematical Analysis of Bluetooth Energy Efficiency Andrea Zanella, Silvano Pupolin {zanella, pupolin}@dei.unipd.it COST273 Barcelona, 15-17 January 2003

  2. Outline of the contents • Motivations & Purposes • Bluetooth reception mechanism • System Model • Results • Conclusions TD (03)-028

  3. What & Why… Motivations & Purposes TD (03)-028

  4. Motivations • Bluetooth was designed to be integrated in portable battery driven electronic devices  Energy Savingis 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 TD (03)-028

  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 TD (03)-028

  6. What standard says… Bluetooth reception mechanism TD (03)-028

  7. 54 72 0-2745 AC HEC CRC access code packet header payload Access Code field PAYL • 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 does NOT checkreception stops and pck is immediately discarded TD (03)-028

  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 TD (03)-028

  9. 54 72 0-2745 AC HEC CRC accesscode packet header payload Packet HEADer field PAYL • 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 TD (03)-028

  10. 54 72 0-2745 AC HEC CRC accesscode packet header payload Packet PAYLoad field PAYL • 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) TD (03)-028

  11. Conditioned probabilities DHn: Unprotected DMn: (15,10) Hamming FEC 2-time bit rep. (1/3 FEC) Receiver- Correlator Margin (S) AC HEC PAYLOAD CRC 54 bits 72 bits h=2202745 bits 0: BER TD (03)-028

  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 • Slave filters out duplicate packets by checking their sequence number • Slave never transmits duplicate packets! • 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 TD (03)-028

  13. Mathematical Analysis System Model TD (03)-028

  14. Mathematical Model • System dynamic can be modelled by means of a discrete time independent process {en} with state space E • Each state corresponds to a specific system behaviour • For each state Ej E, we define the following reward functions • Dj(x)= Average amount of data delivered by unit x{M,S} • Wj(x)= Average amount of energy consumed by unit x{M,S} • Tj= Average amount of time spent in state Ej • Denoting by j the probability of event Ej, the average amount of reward earned in state Ej is given by: TD (03)-028

  15. System Dynamic • We need to determine: • State space E • System behaviour in each Ej E • System dynamic depends on the packet reception events that occur at Slave and Master units • Let us first focus on events that may occur during the reception of a single packet TD (03)-028

  16. Packet reception events • Let us define the following basic packet reception events • ACer: AC does not check • Packet is not recognized • HECer: AC does check & HEC does not • Packet is not recognized • CRCer: AC & HEC do check, CRC does not • Packet is recognized but PAYL contains unrecoverable errors • CRCok: AC & HEC & CRC do check • Packet is successfully received • Furthermore, we introduce the following notation • Recognition Error: RECer={ACer or HECer} • Recognition OK: RECok={CRCer orCRCok} TD (03)-028

  17. Basic reception events (1) • Looking at the reception status of both the downlink (master to slave) and uplink (slave to master) packets, we can identify four basic reception events • r1: both downlink and uplink packet are recognized by the slave and master unit, respectively • r2: downlink packet is not recognized by the slave unit (uplink packet is not returned) • r3: downlink packet is recognized by the slave unit, but PAYL is not correct, uplink packet is not recognized by the master unit • r4: downlink packet is successfully received by the slave unit, uplink packet is not recognized by the master unit TD (03)-028

  18. Basic reception events (2) • Note that, • Basic events are disjoint: • Their probabilities adds to one: • The occurrence of each basic event determines a specific system dynamic for a given number of steps • We define a state Ei to each basic event ri: ri Ei • State Ei collects the system dynamic after the occurrence of the basic event ri TD (03)-028

  19. Notations • Let us introduce some notation: • Dxn= downlink (Master to Slave) packet type, n=1,3,5 • Dym= uplink (Slave to Master) packet type, m=1,3,5 • L(Dxn) = number of data bits carried by the Dxn packet type • wTX(X)= amount of power consumed by transmitting packet field X • wRX(X)= amount of power consumed by receiving packet field X • w0= average amount of power consumed by the receiving unit in case the incoming packet is not recognized, i.e., RECer occurs: TD (03)-028

  20. System Dynamic: E1 MASTER Transmission Reception SLAVE T1 • Rewards earned in state E1 are given by: • Time spent is E1 • Energy consumed by Master • Energy consumed by Slave • Data delivered by Master • Data delivered by Slave TD (03)-028

  21. System Dynamic: E2 MASTER Transmission Reception SLAVE T2 • Rewards earned in state E2 are given by: • Time spent is E2 • Energy consumed by Master • Energy consumed by Slave • Data delivered by Master • Data delivered by Slave TD (03)-028

  22. System Dynamic: E3 MASTER Transmission Reception SLAVE T3 • Rewards earned in state E3 are given by: • Time spent is E3 • Energy consumed by Master • Energy consumed by Slave • Data delivered by Master • Data delivered by Slave TD (03)-028

  23. System Dynamic: E4 T4 • State E4 is entered when r4 event occurs: • Downlink packet is perfectly received, while uplink packet is not recognized • Master keeps retransmitting duplicate pcks until a return pck is recognized • Slave listens only for AC and HEAD fields of duplicate packets and returns an uplink packet for each duplicate packet it recognizes • State E4 is left when r1 event occurs: • Both downlink and uplink packets are recognized by the respective units TD (03)-028

  24. Performance Analysis Results TD (03)-028

  25. Performance Indexes • From the renewal reward analysis, we can evaluate the following performance indexes • Goodput: G • Amount of data successfully delivered per unit of time • Energy Efficiency:  • Amount of data successfully delivered per unit of energy consumed TD (03)-028

  26. Asymmetric connection: M>S Data flows from Master to Slave SNRdB<14, G  0 SNRdB=1418, DMn outperforms DHn SNRdB>18, DHn achieves better G AWGN channel: M>S • Energy efficiency curves resemble Goodput curves • However, performance gap between Dx5 and Dx3 pck types is reduced TD (03)-028

  27. AWGN channel: S>M • Asymmetric connection: S>M • Data flows from Slave to Master • Swapping Master and Slave role: • DM5 & DM3 Goodput increases up to 15 % • Other pck types do not improve, but neither loose performance… • Energy efficiency improvement for DM5 & Dm3 pcks is up to 22 % • However, for greater SNR values, performance improvement is lower… TD (03)-028

  28. Rayleigh channel: M>S • Performance in Rayleigh channels is drastically reduced! • SNRdB<14, G  0 • SNRdB<18, DMn & DHn types achieve similar performance • SNRdB>18, DH5 achieves higher G • Energy efficiency curves resemble Goodput curves • Curves shape is smoother than for AWGN TD (03)-028

  29. Rayleigh channel: S>M • For Rayleigh fading channel, S>M configuration is much better performing than M>S configuration, for almost all the packet types • DM5 & DM3 Goodput increases up to 55 % • DH5 & DH3 Goodput increases up to 15 % • All the packet types improve energy efficiency performance • For DM5 & DM3, Δ up to 88 %!!! • For DH5 & DH3, Δ up to 20 % TD (03)-028

  30. Impact of parameter S • The receiver correlator margin S has strong impact on system performance • G improves for high S values (from 30% up to 230% for SNRdB=15) •  improves for DMn and DH1 types •  slightly decreases for DH5 & DH3 types (less 6 % performance loss) • Relaxing AC selectivity is convenient, since G gain is much higher than  loss • Impact of S, however, rapidly reduces for SNRdB>15 TD (03)-028

  31. Conclusions • Average traffic rate shows a tradeoff between different packet types • Unprotected and long types yield better Goodput for SNR> 18 • For lower SNR, better performance are achieved by short and protected formats • Performance gap between protected and unprotected formats is drastically reduced in fading channels • Slave to Master configuration yields performance improvement in terms of both Goodput and Energy Efficiency • Server (slave) never retransmits pcks that were already received by the client (master) • 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 algorithms for the piconet management TD (03)-028

  32. That’s all! Thanks for you attention! TD (03)-028

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