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Complexity Comparison of TG2 AFH Mechanisms

This presentation compares the complexity estimations for adaptive frequency hopping (AFH) mechanisms in TG2.

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Complexity Comparison of TG2 AFH Mechanisms

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  1. Project: IEEE P802.15 Working Group for Wireless Personal Area Networks (WPANs) Submission Title:Complexity Comparison of TG2 AFH Mechanisms Date Submitted: October 8, 2001 Source: (1) HK Chen, YC Maa, and KC Chen(2) Anuj Batra, Kofi Anim-Appiah, and Jin-Meng Ho Company: (1) Integrated Programmable Communications, Inc. (2) Texas Instruments, Inc. Address: (1)Taiwan Laboratories Address: P.O. Box 24-226, Hsinchu, Taiwan 300 (2) 12500 TI Boulevard, Dallas, TX 75243 TEL(1) +886 3 516 5106, FAX: +886 3 516 5108, E-Mail: {hkchen, ycmaa, kc}@inprocomm.com (2) +1 214 480 4220, FAX: 972 761 6966, E-Mail: {batra, kofi, jinmengho}@ti.com Re: [] Abstract: This presentation shows the complexity estimations for AFH mechanisms Purpose: Submission to Task Group 2 to resolve the complexity consideration. Notice: This document has been prepared to assist the IEEE P802.15. It is offered as a basis for discussion and is not binding on the contributing individual(s) or organization(s). The material in this document is subject to change in form and content after further study. The contributor(s) reserve(s) the right to add, amend or withdraw material contained herein. Release: The contributor acknowledges and accepts that this contribution becomes the property of IEEE and may be made publicly available by P802.15. Integrated Programmable Communications, Inc. and Texas Instruments, Inc.

  2. Complexity Comparison of TG2 AFH Mechanisms HK Chen, YC Maa, and KC Chen Integrated Programmable Communications Anuj Batra, Kofi Anim-Appiah, and Jin-Meng Ho Texas Instruments Integrated Programmable Communications, Inc. and Texas Instruments, Inc.

  3. Scope of Complexity Estimation • What IS NOT in this complexity estimation • Channel classification algorithm • Pseudo-random number generator • What IS in this complexity estimation • Major components for adaptive hopping sequence generation • Mapping function • Partition sequence generation • Comparison of hardware/software/mixed implementations. Integrated Programmable Communications, Inc. and Texas Instruments, Inc.

  4. Hardware Implementation Assumption • Unit of gate count: NAND gate. • Use one hardware block for multiple occurrences of the same operation. • Ex: there may be several mod operations, but only one div/mod hardware is needed. • Variable storage/mapping table: 4 gates per bits. • Division/Mod operation • A=B*Q+R, Q=floor(A/B), R = A mod B • It can be implement in hardware by long-division : • Multiple clock implementation, shift-in one bit of operand “A” at each clock. • Require WA clocks to finish one operation, where WA is the width (number of bits) of operand A. • Gate count required is in proportional to WB . Integrated Programmable Communications, Inc. and Texas Instruments, Inc.

  5. Hardware Implementation: Mode L Mapping • Hardware blocks: • Adder • 12-bits • Gate count = 0.1K • Mod • WB=7 • Gate count = 1K • Mapping table • 79*7 bits • Gate count = 2K • Total gate count = 3.1K Integrated Programmable Communications, Inc. and Texas Instruments, Inc.

  6. Hardware Implementation: Mode H Mapping • Hardware blocks: • Adder • 12-bits • Gate count = 0.1K • Mod • WB=7 • Gate count = 1K • Mapping table • 79*7 bits • Gate count = 2K • Misc • 0.2 K • Total gate count = 3.3K Integrated Programmable Communications, Inc. and Texas Instruments, Inc.

  7. Hardware Implementation: Mode H Partition Sequence • Hardware blocks: • Multiplier: 8bit x 8 bit, parallel multiplier • Gate count = 0.5K • Division/Mod • WB=8 • Gate count = 1K • Add/Sub • Gate count = 0.1K • Variable storage and procedure control • Gate count = 1K • Misc • Gate count = 0.2K • Total gate count = 2.8 K Integrated Programmable Communications, Inc. and Texas Instruments, Inc.

  8. Hardware Implementation: Mode H • The complexity of mode H is the sum of mapping and partition sequence • Direct summation of the two gate count numbers: 3.3K + 2.8K = 6.1K • Note that the mod/division block can be further shared • Gate count can be reduced to 5.1K Integrated Programmable Communications, Inc. and Texas Instruments, Inc.

  9. Software Implementation Assumption(1) • Division/Mod operation • A=B*Q+R, Q=floor(A/B), R = A mod B • It can be implement in software by long-division : • Each iteration requires four operations: • One conditional subtraction • Two shift operations • One loop instruction • Number of iterations required is equal to the width ( number of bits) of A, WA. • The total instruction cycles required is roughly 4* WA. Integrated Programmable Communications, Inc. and Texas Instruments, Inc.

  10. Software Implementation Assumption(2) • Multiplication • Many processors have special instruction for multiplication (C=A*B). • If not, it can be implement in software • Each iteration requires 3 operations: • One conditional addition • One shift operation • One loop instruction • Number of iterations required is equal to min{WA ,WB}-1 • The total instruction cycles required is roughly 3*(min{WA ,WB}-1) Integrated Programmable Communications, Inc. and Texas Instruments, Inc.

  11. Software Implementation: Mode L Mapping • Instructions • Mod operation X 1: • Assume 12-bits pseudo-random signal, thus 12-bit mod operation • 48 instruction cycles • Misc instructions • Add/if-then-else/table-lookup/load-store variables • 10 instruction cycles • Totally 58 instruction cycles • Load • 58/625us = 0.0928 MIPS Integrated Programmable Communications, Inc. and Texas Instruments, Inc.

  12. Software Implementation: Mode H Mapping • Instructions • Mod operation X 1: • Assume 12-bits pseudo-random signal, thus 12-bit mod operation • 48 instruction cycles • Misc instructions • Add/if-then-else/table-lookup/load-store variables • 20 instruction cycles • Totally 68 instruction cycles • Load • 68/625us = 0.1088 MIPS Integrated Programmable Communications, Inc. and Texas Instruments, Inc.

  13. Software Implementation: Mode H Partition Sequence-SCO (1) • For the first MAU (master-slave pair) • Distribution unit: Variables initial calculations • Div/Mod operations X 6 • 27bits x 1, 9bits x 1, 8bits x 1, 7bits x 3 • 4*(27+9+8+7*3)= 260 instruction cycles • Multiplications X 2 • 3bits X 2 • 12 instructions cycles • Misc instructions • 20 instruction cycles • Arrangement unit: • if-then-else/table-lookup • 10 instruction cycles • Totally 302 instruction cycles Integrated Programmable Communications, Inc. and Texas Instruments, Inc.

  14. Software Implementation: Mode H Partition Sequence-SCO (2) • For the remaining MAUs within one superframe • Distribution unit: • Variables update • 30 instructions cycles • Arrangement unit: • if-then-else/table-lookup • 10 instruction cycles • Totally 40 instruction cycles • For MAUs after one superframe • The partition sequence is periodic with superframe • The maximum length of superframe is 3*79 MAUs • Require 237 bits (about 30 bytes) to store one period • Table-lookup/index update: 10 instructions Integrated Programmable Communications, Inc. and Texas Instruments, Inc.

  15. Software Implementation: Mode H • The complexity of mode H is the sum of mapping and partition sequence • Note that partition sequence is not calculated every slot, but every MAU (two slots) • For the first MAU: • 0.1088MIPS + 302/(625us*2) = 0.3504 MIPS • For the remaining MAUs within one superframe • 0.1088MIPS + 40/(625us*2) = 0.1408 MIPS • After one superframe • 0.1088MIPS + 10/(625us*2) = 0.1168 MIPS • For comparison, the number for mode L is reproduced here : 0.0928 MIPS Integrated Programmable Communications, Inc. and Texas Instruments, Inc.

  16. Comparison to some Bluetooth mechanisms • Some Bluetooth mechanisms also utilize sort of frame/superframe structure • SCO, sniff mode, park mode • They requires some mod/division operations at initialization. • SCO as an example • CLK27-1 mod Tsco = Dsco (Initialization 1) • 27bits mod operation • requires 108 instruction cycles • The utilization of mod operation and having higher computation burden at initialization are common in Bluetooth. Integrated Programmable Communications, Inc. and Texas Instruments, Inc.

  17. Mixed Hardware/Software Implementations • Implementations is generally somewhere between the two extents of full hardware and full software implementations. • One possibility: • It is easily seen that the major software computation burden comes from the mod/division operation. • One mod/division block takes about 1K gates. • The remaining software computation power would be less than 0.1MIPS. • Mode H: 1K gates in hardware + 0.07 MIPS in software • Mode L: 1K gates in hardware + 0.02 MIPS in software Integrated Programmable Communications, Inc. and Texas Instruments, Inc.

  18. Reference Numbers for Bluetooth Complexity • The hardware implementation of Bluetooth baseband is about 30K ~ 50K gates (not including digital modem function) • The computation power required for LMP, L2CAP, and HCI is about 10 ~ 20 MIPs, while typical processors can easily provide up to 40 MIPs. Integrated Programmable Communications, Inc. and Texas Instruments, Inc.

  19. Conclusions (1) • Complexity comparisons of AFH mechanisms in hardware, software and mixed implementations are presented. • The gate count of full hardware implementation is in the reasonable range. • The computation burden of mode H software implementation is quite low with today’s popular processors. • The low computation burden is mainly because that AFH is operated once per slot, which is a long period. Integrated Programmable Communications, Inc. and Texas Instruments, Inc.

  20. Conclusions (2) • Some mixed hardware/software implementation can have both a smaller gate count and require extremely low computation power. • AFH actually only contributes a very small fraction to the complexity required for the whole system. Thus we should consider for best performance rather than complexity reduction. Integrated Programmable Communications, Inc. and Texas Instruments, Inc.

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