Wireless Technologies Outline Wireless technology overview Cellular communications

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Wireless Technologies

Wireless Technologies

Outline • • Wireless technology overview Cellular communications Satellite systems Wireless LAN – 802.

Outline • • Wireless technology overview Cellular communications Satellite systems Wireless LAN – 802. 11, Bluetooth, UWB • Mobility support – WAP • Wireless applications

Why Wireless? • Human freedom – Portability v. Mobility • Objective: “anything, anytime, anywhere”

Why Wireless? • Human freedom – Portability v. Mobility • Objective: “anything, anytime, anywhere” • Mobility – Size, weight, power – Functionality – Content • Infrastructure required • Cost – Capital, operational

Worldwide Mobile Subscribers SOURCE: CTIA, i. Gillott. Research, 2001 20 -751 ECOMMERCE TECHNOLOGY FALL

Worldwide Mobile Subscribers SOURCE: CTIA, i. Gillott. Research, 2001 20 -751 ECOMMERCE TECHNOLOGY FALL 2003 COPYRIGHT © 2003 MICHAEL I. SHAMOS

Electromagnetic Spectrum SOUND RADIO VHF = VERY HIGH FREQUENCY UHF = ULTRA HIGH FREQUENCY

Electromagnetic Spectrum SOUND RADIO VHF = VERY HIGH FREQUENCY UHF = ULTRA HIGH FREQUENCY SHF = SUPER HIGH FREQUENCY EHF = EXTRA HIGH FREQUENCY LIGHT HARMFUL RADIATION 3 G CELLULAR 1. 5 -5. 2 GHz 1 G, 2 G CELLULAR 0. 4 -1. 5 GHz 4 G CELLULAR 56 -100 GHz UWB 3. 1 -10. 6 GHz SOURCE: JSC. MIL 20 -751 ECOMMERCE TECHNOLOGY FALL 2003 COPYRIGHT © 2003 MICHAEL I. SHAMOS

MARITIME MOBILE FIXED BROADCAST MOBILE AERO RADIOLOCATION 20 -751 ECOMMERCE TECHNOLOGY FALL 2003 COPYRIGHT

MARITIME MOBILE FIXED BROADCAST MOBILE AERO RADIOLOCATION 20 -751 ECOMMERCE TECHNOLOGY FALL 2003 COPYRIGHT © 2003 MICHAEL I. SHAMOS

Wireless Telephony AIR LINK WIRED PUBLIC SWITCHED TELEPHONE NETWORK SOURCE: IEC. ORG 20 -751

Wireless Telephony AIR LINK WIRED PUBLIC SWITCHED TELEPHONE NETWORK SOURCE: IEC. ORG 20 -751 ECOMMERCE TECHNOLOGY FALL 2003 COPYRIGHT © 2003 MICHAEL I. SHAMOS

Cell Clusters ACTUAL COVERAGE AREA OF CELL 3 CELL 1 OVERLAPS 6 OTHERS DIFFERENT

Cell Clusters ACTUAL COVERAGE AREA OF CELL 3 CELL 1 OVERLAPS 6 OTHERS DIFFERENT FREQUENCIES MUST BE USED IN ADJACENT CELLS SEVEN DIFFERENT SETS OF FREQUENCIES REQUIRED ACTUAL COVERAGE AREA OF CELL 1 SOURCE: IEC. ORG 20 -751 ECOMMERCE TECHNOLOGY FALL 2003 COPYRIGHT © 2003 MICHAEL I. SHAMOS

Space Division Multiple Access (SDMA) MANY CELLS CAN SHARE SAME FREQUENCIES IF SEPARATED IN

Space Division Multiple Access (SDMA) MANY CELLS CAN SHARE SAME FREQUENCIES IF SEPARATED IN SPACE PATTERN CAN BE REPLICATED OVER THE ENTIRE EARTH 200 FREQUENCIES IN ONE CELL TOTAL NUM BER OF FREQUENCIES = 1400 WORLDWIDE 20 -751 ECOMMERCE TECHNOLOGY FALL 2003 COPYRIGHT © 2003 MICHAEL I. SHAMOS

Cell Handover AS PHONE MOVES FROM CELL “A” TO CELL “B”: • CELL “A”

Cell Handover AS PHONE MOVES FROM CELL “A” TO CELL “B”: • CELL “A” MUST HAND THE CALL OVER TO “B” • PHONE MUST CHANGE FREQUENCIES • CELL “A” MUST STOP TRANSMITTING Minimum performance contour A x y B z Handover threshold contour ANIMATION 20 -751 ECOMMERCE TECHNOLOGY FALL 2003 SOURCE: R. C. LEVINE, SMU COPYRIGHT © 2003 MICHAEL I. SHAMOS

Cell Sizes GSM: 100 m - 50 km 250 km/hr MACROCELL: $1 M FAST-MOVING

Cell Sizes GSM: 100 m - 50 km 250 km/hr MACROCELL: $1 M FAST-MOVING SUBSCRIBERS PICOCELLS MICROCELL: $250 K SLOW-MOVING SUBSCRIBERS 20 -751 ECOMMERCE TECHNOLOGY FALL 2003 COPYRIGHT © 2003 MICHAEL I. SHAMOS

Multiple Access • Many users sharing a resource at the “same time” • Needed

Multiple Access • Many users sharing a resource at the “same time” • Needed because user must share cells • FDMA (frequency division) – Use different frequencies • TDMA (time division) – Use same frequency, different times • CDMA (code division) – Use same frequency, same time, different “codes” 20 -751 ECOMMERCE TECHNOLOGY FALL 2003 COPYRIGHT © 2003 MICHAEL I. SHAMOS

Frequency Division Multiplexing (FDMA) Each channel gets a band (range) of frequencies Used in

Frequency Division Multiplexing (FDMA) Each channel gets a band (range) of frequencies Used in traditional radio, TV, 1 G cellular Advantages: • No dynamic coordination Disadvantages: • Inflexible & inefficient if channel load is dynamic and uneven k 1 k 2 k 3 k 4 k 5 k 6 c f EACH CHANNEL OCCUPIES SAME FREQUENCY AT ALL TIMES t SOURCE: NORMAN SADEH 20 -751 ECOMMERCE TECHNOLOGY FALL 2003 COPYRIGHT © 2003 MICHAEL I. SHAMOS

Time Division Multiplexing (TDMA) Each channel gets entire spectrum for a certain (rotating) time

Time Division Multiplexing (TDMA) Each channel gets entire spectrum for a certain (rotating) time period k 1 k 2 c k 3 k 4 k 5 k 6 FREQUENCY BAND f t Advantage: Can assign more time to senders with heavier loads 3 X capacity of FDMA, 1/3 of power consumption Disadvantage: Requires precise synchronization SOURCE: NORMAN SADEH 20 -751 ECOMMERCE TECHNOLOGY FALL 2003 COPYRIGHT © 2003 MICHAEL I. SHAMOS

Combining TDMA and FDMA Each channel gets a certain frequency band for a certain

Combining TDMA and FDMA Each channel gets a certain frequency band for a certain amount of time. Example: GSM Advantages: • More robust against frequencyselective interference • Much greater capacity with time compression • Inherent tapping protection Disadvantages • Frequency changes must be coordinated k 1 k 2 k 3 k 4 k 5 k 6 c f t SOURCE: NORMAN SADEH 20 -751 ECOMMERCE TECHNOLOGY FALL 2003 COPYRIGHT © 2003 MICHAEL I. SHAMOS

Time-Division Multiple Access SOURCE: QUALCOMM 20 -751 ECOMMERCE TECHNOLOGY FALL 2003 COPYRIGHT © 2003

Time-Division Multiple Access SOURCE: QUALCOMM 20 -751 ECOMMERCE TECHNOLOGY FALL 2003 COPYRIGHT © 2003 MICHAEL I. SHAMOS

Code Division Multiplexing (CDMA) • Each channel has unique k 1 k 2 k

Code Division Multiplexing (CDMA) • Each channel has unique k 1 k 2 k 3 “code” • All channels use same spectrum at same time but orthogonal codes • Advantages: – bandwidth efficient – code space is huge – no coordination or synchronization between different channels – resists interference and tapping – 3 X capacity of TDMA, 1/25 power consumption • Disadvantages: – more complex signal regeneration • Implemented using spread spectrum t 20 -751 ECOMMERCE TECHNOLOGY FALL 2003 k 4 k 5 k 6 c f COPYRIGHT © 2003 MICHAEL I. SHAMOS

Cellular Generations • First – Analog, circuit-switched (AMPS) • Second – Digital, circuit-switched (GSM,

Cellular Generations • First – Analog, circuit-switched (AMPS) • Second – Digital, circuit-switched (GSM, Palm) 10 Kbps • Advanced second – Digital, circuit switched, Internet-enabled (WAP) 10 Kbps • 2. 5 – Digital, packet-switched, TDMA (GPRS, EDGE) 40 -400 Kbps • Third – Digital, packet-switched, wideband CDMA (UMTS) 0. 4 – 2 Mbps • Fourth – Data rate 100 Mbps; achieves “telepresence”

CELL TRANSMITTER & RECEIVER GSM Architecture INTERFACE TO LAND TELEPHONE NETWORKS HIERARCHY OF CELLS

CELL TRANSMITTER & RECEIVER GSM Architecture INTERFACE TO LAND TELEPHONE NETWORKS HIERARCHY OF CELLS DATA RATE: 9. 6 Kbps PHONE STOLEN, BROKEN CELLPHONE LIST ENCRYPTION, AUTHENTICATION SIM: IDENTIFIES A SUBSCRIBER LIST OF ROAMING VISITORS LIST OF SUBSCRIBERS IN THIS AREA SOURCE: UWC 20 -751 ECOMMERCE TECHNOLOGY FALL 2003 COPYRIGHT © 2003 MICHAEL I. SHAMOS

SMS – Short Message Service • Integral part of GSM standard – Added to

SMS – Short Message Service • Integral part of GSM standard – Added to other standards as well Technology Message Length GSM 160 bytes Yes TDMA/PDC 160 bytes No CDMA 256 bytes Yes i. DEN 140 bytes Yes • Uses control channel of phone – Send/Receive short text messages – Sender pays (if from mobile phone) • Phone has "email" address 2 way? – SMTP Interface • Only in the US, not the rest of the world • Allows messages to be sent for free! – 3125551234@wireless. att. net • 1 BILLION SMS/day worldwide 20 -751 ECOMMERCE TECHNOLOGY FALL 2003 SOURCE: GEMBROOK SYSTEMS COPYRIGHT © 2003 MICHAEL I. SHAMOS

SMS in Banking Bank Web Site Customer Alert me to all credit card transactions

SMS in Banking Bank Web Site Customer Alert me to all credit card transactions greater than $100. Message from Your. Bank: Credit card purchase of $1245 at Joe’s Hi. Fi. Internet SMS Monitoring Application Bank Back-end Systems Air Message appears within seconds on the customer’s phone 20 -751 ECOMMERCE TECHNOLOGY Wireless Carrier Cell Tower SMS Carrier Credit card used Joe’s Hi. Fi $1245 SOURCE: GEMBROOK SYSTEMS FALL 2003 COPYRIGHT © 2003 MICHAEL I. SHAMOS

Satellite Systems GEO (22, 300 mi. , equatorial) high bandwidth, power, latency M EO

Satellite Systems GEO (22, 300 mi. , equatorial) high bandwidth, power, latency M EO LEO MEO high bandwidth, power, latency LEO (400 mi. ) low power, latency more satellites small footprint V-SAT (Very Small Aperture) private WAN SATELLITE MAP SOURCE: WASHINGTON UNIV.

Geostationary Orbit SOURCE: BILL LUTHER, FCC 20 -751 ECOMMERCE TECHNOLOGY FALL 2003 COPYRIGHT ©

Geostationary Orbit SOURCE: BILL LUTHER, FCC 20 -751 ECOMMERCE TECHNOLOGY FALL 2003 COPYRIGHT © 2003 MICHAEL I. SHAMOS

GPS Satellite Constellation • Global Positioning System • Operated by USAF • 28 satellites

GPS Satellite Constellation • Global Positioning System • Operated by USAF • 28 satellites • 6 orbital planes at a height of 20, 200 km • Positioned so a minimum of 5 satellites are visible at all times • Receiver measures distance to satellite SOURCE: NAVSTAR

GPS Trilateration DISTANCE MEASUREMENTS MUST BE VERY PRECISE LIGHT TRAVELS 1018 FEET EACH MICROSECOND

GPS Trilateration DISTANCE MEASUREMENTS MUST BE VERY PRECISE LIGHT TRAVELS 1018 FEET EACH MICROSECOND SOURCE: PETER DANA 20 -751 ECOMMERCE TECHNOLOGY FALL 2003 COPYRIGHT © 2003 MICHAEL I. SHAMOS

Automatic Vehicle Location (AVL) Benefits of AVL • Fast dispatch • Customer service •

Automatic Vehicle Location (AVL) Benefits of AVL • Fast dispatch • Customer service • Safety, security • Digital messaging • Dynamic route optimization • Driver compliance Sample AVL Users • Chicago 911 • Inkombank, Moscow • Taxi companies Intelligent Highway demo CA SOURCE: TRIMBLE NAVIGATION

Location-Aware Applications • • • Vehicle tracking Firemen in buildings, vital signs, oxygen remaining

Location-Aware Applications • • • Vehicle tracking Firemen in buildings, vital signs, oxygen remaining Asset tracking Baggage Shoppers assistance Robots Corporate visitors Insurance Barges 20 -751 ECOMMERCE TECHNOLOGY FALL 2003 COPYRIGHT © 2003 MICHAEL I. SHAMOS

Wireless LAN • Idea: just a LAN, but without wires • Not as easy

Wireless LAN • Idea: just a LAN, but without wires • Not as easy since signals are of limited range – Unlike wired LAN, if A can hear B and B can hear C, not necessarily true that A can hear C • • Uses unlicensed frequencies, low power 802. 11 from 2 Mb to 54 Mb Bluetooth UWB 20 -751 ECOMMERCE TECHNOLOGY FALL 2003 COPYRIGHT © 2003 MICHAEL I. SHAMOS

Wireless LAN Components Wave. LAN ISA (Industry Standard Architecture) Card Extended Range Antenna Wave.

Wireless LAN Components Wave. LAN ISA (Industry Standard Architecture) Card Extended Range Antenna Wave. POINT II Transmitter Ethernet Converter 11 Mbps Wave. LAN PCMCIA Card SOURCE: LUCENT 20 -751 ECOMMERCE TECHNOLOGY FALL 2003 COPYRIGHT © 2003 MICHAEL I. SHAMOS

Wireless LAN Configurations CLIENT AND ACCESS POINT WIRELESS PEER-TO-PEER BRIDGING WITH DIRECTIONAL ANTENNAS MULTIPLE

Wireless LAN Configurations CLIENT AND ACCESS POINT WIRELESS PEER-TO-PEER BRIDGING WITH DIRECTIONAL ANTENNAS MULTIPLE ACCESS POINTS + ROAMING UP TO 17 KM ! SOURCE: PROXIM. COM 20 -751 ECOMMERCE TECHNOLOGY FALL 2003 COPYRIGHT © 2003 MICHAEL I. SHAMOS

Bluetooth • • • A standard permitting for wireless connection of: Personal computers Printers

Bluetooth • • • A standard permitting for wireless connection of: Personal computers Printers Mobile phones Handsfree headsets LCD projectors Modems Wireless LAN devices Notebooks Desktop PCs PDAs 20 -751 ECOMMERCE TECHNOLOGY FALL 2003 COPYRIGHT © 2003 MICHAEL I. SHAMOS

Bluetooth Characteristics • Operates in the 2. 4 GHz Industrial-Scientific-Medical (ISM) (unlicensed)! band. Packet

Bluetooth Characteristics • Operates in the 2. 4 GHz Industrial-Scientific-Medical (ISM) (unlicensed)! band. Packet switched. 1 milliwatt (as opposed to 500 m. W cellphone. Low cost. • 10 m to 100 m range • Uses Frequency Hop (FH) spread spectrum, which divides the frequency band into a number of hop channels. During connection, devices hop from one channel to another 1600 times per second • Bandwidth 1 -2 megabits/second • Supports up to 8 devices in a piconet (two or more Bluetooth units sharing a channel). • Built-in security. • Non line-of-sight transmission through walls and briefcases. • Easy integration of TCP/IP for networking. 20 -751 ECOMMERCE TECHNOLOGY FALL 2003 COPYRIGHT © 2003 MICHAEL I. SHAMOS

Bluetooth Devices ALCATEL One Touch. TM 700 GPRS, WAP ERICSSON R 520 GSM 900/1800/1900

Bluetooth Devices ALCATEL One Touch. TM 700 GPRS, WAP ERICSSON R 520 GSM 900/1800/1900 NOKIA 9110 + FUJI DIGITAL CAMERA 20 -751 ECOMMERCE TECHNOLOGY ERICSSON BLUETOOTH CELLPHONE HEADSET ERICSSON COMMUNICATOR FALL 2003 COPYRIGHT © 2003 MICHAEL I. SHAMOS

Bluetooth Piconets • Piconet = small area network • “Ad hoc” network: no predefined

Bluetooth Piconets • Piconet = small area network • “Ad hoc” network: no predefined structure • Based on available nodes and their locations • Formed (and changed) in real time 20 -751 ECOMMERCE TECHNOLOGY FALL 2003 COPYRIGHT © 2003 MICHAEL I. SHAMOS

Bluetooth Scatternets Scatternet Piconets Master / Slave Piconet Scatter. Net SOURCE: KRISHNA BHOUTIKA 20

Bluetooth Scatternets Scatternet Piconets Master / Slave Piconet Scatter. Net SOURCE: KRISHNA BHOUTIKA 20 -751 ECOMMERCE TECHNOLOGY FALL 2003 COPYRIGHT © 2003 MICHAEL I. SHAMOS

Time-Modulated Ultra-Wideband (TM-UWB) • Not a sinewave, but millions of pulses per second 500

Time-Modulated Ultra-Wideband (TM-UWB) • Not a sinewave, but millions of pulses per second 500 ps Spread Spectrum 20 -751 ECOMMERCE TECHNOLOGY 0 -40 Time “ 0” “ 1” • Pulse position modulation Frequency (GHz) Power Spectral Density (d. B) • Time coded to make noise-like signal Amplitude Randomized Time Coding -80 Random noise signal 1 2 3 4 5 Frequency (GHz) d d d = 125 ps FALL 2003 SOURCE: TIME DOMAIN COPYRIGHT © 2003 MICHAEL I. SHAMOS

Ultra Wideband Properties • VERY low power: 0. 01 milliwatt – Bluetooth 1 milliwatt

Ultra Wideband Properties • VERY low power: 0. 01 milliwatt – Bluetooth 1 milliwatt (100 x UWB) – Cellphone 500 milliwatts (50, 000 x UWB) • Range: 30 to 300 feet • Very small • Low cost • 100 Mbits/second • Up to 500 Mbps for short distances (USB speed) • No interference Puls. ON, A Chip Based Solution • Secure 20 -751 ECOMMERCE TECHNOLOGY FALL 2003 COPYRIGHT © 2003 MICHAEL I. SHAMOS

Wireless Application Support • WAP (Wireless Application Protocol) and i. Mode • High-level protocols

Wireless Application Support • WAP (Wireless Application Protocol) and i. Mode • High-level protocols that use cellular transport • WAP: – – Uses WML (Wireless Markup Language) Divides content into “cards” equal to one telephone screen Simplified but incompatible form of HTML To send to a WAP phone, must broadcast WML content 20 -751 ECOMMERCE TECHNOLOGY FALL 2003 COPYRIGHT © 2003 MICHAEL I. SHAMOS

WAP Applications Internet Web Content Server Non Mobile Internet User WAP Gateway Mobile Terminal

WAP Applications Internet Web Content Server Non Mobile Internet User WAP Gateway Mobile Terminal i. Nexware Mobile Network WAP simulator 20 -751 ECOMMERCE TECHNOLOGY Database Server SOURCE: DANET FALL 2003 COPYRIGHT © 2003 MICHAEL I. SHAMOS

i. Mode • Telephone, pager, email, browser, location tracking, banking, airline tickets, entertainment tickets,

i. Mode • Telephone, pager, email, browser, location tracking, banking, airline tickets, entertainment tickets, games • NTT Do. Co. Mo (ドコモ means “anywhere”) • Japan is the wireless Internet leader: i. Mode FAQ SOURCE: EUROTECHNOLOGY JAPAN K. K. 20 -751 ECOMMERCE TECHNOLOGY FALL 2003 COPYRIGHT © 2003 MICHAEL I. SHAMOS

i. Mode • Sits on top of packet voice/data transport • As of July

i. Mode • Sits on top of packet voice/data transport • As of July 31, 2003, > 39 million subscribers – 28, 000 new ones per day • • • 26% of Japan >3000 “official” sites >1000 application partners >40, 000 unofficial sites Fee based on amount of data transmitted SOURCES: XML. COM, EUROTECHNOLOGY. COM 20 -751 ECOMMERCE TECHNOLOGY FALL 2003 COPYRIGHT © 2003 MICHAEL I. SHAMOS

i. Mode • Phonetic text input (better for Japanese) • SLOW: 9. 6 Kbps,

i. Mode • Phonetic text input (better for Japanese) • SLOW: 9. 6 Kbps, but 3 G will raise to 384 K • Uses c. HTML (compact HTML) – same rendering model as HTML (whole page at a time) – low memory footprint (no tables or frames) • Standby time: 400 min. , device weight 2. 4 oz. (74 g) SOURCES: XML. COM, NTT 20 -751 ECOMMERCE TECHNOLOGY FALL 2003 COPYRIGHT © 2003 MICHAEL I. SHAMOS

i. Mode Operation INFO PROVIDER HTTP INTERNET IP i. Mode Servers BILLING DB USER

i. Mode Operation INFO PROVIDER HTTP INTERNET IP i. Mode Servers BILLING DB USER DB Do. Co. Mo Packet Network PACKET DATA (PDC-P) IP SOURCE: SAITO & SHIN 20 -751 ECOMMERCE TECHNOLOGY FALL 2003 COPYRIGHT © 2003 MICHAEL I. SHAMOS

Wireless Standards • • • 802. 11 b (2. 4 GHz 300’ radius 11

Wireless Standards • • • 802. 11 b (2. 4 GHz 300’ radius 11 Mbps) 802. 11 a (5 GHz 54 Mbps incompatible with b) 802. 11 g (2. 4 GHz 54 Mbps backward compatible with b) 802. 20 (<3. 5 GHz >1 Mbps @250 kph) Blue. Tooth (2. 4 Ghz 30’ radius) GSM (9. 6 Kbps) GPRS (28. 8 Kbps up to 60 Kbps ) 3 G (UMTS 1. 1 Mbit/s shared typically giving 80 Kbit/s ) 4 G 2010? (10 Mbs? ) UWB potential to deliver 500 Mbps over short distances SOURCE: JOHN DOWNARD 20 -751 ECOMMERCE TECHNOLOGY FALL 2003 COPYRIGHT © 2003 MICHAEL I. SHAMOS

Key Takeaways • • • Mobile growing very rapidly Cell systems need large infrastructure

Key Takeaways • • • Mobile growing very rapidly Cell systems need large infrastructure Wireless LAN does not Content preparation is a problem Wireless business models largely unexplored Bandwidth, bandwidth 20 -751 ECOMMERCE TECHNOLOGY FALL 2003 COPYRIGHT © 2003 MICHAEL I. SHAMOS

Q&A 20 -751 ECOMMERCE TECHNOLOGY FALL 2003 COPYRIGHT © 2003 MICHAEL I. SHAMOS

Q&A 20 -751 ECOMMERCE TECHNOLOGY FALL 2003 COPYRIGHT © 2003 MICHAEL I. SHAMOS

Code Division DATA 1 0 “CODE” 0 1 0 DATA CODE 1 0 1

Code Division DATA 1 0 “CODE” 0 1 0 DATA CODE 1 0 1 1 1 0 0 1 0 0 0 1 1 0 0 +1 ACTUAL SIGNAL -1 SOURCE: JOCHEN SCHILLER

Code Division DATA B 1 0 “CODE” B 0 0 0 1 1 0

Code Division DATA B 1 0 “CODE” B 0 0 0 1 1 0 DATA CODE 1 1 1 0 0 1 1 0 ACTUAL SIGNAL B 1 0 0 0 1 1 1 1 0 0 1 0 1 1 1 +1 -1 SOURCE: JOCHEN SCHILLER

Two CDMA Signals ACTUAL SIGNAL A ACTUAL SIGNAL B +1 -1 +2 ACTUAL SIGNAL

Two CDMA Signals ACTUAL SIGNAL A ACTUAL SIGNAL B +1 -1 +2 ACTUAL SIGNAL A+B -2 SOURCE: JOCHEN SCHILLER

Recovering Data A From A+B ACTUAL SIGNAL A+B “CODE” A +2 -2 +1 -1

Recovering Data A From A+B ACTUAL SIGNAL A+B “CODE” A +2 -2 +1 -1 0 1 0 0 0 1 1 +2 -(A+B) * CODE A -2 INTEGRAL 0 1 1 SOURCE: JOCHEN SCHILLER