ECEN5533 Modern Commo Theory Dr. George Scheets Lesson #19 29 October 2013

ECEN5533 Modern Commo TheoryDr. George ScheetsLesson #19 21 October 2014

Read Section 4.9 - 4.10Read Section 4.9 - 4.10 Problems: 4.11, 4.16, 4.18, 4.19 Problems: 4.11, 4.16, 4.18, 4.19 No Class ThursdayNo Class Thursday Corrected Quizzes due 28 OctoberCorrected Quizzes due 28 October Exam #2, 6 NovemberExam #2, 6 November Design 2 due 11 NovemberDesign 2 due 11 November

ECEN5533 Modern Commo TheoryDr. George ScheetsLesson #21 28 October 2014

Read Section 9.1 - 9.5Read Section 9.1 - 9.5 Problems: Chapter 5 #19, 22, 25, 26 Problems: Chapter 5 #19, 22, 25, 26 Corrected Quizzes due 28 OctoberCorrected Quizzes due 28 October Exam #2, 6 NovemberExam #2, 6 November Design 2 due 11 NovemberDesign 2 due 11 November

ECEN5533 Modern Commo TheoryDr. George ScheetsLesson #22 30 October 2014 Read Section 9.6 - 9.7Read Section 9.6 - 9.7 Problems: 5.27 & Fiber Optics (on web)Problems: 5.27 & Fiber Optics (on web) Exam #2, 6 NovemberExam #2, 6 November Design 2 due 11 NovemberDesign 2 due 11 November

ECEN5533 Modern Commo TheoryDr. George ScheetsLesson #23 4 November 2014

Read Section 6.1 – 6.3Read Section 6.1 – 6.3 Problems: Old Exam #2Problems: Old Exam #2 Exam #2, 6 NovemberExam #2, 6 November

Focus on chapters 2 - 5 & 9Focus on chapters 2 - 5 & 9 Maybe a block FEC coder problem similar to Maybe a block FEC coder problem similar to

classworkclasswork Design 2 due 11 NovemberDesign 2 due 11 November

Point Spreads as of Today Quiz #1 (20 points)Quiz #1 (20 points)

Hi = 19.1, Low = 9.7, Ave = 13.45, Hi = 19.1, Low = 9.7, Ave = 13.45, σσ = 3.20 = 3.20 Exam #1 (100 points)Exam #1 (100 points)

Hi = 86, Low = 46, Ave = 65.83, Hi = 86, Low = 46, Ave = 65.83, σσ = 17.23 = 17.23Note: Average should be ≈ 70Note: Average should be ≈ 70 5 of 6 exams returned corrected5 of 6 exams returned corrected

A A >> 85, B 85, B >> 69, C 69, C >> 59, D 59, D >> 49 49 Design #1 (70 points)Design #1 (70 points)

Hi = 66, Low = 59, Ave = 63.33, Hi = 66, Low = 59, Ave = 63.33, σσ = 3.39 = 3.39

Design #2: RoboCop RFP Design a digital RF Public Safety Commo Design a digital RF Public Safety Commo

system for the city of Metropolis.system for the city of Metropolis. Info Sinks can be anywhere in cityInfo Sinks can be anywhere in city Provide system analysis for worst case link.Provide system analysis for worst case link.

(0,0)

(62,47)

Info Source(49, 41)

Design #1: RoboCop RFP Configure Transmitter Site(s)Configure Transmitter Site(s)

Where to locate? Where to locate? Height of tower f(worst case distance)Height of tower f(worst case distance)

All transmit towers All transmit towers should be identicalshould be identical

HeightHeight Electronic ConfigurationElectronic Configuration Type of AntennaType of Antenna

Orientation May DifferOrientation May Differ Power OutPower Out Uplink center frequencyUplink center frequency Type of ModulationType of Modulation

Impacts BWImpacts BW

Info Source

Design #1: RoboCop RFP Path Loss is cubed not squaredPath Loss is cubed not squared

(4πd/λ)3

Antenna GainAntenna Gain Two sectorsTwo sectors

Hi GainHi Gain Low GainLow Gain

Design for WorstDesign for WorstCase G/Ls ratio.Case G/Ls ratio.

GHi

GLo

GHi/Ls1

GLo/Ls2GHi

GLo

Design #1: RoboCop RFP

Configure Standard Receiver SystemConfigure Standard Receiver System 17,700 units17,700 units Specify Matched Filter FSpecify Matched Filter F Data Compression?Data Compression? Forward Error Correction?Forward Error Correction? All choices have $$$ impactAll choices have $$$ impact Many extra credit points available Many extra credit points available

Trading off SNR for Capacity C Channel Capacity Defines the LimitChannel Capacity Defines the Limit

C = W*LogC = W*Log22(1 + SNR) bps(1 + SNR) bps Suppose at/near C limit & no extra BW available and...Suppose at/near C limit & no extra BW available and... Current SNR = 10 Current SNR = 10 (C = W3.459) (C = W3.459) ??

Need to bump SNR up to 120 to double bps Need to bump SNR up to 120 to double bps (C = W6.919) (C = W6.919) Current SNR = 120?Current SNR = 120?

Need to bump SNR up to 14,640 to double bps Need to bump SNR up to 14,640 to double bps (C = W13.84) (C = W13.84) Current SNR = 14,640?Current SNR = 14,640?

Need to bump SNR up to 214.4M to double bps Need to bump SNR up to 214.4M to double bps (C = W27.68) (C = W27.68) To increase C by factor of 8To increase C by factor of 8

Can't increase W?Can't increase W? Increase SNR by factor of 21,435,888Increase SNR by factor of 21,435,888

Trading off W for Capacity C Channel Capacity Defines the LimitChannel Capacity Defines the Limit

C = W*LogC = W*Log22(1 + SNR) bps(1 + SNR) bps C = W*LogC = W*Log22(1 + Psignal/Pnoise) (1 + Psignal/Pnoise) C = W*LogC = W*Log22(1 + Psignal/((1 + Psignal/(NNooW)) W))

Suppose at/near C limit & you're power limited...Suppose at/near C limit & you're power limited... Current SNR = 10; C = W*LogCurrent SNR = 10; C = W*Log22(1 + 10) = W3.459 (1 + 10) = W3.459 Doubling W yields C = 2W*LogDoubling W yields C = 2W*Log22(1 + 5) = W5.170(1 + 5) = W5.170

Doubling W again yields C = 4W*LogDoubling W again yields C = 4W*Log22(1 + 2.5) = W7.229(1 + 2.5) = W7.229 As W → ∞, C → W14.43As W → ∞, C → W14.43

To increase C by factor of 8 requires C = W3.459*8 = W27.68To increase C by factor of 8 requires C = W3.459*8 = W27.68Can't do this only by increasing W!Can't do this only by increasing W!

Trading off W & Signal Power for Capacity C

Channel Capacity Defines the LimitChannel Capacity Defines the Limit C = W*LogC = W*Log22(1 + Psignal/((1 + Psignal/(NNooW)) W))

Suppose at/near C limit & Current SNR = 10Suppose at/near C limit & Current SNR = 10C = W*LogC = W*Log22(1 + 10) = W3.45(1 + 10) = W3.45

Increasing both W & Signal Power can yield more reasonable solutions Increasing both W & Signal Power can yield more reasonable solutions Increasing W by a factor of 8 yields Increasing W by a factor of 8 yields

C = 8W*LogC = 8W*Log22(1 + 1.25) = W9.359(1 + 1.25) = W9.359 Bumping Psignal by 8.008 yieldsBumping Psignal by 8.008 yields

C = 8W*LogC = 8W*Log22(1 + 10.01) = W27.69(1 + 10.01) = W27.69Result: Channel Capacity increases by factor of 8Result: Channel Capacity increases by factor of 8

Operating well below the Channel Capacity limit?

Channel Capacity Defines the LimitChannel Capacity Defines the Limit C = W*LogC = W*Log22(1 + SNR) bps(1 + SNR) bps

Doubling the signal power will generally Doubling the signal power will generally allow the bit rate to be doubled, or nearly so.allow the bit rate to be doubled, or nearly so. Provided Sufficient BW Available Provided Sufficient BW Available

Eb/Eb/NNo = EIRP - R + Other Terms (dB)o = EIRP - R + Other Terms (dB)(Digital Link Equation)(Digital Link Equation)

Eb/No versus C/W bps per Hz Want 30 bps/Hz?Want 30 bps/Hz?

Need Eb/Need Eb/No No >> 75.53 dB 75.53 dB Want 3 bps/Hz?Want 3 bps/Hz?

Need Eb/Need Eb/No No >> 3.68 dB 3.68 dB Want 1 bps/Hz?Want 1 bps/Hz?

Need Eb/Need Eb/No No >> 0 dB 0 dB Note as C/W → 0Note as C/W → 0

Required Eb/Required Eb/No No >> -1.6 dB -1.6 dBa.k.a. a.k.a. Shannon LimitShannon Limit

Entropy Average number of bits/symbol required to Average number of bits/symbol required to

represent a set of symbolsrepresent a set of symbols Based on symbol probability Based on symbol probability

Lower bound regarding the amount of data Lower bound regarding the amount of data compression possiblecompression possible

Equation presented does NOT account for spatial or Equation presented does NOT account for spatial or time redundanciestime redundancies

Can be represented as conditional probabilitesCan be represented as conditional probabilites

BER for Coherent M-PSK As M = 2As M = 2kk ↑, BER ↑ ↑, BER ↑ BW required stays BW required stays

the same.the same. Baud rate sameBaud rate same Symbol shape sameSymbol shape same

Image Source: Bernard Sklar's Digital Communcations

BER for Coherent Orthogonal M-FSK As M = 2As M = 2kk ↑, BER ↓ ↑, BER ↓ BW required ↑BW required ↑

Violating Shannon's Violating Shannon's Limit?Limit?

Image Source: Bernard Sklar's Digital Communcations

Communication SystemSource

Data, Digitized audio or video.Outputs bits.

Channel CoderAdds extra FEC bits.

ChannelAttenuates,

distorts,& adds noise to symbols.

ModulatorConverts bitsto a symbol suitable for

channel.

Symbol DetectorExamines

received symbol& outputs 1

(binary) or more(M-Ary) bits.

Channel DecoderExamines blocks

of bits. If possible, corrects or

detects bit errors.Outputs estimate ofsource bit stream.

Channel Coder FEC codes used in power-limited environmentsFEC codes used in power-limited environments

Cell PhonesCell Phones Deep Space Probes Deep Space Probes Compact DiskCompact Disk

FEC codes work best for random errorsFEC codes work best for random errors Errors frequently occur in burstsErrors frequently occur in bursts Interleaving used to make bursty errors appear randomInterleaving used to make bursty errors appear random

Modulation Copper CableCopper Cable

Electrical pulses frequently used Electrical pulses frequently used Fiber CableFiber Cable

Electrical pulses converted to optical pulsesElectrical pulses converted to optical pulses RF SystemsRF Systems

Sinusoid symbols usedSinusoid symbols used Center frequency impacts antenna sizeCenter frequency impacts antenna size

Binary versus M-Ary (excluding M-FSK) Binary versus M-Ary (excluding M-FSK) M-Ary packs more bits in the bandwidthM-Ary packs more bits in the bandwidth M-Ary more susceptible to decoding errorsM-Ary more susceptible to decoding errors M-Ary used when bandwidth is tight & SNR decentM-Ary used when bandwidth is tight & SNR decent

Symbol Detector Extremes: Extremes:

Single Sample Single Sample Not affected by increase in bit rate if SNR sameNot affected by increase in bit rate if SNR same

Infinite Sample (Matched Filter Detector)Infinite Sample (Matched Filter Detector)P(BE) gets worse as bit time decreasesP(BE) gets worse as bit time decreasesAs T As T 0, P(BE) 0, P(BE)MFDMFD P(BE) P(BE)SSDSSD

INPUT:INPUT:Binary ASK, PSK, FSK, or PulseBinary ASK, PSK, FSK, or PulseM-Ary Pulse (PAM) or 4-PSK (a.k.a. QPSK) or M-Ary Pulse (PAM) or 4-PSK (a.k.a. QPSK) or

QAM (combo of ASK & PSK)QAM (combo of ASK & PSK) OUTPUT:OUTPUT:

Baseband bits (square pulses)Baseband bits (square pulses)

Linear Block Codes Parity Bits add redundancyParity Bits add redundancy

Move Legal Words to Higher DimensionMove Legal Words to Higher Dimension Transmitter can use Transmitter can use GG to generate Code words to generate Code words

from Data wordsfrom Data words Receiver can use Receiver can use HH to generate Syndrome from to generate Syndrome from

received Code wordsreceived Code words Syndrome provides clues as to underlying Syndrome provides clues as to underlying

‘illness’‘illness’

Syndrome

"A complex of symptoms indicating the "A complex of symptoms indicating the existence of an undesirable condition or existence of an undesirable condition or quality." quality." American Heritage DictionaryAmerican Heritage Dictionary

Medical ConditionsMedical Conditions CoughCough FeverFever Knife sticking out of side of the headKnife sticking out of side of the head etc.etc.

Linear Block Codes When plotted in multi-dimensional spaceWhen plotted in multi-dimensional space

Data words are adjacentData words are adjacent Code words are not adjacentCode words are not adjacent

Hamming Distance, Minimum DistanceHamming Distance, Minimum Distance Guaranteed Error Detecting Capability =Guaranteed Error Detecting Capability =

MinDistance - 1MinDistance - 1 May detect other errors, but not guaranteedMay detect other errors, but not guaranteed

Guaranteed Error Correcting Capability Guaranteed Error Correcting Capability = (Error = (Error Detecting Capability)/2Detecting Capability)/2 May correct other errors, but not guaranteedMay correct other errors, but not guaranteed

Linear Block Codes

Minimum Distance RuleMinimum Distance Rule Typically P(Code Bit Error) > Typically P(Code Bit Error) >

P(Data Bit Error)P(Data Bit Error) Linear Block Code PerformanceLinear Block Code Performance

Compare Compare P(uncoded P(uncoded data worddata word is received correctly) is received correctly) versus versus P( P(code wordcode word is correctable) is correctable)

Both of these word probabilities can beBoth of these word probabilities can beconverted to recovered converted to recovered datadata P(Bit Error) P(Bit Error)

No Coding (In Class Example)

Modulator11 Data bits in

Transmitter

Matched Filter

DetectorData bits outP(Data BE) = 9.730*10-6

P(Data Word Error) = 107.0*10-6

Receiver

11 BPSK Data bits out

11 BPSK Data bits in

FEC Coding

FEC CoderAdds extra parity bits.

11 Data bits in 15 Code bits out

Transmitter

FEC DecoderRemoves parity bits.

Detects and/or correctserrors.

15 Code bits inP(Code BE) = 127.6*10-6

11 Data bits outP(Data Word Error) ≈ 1.707*10-6

P(Data BE) ≈ .2278*10-6

(was 9.720*10-6)

From ReceiverMatched Filter

Detector

Equation 6.46

FEC Example

Uncoded (15,11) Code

Bit Rate 4800 bps 6545 bps

P(BE) out of 9.720(10-6) 127.6(10-6) Matched Filter detector

P(11 bit Data 107.0(10-6) ≈ 1.708(10-6) Word Error)

P(data BE) 9.720(10-6) ≈ 0.2278(10-6)(using Eqn 6.46)

Coding Gain

Eb/No

P(BE) Coded

TargetData

P(BE)Required Eb/No

Uncoded

Coding Gain

Eb/No

P(BE) Coded

TargetData

P(BE) Eb/No you can get by with using coder

Uncoded

Coding Gain

Eb/No

P(BE) Coded

TargetData

P(BE) Coding Gain

Uncoded

Link Analysis using FEC:1) Increase Bit Rate R2) Include Coding Gain3) Use Uncoded P(BE) equation.

Coding sometimes makes things worse

Eb/No

P(BE) Coded

Uncoded

System is usually unusable by time Eb/No drops this low.