ECEN4523 Commo TheoryECEN4523 Commo TheoryLecture #32 2 November 2015Lecture #32 2 November 2015Dr. George ScheetsDr. George Scheetswww.okstate.edu/elec-engr/scheets/ecen4533www.okstate.edu/elec-engr/scheets/ecen4533

ECEN4523 Commo TheoryECEN4523 Commo TheoryLecture #32 2 November 2015Lecture #32 2 November 2015Dr. George ScheetsDr. George Scheetswww.okstate.edu/elec-engr/scheets/ecen4533www.okstate.edu/elec-engr/scheets/ecen4533

Read 8.1Read 8.1 Problems: 8.1-1, 3, & 8Problems: 8.1-1, 3, & 8 Quiz #7, 6 November (Live) [Digital Signaling]Quiz #7, 6 November (Live) [Digital Signaling]

Remote DL students Remote DL students << 13 November 13 November Design Problem, due 6 November (Live) Design Problem, due 6 November (Live)

Remote DL students Remote DL students << 13 November 13 November Late Designs AcceptedLate Designs Accepted

Cost = -1 point per Working DatyCost = -1 point per Working Daty

ECEN4523 Commo TheoryECEN4523 Commo TheoryLecture #33 4 November 2015Lecture #33 4 November 2015Dr. George ScheetsDr. George Scheetswww.okstate.edu/elec-engr/scheets/ecen4533www.okstate.edu/elec-engr/scheets/ecen4533

ECEN4523 Commo TheoryECEN4523 Commo TheoryLecture #33 4 November 2015Lecture #33 4 November 2015Dr. George ScheetsDr. George Scheetswww.okstate.edu/elec-engr/scheets/ecen4533www.okstate.edu/elec-engr/scheets/ecen4533

Read 8.2Read 8.2 Problems: 8.1-9, 8.2-1 & 4Problems: 8.1-9, 8.2-1 & 4 Quiz #7, 6 November (Live) [Chapter 7 Digital Signaling]Quiz #7, 6 November (Live) [Chapter 7 Digital Signaling]

Remote DL students Remote DL students << 13 November 13 November Design Problem, due 6 November (Live) Design Problem, due 6 November (Live)

Remote DL students Remote DL students << 13 November 13 November Late Designs Late Designs Cost = -1 point per Working DayCost = -1 point per Working Day

Exam #2 ResultsExam #2 Results Hi = 94, Low = 39, Average = 63.08, Hi = 94, Low = 39, Average = 63.08, σσ = 18.09 = 18.09 A A >> 88, B 88, B >> 77, C 77, C >> 61, D 61, D >> 49 49

PSK Signal ConstellationsPSK Signal Constellations

Distance along I axis is cosine VpeakDistance along I axis is cosine Vpeak Distance along Q axis is sine VpeakDistance along Q axis is sine Vpeak Distance from origin is magnitudeDistance from origin is magnitude

[Vcosine_peak[Vcosine_peak22 + Vsine_peak + Vsine_peak22] ] 0.50.5

source: slideplayer.com

16 QAM Signal Constellations16 QAM Signal Constellations

Distance along I axis is cosine VpeakDistance along I axis is cosine Vpeak Distance along Q axis is sine VpeakDistance along Q axis is sine Vpeak Distance from origin is magnitudeDistance from origin is magnitude

[Vcosine_peak[Vcosine_peak22 + Vsine_peak + Vsine_peak22] ] 0.50.5

source: waltertech426.blogspot.com/2013/08/matlab-m-ary-quadrature-signal.html & Wikipedia

Noise at RCVRNoise at RCVR

Smears the Smears the ConstellationConstellation

Figure C is Figure C is starting to have starting to have problemsproblems

source: Ziber, D., et al, Nonlinear impairment compensation using expectation maximization for dispersion managed and unmanaged PDM 16-QAM transmission, Optics Express, Volume 20, Issue 26

SNR = Average Signal Power = Infinity Average Noise PowerSNR = Average Signal Power = Infinity Average Noise Power

0 20 40 60 80 100

0

4.5

4.5

z2k

xk

990 k

Bipolar Binary SignalSequence = 0011010111

SNR = 100SNR = 100

0 20 40 60 80 100

0

4.5

4.5

z2k

xk

990 k

Signal a sequence +1 and -1 volt pulsesFor your info, SSD BER ≈ 0.0

SNR = 10SNR = 10

0 20 40 60 80 100

0

4.5

4.5

z2k

xk

990 k

Signal a sequence +1 and -1 volt pulsesFor your info, SSD P(BE) = 0.000783 = 1/1277

SNR = 1SNR = 1

0 20 40 60 80 100

0

4.5

4.5

z2k

xk

990 k

Signal a sequence +1 and -1 volt pulsesFor your info, SSD P(BE) = 0.1587 = 1/6.3

SNR = .1SNR = .1

0 20 40 60 80 100

0

8.5

8.5

z2k

xk

990 k

Signal a sequence +1 and -1 volt pulsesFor your info, SSD P(BE) = 0.3759

Fall Tcom Systems 2002 FinalFall Tcom Systems 2002 Final 'Average' based on 1 test chosen at random'Average' based on 1 test chosen at random

126.00 out of 150126.00 out of 150 Analogous with "Single Sample" DetectorAnalogous with "Single Sample" Detector

'Average' based on 10 tests chosen randomly'Average' based on 10 tests chosen randomly109.44 out of 150109.44 out of 150 Analogous with "Multiple Sample" DetectorAnalogous with "Multiple Sample" Detector Average based on 10 samples tends to be more accurate than Average based on 10 samples tends to be more accurate than

"Average" based on 1 sample"Average" based on 1 sample Actual Midterm AverageActual Midterm Average

106.85 out of 150106.85 out of 150

Single Sample Detector: SNR = 1Single Sample Detector: SNR = 1

0 20 40 60 80 100

0

4.5

4.5

990 k

Threshold is placed midway between nominal Logic 1 and 0 values.

Detected sequence = 0011010111 at the receiver,but there were some near misses.

Matched Filter Detector: SNR = 1Matched Filter Detector: SNR = 1

0 20 40 60 80 100

0

4.5

4.5

990 k

Orange Bars are average voltage over that symbol interval.

Averages are less likely to be way off the mark.SSD P(BE) = 0.3759, P(BE) = 0.000783 (10 samples/bit)

Direct Conversion ReceiverDirect Conversion Receiver

source: http://www.microwavejournal.com/articles/3226-on-the-direct-conversion-receiver-a-tutorial

Sample

Sample

sinωtcosωt

Decision

OutputLog2M

bits/symbol

αcosωt

0.5αsin(0)

0.5αcos(0)

Direct Conversion ReceiverDirect Conversion Receiver

source: http://www.microwavejournal.com/articles/3226-on-the-direct-conversion-receiver-a-tutorial

Integrateover Ts

sinωtcosωt

LocateSymbol on

Signal Constellation

OutputLog2M

bits/symbol

αcosωt

0.5αsin(0)

0.5αcos(0) Integrateover Ts

Integrate and DumpIntegrate and Dump Integrate received symbolIntegrate received symbol

Result = area under received symbolResult = area under received symbol Sample integrator voltage at end of symbolSample integrator voltage at end of symbol

Sampled voltage = area under received symbolSampled voltage = area under received symbol Dump the integrator value (reset to zero)Dump the integrator value (reset to zero) Compare sampled I & Q values to Signal ConstellationCompare sampled I & Q values to Signal Constellation

Go with whatever symbol is closestGo with whatever symbol is closest

What is the impulse response h(t) of an integrator using Integrate & What is the impulse response h(t) of an integrator using Integrate & Dump?Dump? input = input = δδ(t), output = h(t) = ?(t), output = h(t) = ?

Smearing (a.k.a. Inter-symbol Interference)Smearing (a.k.a. Inter-symbol Interference)

0 20 40 60 80 100 120 140

0

4.5

4.5

zk

z2k

1270 k

outputinput

Pulse energy is no longer confined to a T second time interval.Makes receiver symbol detector's life more difficult.

Channel CapacityChannel Capacity Bandwidth affects usable symbol rateBandwidth affects usable symbol rate

Rapidly changing symbols need hi frequenciesRapidly changing symbols need hi frequencies Baud rate too high? Distortion!!Baud rate too high? Distortion!!

M-Ary allows increased bit rateM-Ary allows increased bit rate Each symbol can represent multiple bitsEach symbol can represent multiple bits

SNRSNR Affects RCVR ability to tell symbols apartAffects RCVR ability to tell symbols apart

Bandwidth & SNR affect usable bit rateBandwidth & SNR affect usable bit rate

Channel Capacity(a.k.a. Shannon-Hartley Theorem)

Channel Capacity(a.k.a. Shannon-Hartley Theorem)

Claude Shannon Ralph Hartley

bps per Hertzbps per Hertz Binary System, Square Pulses, RBinary System, Square Pulses, Rbb = 1 Mbps = 1 Mbps

FT = sinc, Main Lobe BW = 1 MHz → 1 bps/HzFT = sinc, Main Lobe BW = 1 MHz → 1 bps/Hz

4-ary System, Square Pulses, R4-ary System, Square Pulses, RSS = 1 Msps = 1 Msps FT = sinc, Main Lobe BW = 1 MHz FT = sinc, Main Lobe BW = 1 MHz

2 bits/symbol → 2*R2 bits/symbol → 2*RSS/BW =2 bps/Hz/BW =2 bps/Hz

8-ary System, Square Pulses, R8-ary System, Square Pulses, RSS = 1 Msps = 1 Msps FT = sinc, Main Lobe BW = 1 MHz FT = sinc, Main Lobe BW = 1 MHz

3 bits/symbol → 3*R3 bits/symbol → 3*RSS/BW =3 bps/Hz/BW =3 bps/Hz

LogLog22(1 + SNR)(1 + SNR) 22Log(1+SNR)/Log(2) Log(1+SNR)/Log(2) = M in M-ary= M in M-ary

Channel Capacity (C)Channel Capacity (C) Bandwidth, Bit Rate, SNR, and BER relatedBandwidth, Bit Rate, SNR, and BER related Channel Capacity defines relationshipChannel Capacity defines relationship

C = Maximum reliable bit rate C = Maximum reliable bit rate C = W*Log C = W*Log22(1 + SNR) bps(1 + SNR) bps

Bandwidth sets the maximum Baud rateIf move too many Baud, symbols will smear.

SNR sets the maximum number ofdifferent symbols (the "M" in M-ary)you can reliably tell apart.

M-Ary signalingM-Ary signaling

M-Ary signaling used whenM-Ary signaling used when Bandwidth is tightBandwidth is tight SNR's & signal distortion tolerableSNR's & signal distortion tolerable

P(Bit Error) OKP(Bit Error) OK

Dial-Up Phone Modems Dial-Up Phone Modems (3500 Hz Channel Bandwidth)(3500 Hz Channel Bandwidth) 1960's: 300 bps using binary signaling1960's: 300 bps using binary signaling 1980's: 14,400 bps using 128-Ary signaling1980's: 14,400 bps using 128-Ary signaling 1996: 33,600 bps using 1664-Ary signaling1996: 33,600 bps using 1664-Ary signaling