ECEN4523 Commo Theory Lecture #32 2 November 2015 Dr. George Scheets n Read 8.1 n Problems: 8.1-1, 3, & 8 n Quiz #7, 6 November (Live) [Digital Signaling] u Remote DL students < 13 November n Design Problem, due 6 November (Live) u Remote DL students < 13 November u Late Designs Accepted F Cost = -1 point per Working Daty

ECEN4523 Commo Theory Lecture #33 4 November 2015 Dr. George Scheets n Read 8.2 n Problems: 8.1-9, & 4 n Quiz #7, 6 November (Live) [Chapter 7 Digital Signaling] u Remote DL students < 13 November n Design Problem, due 6 November (Live) u Remote DL students < 13 November u Late Designs Cost = -1 point per Working Day n Exam #2 Results u Hi = 94, Low = 39, Average = 63.08, σ = u A > 88, B > 77, C > 61, D > 49

PSK Signal Constellations n Distance along I axis is cosine Vpeak n Distance along Q axis is sine Vpeak n Distance from origin is magnitude u [Vcosine_peak 2 + Vsine_peak 2 ] 0.5 source: slideplayer.com

16 QAM Signal Constellations n Distance along I axis is cosine Vpeak n Distance along Q axis is sine Vpeak n Distance from origin is magnitude u [Vcosine_peak 2 + Vsine_peak 2 ] 0.5 source: waltertech426.blogspot.com/2013/08/matlab-m-ary-quadrature-signal.html & Wikipedia

Noise at RCVR n Smears the Constellation n Figure C is starting to have problems 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 Power Bipolar Binary Signal Sequence =

SNR = 100 Signal a sequence +1 and -1 volt pulses For your info, SSD BER ≈ 0.0

SNR = 10 Signal a sequence +1 and -1 volt pulses For your info, SSD P(BE) = = 1/1277

SNR = 1 Signal a sequence +1 and -1 volt pulses For your info, SSD P(BE) = = 1/6.3

SNR =.1 Signal a sequence +1 and -1 volt pulses For your info, SSD P(BE) =

Fall Tcom Systems 2002 Final 'Average' based on 1 test chosen at random out of 150 'Average' based on 1 test chosen at random out of 150 Analogous with "Single Sample" Detector Analogous with "Single Sample" Detector 'Average' based on 10 tests chosen randomly out of 150 'Average' based on 10 tests chosen randomly out of 150 Analogous with "Multiple Sample" Detector Analogous with "Multiple Sample" Detector Average based on 10 samples tends to be more accurate than "Average" based on 1 sample Average based on 10 samples tends to be more accurate than "Average" based on 1 sample Actual Midterm Average out of 150 Actual Midterm Average out of 150

Single Sample Detector: SNR = k Threshold is placed midway between nominal Logic 1 and 0 values. Detected sequence = at the receiver, but there were some near misses.

Matched Filter Detector: SNR = k Orange Bars are average voltage over that symbol interval. Averages are less likely to be way off the mark. SSD P(BE) = , P(BE) = (10 samples/bit)

Direct Conversion Receiver source: Sample sinωt cosωt Decision Output Log 2 M bits/symbol αcosωt 0.5αsin(0) 0.5αcos(0)

Direct Conversion Receiver source: Integrate over Ts sinωt cosωt Locate Symbol on Signal Constellation Output Log 2 M bits/symbol αcosωt 0.5αsin(0) 0.5αcos(0) Integrate over Ts

Integrate and Dump n Integrate received symbol u Result = area under received symbol n Sample integrator voltage at end of symbol u Sampled voltage = area under received symbol n Dump the integrator value (reset to zero) n Compare sampled I & Q values to Signal Constellation u Go with whatever symbol is closest n What is the impulse response h(t) of an integrator using Integrate & Dump? u input = δ(t), output = h(t) = ?

Smearing (a.k.a. Inter-symbol Interference) z k z2 k 1270k output input Pulse energy is no longer confined to a T second time interval. Makes receiver symbol detector's life more difficult.

Channel Capacity Bandwidth affects usable symbol rate Bandwidth affects usable symbol rate Rapidly changing symbols need hi frequencies Rapidly changing symbols need hi frequencies Baud rate too high? Distortion!! Baud rate too high? Distortion!! M-Ary allows increased bit rate M-Ary allows increased bit rate Each symbol can represent multiple bits Each symbol can represent multiple bits SNR SNR Affects RCVR ability to tell symbols apart Affects RCVR ability to tell symbols apart Bandwidth & SNR affect usable bit rate Bandwidth & SNR affect usable bit rate

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

bps per Hertz Binary System, Square Pulses, R b = 1 Mbps Binary System, Square Pulses, R b = 1 Mbps FT = sinc, Main Lobe BW = 1 MHz → 1 bps/Hz FT = sinc, Main Lobe BW = 1 MHz → 1 bps/Hz 4-ary System, Square Pulses, R S = 1 Msps 4-ary System, Square Pulses, R S = 1 Msps FT = sinc, Main Lobe BW = 1 MHz 2 bits/symbol → 2*R S /BW =2 bps/Hz FT = sinc, Main Lobe BW = 1 MHz 2 bits/symbol → 2*R S /BW =2 bps/Hz 8-ary System, Square Pulses, R S = 1 Msps 8-ary System, Square Pulses, R S = 1 Msps FT = sinc, Main Lobe BW = 1 MHz 3 bits/symbol → 3*R S /BW =3 bps/Hz FT = sinc, Main Lobe BW = 1 MHz 3 bits/symbol → 3*R S /BW =3 bps/Hz Log 2 (1 + SNR) Log 2 (1 + SNR) 2 Log(1+SNR)/Log(2) = M in M-ary 2 Log(1+SNR)/Log(2) = M in M-ary

Channel Capacity (C) Bandwidth, Bit Rate, SNR, and BER related Bandwidth, Bit Rate, SNR, and BER related Channel Capacity defines relationship C = Maximum reliable bit rate C = W*Log 2 (1 + SNR) bps Channel Capacity defines relationship C = Maximum reliable bit rate C = W*Log 2 (1 + SNR) bps Bandwidth sets the maximum Baud rate If move too many Baud, symbols will smear. SNR sets the maximum number of different symbols (the "M" in M-ary) you can reliably tell apart.

M-Ary signaling MMMM-Ary signaling used when BBBBandwidth is tight SSSSNR's & signal distortion tolerable PPPP(Bit Error) OK DDDDial-Up Phone Modems (3500 Hz Channel Bandwidth) 1111960's: 300 bps using binary signaling 1111980's: 14,400 bps using 128-Ary signaling 1111996: 33,600 bps using 1664-Ary signaling