ECEN5533 Modern Commo Theory Lesson #21. 29 February 2016 Dr ECEN5533 Modern Commo Theory Lesson #21 29 February 2016 Dr. George Scheets Read 4.1 – 4.3 Problems 3.13 & 14; 4.1 & 2 Quiz #2 on 7 March

Modulation & Demodulation -B 0 +B f (Hz) Baseband fc-B fc fc+B XMTR RF 2fc-B 2fc 2fc+B RCVR Demod Multiply by a sinusoid carrier at fc Hz Multiply by a sync'd RCVR Local Oscillater sinusoid at fc Hz

ECEN5533 Modern Commo Theory Lesson #22. 2 March 2016 Dr ECEN5533 Modern Commo Theory Lesson #22 2 March 2016 Dr. George Scheets Read 4.4 – 4.5 Problems 4.4, 6, 8, & 9 Quiz #2 on 7 March

OSU IEEE March General Meeting 5:30-6:30 pm, Wednesday, 9 March ES201b Reps from American Electric Power will present Dinner will be served + 3 points extra credit All are invited

Syncing to Anti-podal BPSK Message m(t) = + & - 1volt peak pulses x(t) = m(t)cos(2πfct) Square x(t) to get x(t)2 = m(t)2cos2(2πfct) Band pass filter to get double frequency term cos(2π2fct) Run thru hard limiter to get 2fc Hz square wave Run thru divide by 2 counter to get fc Hz square wave Filter out harmonics to get fc Hz cosine

PSK Signal Constellations Distance along I axis is cosine Vpeak Distance along Q axis is sine Vpeak Distance from origin is magnitude [Vcosine_peak2 + Vsine_peak2] 0.5 source: slideplayer.com

16 QAM Signal Constellations Distance along I axis is cosine Vpeak Distance along Q axis is sine Vpeak Distance from origin is magnitude [Vcosine_peak2 + Vsine_peak2] 0.5 source: waltertech426.blogspot.com/2013/08/matlab-m-ary-quadrature-signal.html & Wikipedia

Direct Conversion Receiver Quadrature Detection Q Channel 0.5αsin(0) + n1(t) Sample αcosωt Decision sinωt cosωt 0.5αcos(0) + n2(t) Sample I Channel Output Log2M bits/symbol source: http://www.microwavejournal.com/articles/3226-on-the-direct-conversion-receiver-a-tutorial

16 QAM Signal Constellations Transmitted Constellation has dots Received Constellation samples are random Divide into bins Get a histogram, in the limit get PDF source: waltertech426.blogspot.com/2013/08/matlab-m-ary-quadrature-signal.html & Wikipedia

fX(x) = In Phase Noise PDF fY(y) = Quadrature Noise PDF 2nd order Gaussian PDF fXY(x,y) = fX(x)fY(y) fX(x) = In Phase Noise PDF fY(y) = Quadrature Noise PDF source: http://users.isr.ist.utl.pt/~mir/pub/probability.pdf

16 QAM Signal Constellations Transmitted Constellation has dots 16 Decision Regions at RCVR P(Symbol OK | Circled Symbol RCV'd) = P[(-0.7 < X < 0) ∩ (0 < Y < 0.7)] source: waltertech426.blogspot.com/2013/08/matlab-m-ary-quadrature-signal.html & Wikipedia

P(symbol is RCV'd OK | circled symbol transmitted) 2nd order Gaussian PDF P(symbol is RCV'd OK | circled symbol transmitted) = ∫ ∫ fX(x)fY(y)dxdy = ∫fX(x)dx ∫fY(y)dy x integrated from -0.7 to 0 y integrated from 0 to +0.7 source: http://users.isr.ist.utl.pt/~mir/pub/probability.pdf

QAM Signal Generation αsin(ωt) + βcos(ωt) = γcos(ωt + θ) γ = [α2 + β2]0.5 θ = tan-1(-α/β)

16 QAM Signal Constellation 3cos(ωt) + 1sin(ωt) 3.162cos(ωt – 18.43◦) source: waltertech426.blogspot.com/2013/08/matlab-m-ary-quadrature-signal.html & Wikipedia

Direct Conversion Receiver Quadrature Detection -1.581sin(-18.43◦) = 0.4998 Q Channel Sample Decision sinωt cosωt 1.581cos(-18.43◦) = 1.50 Sample 3.162cos(ωt – 18.43◦) I Channel AGC Required! source: http://www.microwavejournal.com/articles/3226-on-the-direct-conversion-receiver-a-tutorial

16 QAM Signal Constellation . 1.5cos(ωt) + 0.5sin(ωt) Above is expected RCVR constellation? Closer to wrong symbol → Symbol Error source: waltertech426.blogspot.com/2013/08/matlab-m-ary-quadrature-signal.html & Wikipedia

ECEN5533 Modern Commo Theory Lesson #23. 4 March 2016 Dr ECEN5533 Modern Commo Theory Lesson #23 4 March 2016 Dr. George Scheets Problems: Old Quiz #2 Chapters 2-5 Quiz #2 on 7 March Reworked Design #1 due 11 March Extra Credit Points are still unclaimed

OSU IEEE March General Meeting 5:30-6:30 pm, Wednesday, 9 March ES201b Reps from American Electric Power will present Dinner will be served + 3 points extra credit All are invited

Matched Filter Detection Finished comparing coherent binary ASK vs. PSK vs. FSK for memoryless Gaussian Noise channel Antipodal PSK has best P(Bit Error) Bandwidth Required? ASK & PSK require same amount: 2R Hz FSK a bit more: 2.75R Hz for best P(BE)