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EE359 – Lecture 10 Outline Announcements: Project proposals due today at 5pm (post, link) Midterm will be Nov. 4, 6-8pm, Room TBD, no HW due that week. Exam open book/notes, covers thru Chp. 7. Midterm review will be Nov pm, room TBD. Will be a breif in-class summary as well (next week or 11/3) More MT announcements next week (practice MTs) Average P s (P b ) MGF approach for average P s Combined average and outage P s Effects of Doppler on error probability

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Review of Last Lecture Linear modulation more spectrally efficient but less robust than nonlinear modulation P s approximation in AWGN: Probability of error in fading is random Characterized by outage, average Ps, combination Outage probability Probability P s is above target; Probability s below target Fading severely degrades performance PsPs P s(target) Outage TsTs t or d Used when T c >>T s

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Average P s Expected value of random variable P s Used when T c ~T s Error probability much higher than in AWGN alone Rarely obtain average error probability in closed form Probability in AWGN is Q-function, double infinite integral PsPs PsPs TsTs t or d

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Alternate Q Function Representation Traditional Q function representation Infinite integrand, argument in integral limits Average P e entails infinite integral over Q(z) Craig’s representation: Leads to closed form solution for P e in PSK Very useful in fading and diversity analysis M is MGF of fading distribution g depends on modulation

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Combined outage and average P s Used in combined shadowing and flat-fading P s varies slowly, locally determined by flat fading Declare outage when P s above target value Ps(s)Ps(s) P s target Ps(s)Ps(s) Ps(s)Ps(s) Outage

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Doppler Effects High doppler causes channel phase to decorrelate between symbols Leads to an irreducible error floor for differential modulation Increasing power does not reduce error Error floor depends on B d T s

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Main Points Fading greatly increases average P s or required power for a given target P s with some outage Alternate Q function approach simplifies P s calculation, especially its average value in fading Average P s becomes a Laplace transform. In fast/slow fading, outage due to shadowing, probability of error averaged over fast fading pdf Need to combat flat fading or waste lots of power Adaptive modulation and diversity are main techniques to combat flat fading: adapt to fading or remove it Doppler spread only impacts differential modulation causing an irreducible error floor at low data rates

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