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EE359 – Lecture 9 Outline Announcements: Project proposals due this Friday at 5pm; create website Midterm date: Thurs Nov. 7, 5:30-7:30 or 6-8pm? Practice MTs posted next week, Discussion section 11/5 will be MT review (or could move to Monday). 10/29 class will take place at usual time (no makeup 10/28) Linear Modulation Review Linear Modulation Performance in AWGN Q-Function representations Probability of error in fading Outage probability Average P s (P b )

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Review of Last Lecture Capacity in Flat-Fading: known at TX/RX l Optimal Rate and Power Adaptation l Channel Inversion and Truncated Inversion Received SNR constant; Capacity is Blog 2 (1+ ) above an outage level associated with truncation Capacity of ISI channels Water-filling of power over freq; or time and freq. 1 00 Waterfilling

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Passband Modulation Tradeoffs Want high rates, high spectral efficiency, high power efficiency, robust to channel, cheap. Amplitude/Phase Modulation (MPSK,MQAM) Information encoded in amplitude/phase More spectrally efficient than frequency modulation Issues: differential encoding, pulse shaping, bit mapping. Frequency Modulation (FSK) Information encoded in frequency Continuous phase (CPFSK) special case of FM Bandwidth determined by Carson’s rule (pulse shaping) More robust to channel and amplifier nonlinearities Our focus

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Amplitude/Phase Modulation Signal over ith symbol period: Pulse shape g(t) typically Nyquist Signal constellation defined by (s i1,s i2 ) pairs Can be differentially encoded M values for (s i1,s i2 ) log 2 M bits per symbol P s depends on Minimum distance d min (depends on s ) # of nearest neighbors M Approximate expression: l Standard/alternate Q function

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Linear Modulation in Fading In fading s and therefore P s random Performance metrics: Outage probability: p(P s >P target )=p( < target ) Average P s, P s : Combined outage and average P s

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Outage Probability Probability that P s is above target Equivalently, probability s below target Used when T c >>T s PsPs P s(target) Outage TsTs t or d

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Main Points Linear modulation more spectrally efficient but less robust than nonlinear modulation P s approximation in AWGN: Alternate Q function useful in fading/diversity analysis In fading P s is a random variable, characterized by average value, outage, or combined outage/average Outage probability based on target SNR in AWGN. Fading significantly degrades performance

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