EE359 – Lecture 9 Outline Linear Modulation Review Announcements: Project proposals due this Friday at 5pm; create website My OHs this week: TTh 11:15-12, 1:20-1:50 outside classroom MT will be Nov. 10 6-8pm (2+ weeks): Open book/notes. Covers through diversity. No HW that week. Next week: propose dates for MT review, post practice MTs. Linear Modulation Review Linear Modulation Performance in AWGN Q-Function representations Probability of error in fading Outage probability Average Ps (Pb)

Review of Last Lecture Capacity in Flat-Fading: g known at TX/RX Optimal Adaptation: Power: 1/g0-1/g, Rate: ~log2(g/g0); Depend on p(g) only through g0 Channel Inversion and Truncated Inversion Received SNR constant; Capacity is Blog2(1+s) above an outage level associated with truncation Capacity of ISI channels Divide wideband channel into narrowband flat-fading subchannels of bandwidth B approximately equal to Bc Correction to board lecture: B  Bc, not B<<Bc Each subchannel has NB fading approx. independent from others Water-filling of power over freq; or time and freq. 1/|H(f)|2 Bc P f

Linear Digital Modulation Signal over ith symbol period: Pulse g(t) typically Nyquist, assumed square Signal constellation defined by (si1,si2) pairs M values for (si1,si2)log2 M bits per symbol We focus on MPSK and MQAM MPSK can be differentially encoded Ps depends on Minimum distance dmin (depends on gs) # of nearest neighbors aM Approximate expression: Standard/alternate Q function

Linear Modulation in Fading In fading gs and therefore Ps random Performance metrics: Outage probability: p(Ps>Ptarget)=p(g<gtarget) Average Ps , Ps: Combined outage and average Ps

Outage Probability Ps t or d Outage Ps(target) Outage Ts t or d Probability that Ps is above target Equivalently, probability gs below target Used when Tc>>Ts

Average Ps Ps Ps t or d Expected value of random variable Ps Ts Ps Ps t or d Expected value of random variable Ps Used when Tc~Ts 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

Main Points Ps approximation in AWGN: Alternate Q function useful in fading/diversity analysis In fading Ps is a random variable, characterized by average value, outage, or combined outage/average Fading greatly increases average Ps or required power for a given target Ps with some outage Outage probability based on target SNR in AWGN. Need to combat flat fading or waste lots of power