EE359 – Lecture 10 Outline
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Announcements:
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Project proposals due Friday midnight (post, email link)
Midterm will be Nov. 10 6-8pm
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No HW due that week.
Exam open book/notes, covers thru Chp. 7.
Midterm review date/timeTBD. Brief in-class summary as well
SCPD students can take exam on campus or remotely
More MT announcements next week (practice MTs)
Average Ps (Pb)
MGF approach for average Ps
Combined average and outage Ps
Effects of delay spread on error probability
Review of Last Lecture
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Focus on linear modulation
Ps approximation in AWGN: Ps   M Q  M g s
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Nearest neighbor error dominates
 d s2s 
 d2 
i j 

Q
 Q 
 N0B 
 N0B 
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Probability of error in fading is random
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Outage probability
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for d si s j  d
Correction to
board lecture
Characterized by outage, average Ps, combination
Ps
Outage

Ts
Ps(target)
Used when Tc>>Ts
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t or d
Probability Ps is above target; Probability gs below target
Fading severely degrades performance
Average Ps
Ts
Ps   Ps (g s ) p(g s )dg s
Ps
Ps
t or d
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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
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Probability in AWGN is Q-function, double infinite integral
Alternate Q Function
Representation
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Traditional Q function representation

1  x2 / 2
Q ( z )  p( x  z )  
e
dx, x ~ N (0,1)
z
2
 Infinite integrand, argument in integral limits
 Average Pe entails infinite integral over Q(z)
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Craig’s representation:
 Very
Q( z) 
1
 /2

0
e
 z 2 /(sin2  )
d
useful in fading and diversity analysis

 g 
Ps   M g  2 dx
0
 sin x 
s
Mgs is MGF of fading distribution
gs, g depends on modulation
Combined outage and average Ps
Ps(gs)
Ps(gs)
Outage
Pstarget
Ps(gs)
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Used in combined shadowing and flat-fading
Ps varies slowly, locally determined by flat fading
Declare outage when Ps above target value
Delay Spread (ISI) Effects
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Delay spread exceeding a symbol time causes ISI
(self interference).
1
2
4
Delay Tm
0
Tm
Ts
3
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ISI leads to irreducible error floor:
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5
Increasing signal power increases ISI power
ISI imposes data rate constraint: Ts>>Tm (Rs<<Bc)
Main Points
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Fading greatly increases average Ps or required
power for a given target Ps with some outage
Alternate Q function approach simplifies Ps
calculation, especially its average value in fading
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Average Ps becomes a Laplace transform.
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In fast/slow fading, outage due to shadowing,
probability of error averaged over fast fading pdf
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Need to combat flat fading or waste lots of power
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Adaptive modulation and diversity are main techniques to
combat flat fading: adapt to fading or remove it
Delay spread causes an irreducible error floor at high
data rates