1. 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 pm (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)

2. 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

3. 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

4. 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

5. 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

6. Average Ps Ps Ps t or d Expected value of random variable PsTs 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

7. 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