EE359 – Lecture 11 Outline

Announcements
 Class
project links posted (please check). Will
have comments back this week.
 Midterm announcements
 HW5 posted, due Monday 9am (no late HWs)
 No HW next week (practice MTs)
 Introduction
to Diversity
 Combining Techniques
 Selection Combining
 Maximal Ratio Combining
Midterm Announcements

Midterm: Thursday (11/10), 6-8 pm in 200-303


Review sessions



My midterm review will be during lecture (this Th or next Tue)
TA review: Tuesday 4-6 pm in 364 Packard
Midterm logistics:




Food will be served after the exam!
Open book/notes
Bring textbook/calculators (have extras; adv. notice reqd)
Covers Chapters 1-7 (sections covered in lecture and/or HW)
Special OHs next week:


Me: Tue 10:30am-12pm, Wed: 1:30-3pm, Thu: 10:30am-12pm all in 371 Packard
TAs: Mon 4-5 pm (Mainak outside Packard 340), Tue 6-7 (Milind, 364 Packard), Wed 3.30-4.30pm
(Milind, 364 Packard 364), Thu 3-5 pm (Mainak, outside Packard 340)

No HW next week

Midterms from past 3 MTs posted today:


10 bonus points for “taking” a practice exam
Solutions for all exams given when you turn in practice exam
Review of Last Lecture

Average Ps (Pb):
Ps   Ps ( s ) p( s )d s

MGF approach for average Ps
 Average

Ps becomes a Laplace transform
Combined average and outage Ps
Ps(s)
Ps(s)
Pstarget
Ps(s)
Review Continued:
Delay Spread (ISI) Effects

Delay spread exceeding a symbol time causes ISI
(self interference).
1
2
4
Delay Tm
0
Tm
Ts
3

ISI leads to irreducible error floor:


5
Increasing signal power increases ISI power
ISI imposes data rate constraint: Ts>>Tm (Rs<<Bc)
Introduction to Diversity

Basic Idea
 Send

same bits over independent fading paths
Independent fading paths obtained by time, space,
frequency, or polarization diversity
 Combine
paths to mitigate fading effects
Tb
Multiple paths unlikely to fade simultaneously
t
Combining Techniques

Selection Combining


Maximal Ratio Combining


All paths cophased and summed with optimal
weighting to maximize combiner output SNR
Our
focus
Equal Gain Combining


Fading path with highest gain used
All paths cophased and summed with equal weighting
Array/Diversity gain


Array gain is from noise averaging (AWGN and fading)
Diversity gain is change in BER slope (fading)
Selection Combining
Analysis and Performance

Selection Combining (SC)




Combiner SNR is the maximum of the branch SNRs.
CDF easy to obtain, pdf found by differentiating.
Diminishing returns with number of antennas.
Can get up to about 20 dB of gain.
Outage
Probability
MRC and its Performance

With MRC, S=Si for branch SNRs i




Optimal technique to maximize output SNR
Yields 20-40 dB performance gains
Distribution of S hard to obtain
Standard average BER calculation
Pb   Pb ( S ) p( S )d S    ... Pb ( S ) p( 1 ) * p( 2 ) * ... * p( M )d 1d 2 ...d M



Hard to obtain in closed form
Integral often diverges
Preview: MGF Approach:
Pb 
.5 M
 g

M
;


i
i d
2

 0 i 1  sin  
1
Main Points

Diversity overcomes the effects of fading by
combining fading paths

Diversity typically entails some penalty in terms of
rate, bandwidth, complexity, or size.

Techniques trade complexity for performance.


MRC yields 20-40 dB gain, SC around 20 dB.
Analysis of MRC simplified using MGF approach