1. EE359 – Lecture 11 Outline Announcements Introduction to Diversity
Midterm announcements
OHs today moved to Tuesday 2-3.
Introduction to Diversity
Combining Techniques
Performance of Diversity in Fading
MGF Approach to Performance Analysis
Transmit Diversity

2. Midterm Announcements
Exam is November 7, 11am-1pm in this room.
Open book/notes (bring reader/calculators)
Covers Chapters 1-7
Review Session Thursday (tentative)
Extra Ohs this week.
Midterms from ’01, ’02, ’03 on web
10 bonus points for “taking” a practice exam
Note: These exams don’t necessarily cover Chps. 1-7.
Remote SCPD students: make arrangements today

3. Review of Last Lecture Average Ps in fast fading:
Averaged over fast fading distribution
Good metric when Tc~Ts
Combined outage and average Ps
Used for combined fast and slow fading: average over fast fading, outage relative to slow fading
Irreducible error floor due to Doppler
Differential modulation has noisy phase reference due to phase decorrelation: doesn’t impact high speed systems.
Irreducible error floor due to ISI
Self-interference due to delay spread
Without compensation, severely limits data rates.

4. 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 t
Multiple paths unlikely to fade simultaneously

5. Combining Techniques Selection Combining Maximal Ratio Combining
Fading path with highest gain used
Maximal Ratio Combining
All paths cophased and summed with optimal weighting to maximize combiner output SNR
Equal Gain Combining
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)

6. Diversity 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.
Maximal Ratio Combining (MRC)
Optimal technique (maximizes output SNR)
Combiner SNR is the sum of the branch SNRs.
Distribution of SNR hard to obtain.
Can use MGF approach for simplified analysis.
Exhibits dB gains in Rayleigh fading.

7. MRC and its Performance
With MRC, gS=gi for branch SNRs gi
Optimal technique to maximize output SNR
Yields dB performance gains
Distribution of gS hard to obtain
Standard average BER calculation
Hard to obtain in closed form
Integral often diverges
MGF Approach

8. EGC and Transmit Diversity
EGQ simpler than MRC
Harder to analyze
Transmit diversity
With channel knowledge, similar to receiver diversity, same array/diversity gain
Without channel knowledge, can obtain diversity gain through Alamouti scheme: works over 2 consecutive symbols

9. 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 dB gain, SC around 20 dB.
Performance analysis of MRC greatly simplified using MGF approach

10. Happy Halloween