EE359 – Lecture 12 Outline

AnnouncementsMidterm announcementsHW 5 due Friday, 11/4, at noon (no late

HWs)No HW next week (work on projects)

MGF Approach for Performance of MRC

EGCTransmit DiversityAdaptive ModulationAdaptive MQAM

Review of Last Lecture

Introduction to Diversity Combining Techniques Performance of SC Diversity in Fading

Combiner SNR is maximum of branch SNRs.CDF easy to obtain, pdf found by differentiating.Diminishing returns with number of antennas.Can get up to about 10-20 dB of gain.

Performance of MRC Diversity in FadingHard to get pdf of output SNR, except Rayleigh

fadingIn Rayleigh fading, obtain Pout and average Ps.

Midterm Announcements

Exam is November 7, 11am-1pm in this room. Open book/notes (bring book/calculators) Covers Chapters 1-7, HW 1-5.

HW solutions available onlineGraded HW 3 back today, HW 4 maybe back tomorrow

Review Session Thursday 5-6 or 6-7, room TBDRitesh Extra OHs: Sat-Sun 11-1, Bytes caféMy Extra OHs: Th 3-4pm, F 11-12am, M 9:30-10:30am.

Midterms and Solutions from ’02, ’03, ’04 on web10 bonus points for taking practice exam (due by exam)These exams cover Chps. 1-7, similar format as our exam

Remote SCPD students must have arrangements

MRC and its Performance

With MRC, =i for branch SNRs iOptimal technique to maximize output SNRYields 20-40 dB performance gainsDistribution of hard to obtain

Standard average BER calculation

Hard to obtain in closed form Integral often diverges

MGF Approach

MMbbb dddpppPdpPP ...)(...)()()(...)()( 21**2*1

dgPM

iiib

5.

0 12 ;

sin1 M

EGC and Transmit Diversity

EGQ simpler than MRCHarder to analyzePerformance about 1 dB worse than

MRC

Transmit diversityWith 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

Adaptive Modulation Change modulation relative to fading

Parameters to adapt:Constellation sizeTransmit power Instantaneous BERSymbol timeCoding rate/scheme

Optimization criterion:Maximize throughputMinimize average powerMinimize average BER

Only 1-2 degrees of freedom needed for good performance

Variable-Rate Variable-Power MQAM

UncodedData Bits Delay Point

SelectorM()-QAM ModulatorPower: P()

To Channel

(t) (t)

log2 M() Bits One of theM() Points

BSPK 4-QAM 16-QAM

Goal: Optimize P() and M() to maximize R=Elog[M()]

Optimal Adaptive Scheme

Power Adaptation

Spectral Efficiency

else0

)( 0

0

11KKK

PP

1

0

1K

k

RB

p dK K

log ( ) .2

Equals Shannon capacity with effective power loss K=-1.5/ln(5BER).

Spectral Efficiency

K1

K2

K=-1.5/ln(5BER)

Can reduce gap by superimposing a trellis code

Main Points Analysis of MRC simplified using MGF approach

EGC easier to implement than MRC: hard to analyze.Performance about 1 dB worse than MRC

Transmit diversity can obtain diversity gain even without channel information at transmitter.

Adaptive modulation varies modulation parameters relative to fading.

Variable-rate variable-power MQAM comes within 5-6 dB of capacity (power penalty K)Same adaptation that achieves capacity