Lecture EE359 14 Outline
Midterm Friday, 6-8, Skilling Auditorium
Open book/notes (bring textbook/calculators), Chapters 1-7.
Review of Last Lecture
Introduction to adaptive modulation Variable-rate variable-power MQAM
Optimal power adaptation is water-filling Optimal rate adaptation is R/B=log(/k)
Extra OHs: Me: Th 9:30-10:30am, F 4-5:30 & by appt. Rajiv: 6:30 -7:30pm W (Rm 104),7-8pm Th (Rm 106), 9:3010:30am F (Rm 104) and by appt (+email) Midterms from past 4 MTs posted
Finite Constellation Sets in Adaptive MQAM Update rate Estimation error and delay Introduction to MIMO MIMO channel capacity
Finite Constellation Sets
Use heuristic to assign rates to regions Channel inversion power control in each region
Constellation Restriction
M3 MD() M2 M1 0
Outage M2 M1
Efficiency in Rayleigh Fading
Spectral Efficiency (bps/Hz)
M()=/*
M3
0
1=M1K*
2
3
Power adaptation:
Pj ( ) P ( M 1) /(K ) j < j +1 , j > 0 = j 0 < 1
Average rate:
R N = log 2 M j p( j < j +1 ) B j =1
Average SNR (dB)
Practical Constraints
Constellation updates: fade region duration
j = j
N j+1 + N j > T >>TM
j = AFRD
TM = delay spread N j = level crossing rate at min fade in region N j +1 = level crossing rate at max fade in region
Detailed Formulas
^ Error floor from estimation error ( )
Pb = .2[5BERtarget ] y / p( , ) dd
Joint distribution p(,) depends on estimation: hard to ^ obtain. For PSAM the envelope is bi-variate Rayleigh
0 K
Error floor from estimation error error
Estimation at RX can cause error in absence of noise (e.g. for MQAM) Estimation error at TX causes mismatch of adaptive power and rate to actual channel
Error floor from delay: let =[i]/[i-id].
Pb = .2[5BERtarget ] p( | ) p( ) dd
0 0
Error floor from delay: let (t,)=(t-)/(t).
Feedback delay causes mismatch of adaptive power and rate to actual channel
p(|) known for Nakagami fading
Multiple Input Multiple Output (MIMO)Systems
MIMO systems have multiple (r) transmit and receiver antennas
Capacity of MIMO Systems
Depends on what is known at TX and RX and if channel is static or fading For static channel with perfect channel knowledge at TX and RX, waterfilling over space is optimal power allocation:
Similar idea in fading, based on short-term or longterm power constraint
With perfect channel estimates at TX and RX, decomposes into r independent channels
RH-fold capacity inc...