EE359 – Lecture 14 Outline

Announcements:HW posted tomorrow, due next ThursdayWill send project feedback this week

Practical Issues in Adaptive ModulationUpdate rateEstimation error and delay

Introduction to MIMO Communications

MIMO Channel Decomposition

MIMO Channel Capacity

Review of Last Lecture

Introduction to adaptive modulation Variable-rate variable-power MQAM

Optimal power adaptation is water-fillingOptimal rate adaptation is R/B=log(g/gk)

Adaptive Mod. with Restriction: M(g) MDMap g to straight line M(g)=g/g*

k (optimize g*

k for max rate)Pick region boundaries gi such that M(gi)MDUse inverse waterfilling power control per

region

M(g)=g/gK*

gg0 g1=M1gK*g2 g3

0

M1

M2

OutageM1

M3

M2

M3

MD(g) M(g)=g/gK

Practical Constraints Constellation updates: fade region

duration

Estimation error Estimation error at RX can cause error in

absence of noise (e.g. for MQAM)Estimation error at TX can be caused by

estimator and/or delay in the feedback path

Causes mismatch of adaptive power and rate to actual channel

Can lead to large errors

Mjj

jj TT

NN

1

regionin fademax at ratecrossinglevel

regionin fademin at ratecrossinglevel

spreaddelay

AFRD

1

j

j

M

j

N

N

T

Multiple Input Multiple Output (MIMO)Systems

MIMO systems have multiple (r) transmit and receiver antennas

With perfect channel estimates at TX and RX, decomposes into r independent channelsRH-fold capacity increase over SISO

systemDemodulation complexity reductionCan also use antennas for diversity

(beamforming)Leads to capacity versus diversity

tradeoff in MIMO

MIMO Decomposition

Decompose channel through transmit precoding (x=Vx) and receiver shaping (y=UHy)

Leads to RHmin(Mt,Mr) independent channels with gain si (ith singular value of H) and AWGN

Independent channels lead to simple capacity analysis and modulation/demodulation design

H=USVHy=Hx+n y= S x+n~ ~

yi=six+ni~ ~ ~

~

~ ~

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 CSI at TX and RX, power water-filling over space is optimal:In fading waterfill over space (based on

short-term power constraint) or space-time (long-term constraint)

Without transmitter channel knowledge, capacity metric is based on an outage probabilityPout is the probability that the channel

capacity given the channel realization is below the transmission rate.

Main Points

In practice, constellations cannot be updated faster than 10s-100s of symbol times: OK for most dopplers.

Estimation error/delay causes error floor

MIMO systems exploit multiple antennas at both TX and RX for capacity and/or diversity gain

With TX and RX channel knowledge, channel decomposes into independent channels Linear capacity increase with number of

TX/RX antennasWithout TX CSI, capacity vs. outage is the

capacity metric