short course: wireless communications : lecture 2

Short Course:Wireless Communications: Lecture 2

Professor Andrea Goldsmith

UCSDMarch 22-23La Jolla, ca

Course Outline Overview of Wireless Communications Path Loss, Shadowing, and WB/NB

Fading Capacity of Wireless Channels Digital Modulation and its

Performance Adaptive Modulation Diversity MIMO Systems Multicarrier Modulation Spread Spectrum Multiuser Communications &

Wireless Networks Future Wireless Systems

Lecture 1

Lecture 2

Lecture 1 Summary

Future Wireless Networks

Wireless Internet accessNth generation CellularWireless Ad Hoc NetworksSensor Networks Wireless EntertainmentSmart Homes/SpacesAutomated HighwaysAll this and more…

Ubiquitous Communication Among People and Devices

• Hard Delay/Energy Constraints• Hard Rate Requirements

Signal Propagation

Path LossShadowingMultipath

d

Pr/Pt

d=vt

Statistical Multipath Model

Random # of multipath components, each with varying amplitude, phase, doppler, and delay

Narrowband channelSignal amplitude varies randomly

(complex Gaussian).2nd order statistics (Bessel function), Fade

duration, etc. Wideband channel

Characterized by channel scattering function (Bc,Bd)

Capacity of Flat Fading Channels

Three casesFading statistics knownFade value known at receiverFade value known at receiver and

transmitterOptimal Adaptation

Vary rate and power relative to channel

Optimal power adaptation is water-filling

Exceeds AWGN channel capacity at low SNRs

Suboptimal techniques come close to capacity

Modulation Considerations

Want high rates, high spectral efficiency, high power efficiency, robust to channel, cheap.

Linear Modulation (MPAM,MPSK,MQAM)Information encoded in amplitude/phase More spectrally efficient than nonlinearEasier to adapt.Issues: differential encoding, pulse shaping,

bit mapping.

Nonlinear modulation (FSK)Information encoded in frequency More robust to channel and amplifier

nonlinearities

Linear Modulation in AWGN

ML detection induces decision regionsExample: 8PSK

Ps depends on# of nearest neighborsMinimum distance dmin (depends on gs)

Approximate expression sMMs QP g

dmin

Linear Modulation in Fading

In fading gs and therefore Ps random

Metrics: outage, average Ps , combined outage and average.Ps

Ps(target)

Outage

Ps

Ts

Ts

sssss dpPP ggg )()(

Delay spread exceeding a symbol time causes ISI (self interference).

ISI leads to irreducible error floorIncreasing signal power increases ISI

power

Without compensation, requires Ts>>Tm Severe constraint on data rate

(Rs<<Bc)

ISI Effects

0 Tm

1 2 3 4 5

Ts

Main TakeawayNarrowband wireless channel

characterized by random flat-fading (Bu<<Bc)

Wideband wireless channel characterized by random frequency-selective fading (ISI)

Need to combat flat and frequency-selective fading

Focus of this section of short course

Course Outline Overview of Wireless Communications Path Loss, Shadowing, and Fading

Models Capacity of Wireless Channels Digital Modulation and its



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(g)-QAM ModulatorPower: P(g)

To Channel

g(t) g(t)

log2 M(g) Bits One of theM(g) Points

BSPK 4-QAM 16-QAM

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

Optimization Formulation

Adaptive MQAM: Rate for fixed BER

Rate and Power Optimization

Same maximization as for capacity, except for K=-1.5/ln(5BER).

PPK

PP

BERM )(1)(

)5ln(5.11)( ggggg

PPKEME

PP

)(1logmax)]([logmax 2)(2)(

ggggg

Optimal Adaptive Scheme

Power Adaptation

Spectral Efficiency

else0

)( 0

0

11KKK

PP ggg g

gg

g

1

0g

1gK

gk g

RB

p dK K

log ( ) .2

g

gg

g g

Equals 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

Constellation Restriction

Restrict MD(g) to {M0=0,…,MN}. Let M(g)=g/gK

*, where gK* is later

optimized. Set MD(g) to maxj Mj: Mj M(g). Region boundaries are gj=MjgK*, j=0,

…,N Power control maintains target BER

M(g)=g/gK*

gg0 g1=M1gK* g2 g3

0M1

M2

OutageM1

M3

M2

M3

MD(g)

Power Adaptation and Average Rate

Power adaptation: Fixed BER within each region

Es/N0=(Mj-1)/K Channel inversion within a region

Requires power increase when increasing M(g)

Average Rate

1

1

00,)/()1()(

ggggggg jKM

PP jjjj

)(log 11

2

jj

N

jj pM

BR ggg

Efficiency in Rayleigh Fading

Spec

tral

Eff

icie

ncy

(bps

/Hz)

Average SNR (dB)

Constellation Restriction

M(g)=g/gK*

gg0 g1=M1gK* g2 g3

0M1

M2

OutageM1

M3

M2

M3

MD(g)

Power adaptation:

Average rate:

1

1

00,)/()1()(

ggggggg jKM

PP jjjj

)(log 11

2

jj

N

jj pM

BR ggg

Efficiency in Rayleigh Fading

Spec

tral

Eff

icie

ncy

(bps

/Hz)

Average SNR (dB)

Practical Constraints Constellation updates: fade region

duration

Error floor from estimation errorEstimation error 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 r(t,t)=g(t-t)/g(t).Feedback delay causes mismatch of

adaptive power and rate to actual channel

Mjj

jj TT

NN

1

t

regionin fademax at ratecrossinglevel

regionin fademin at ratecrossinglevel

spreaddelay

AFRD

1

j

j

M

j

N

N

T

t

Detailed Formulas Error floor from estimation error

(gg)

Joint distribution p(g,g) depends on estimation: hard to obtain. For PSAM the envelope is bi-variate Rayleigh

Error floor from delay: let =g[i]/g[i-id].p(|g) known for Nakagami fading

ggggg

g

ddpBERP yb

K

ˆ)ˆ,(]5[2. ˆ/

0target

^

^

ggg ddppBERPb )()|(]5[2.0 0

target

Main Points Adaptive modulation leverages fast

fading to improve performance (throughput, BER, etc.)

Adaptive MQAM uses capacity-achieving power and rate adaptation, with power penalty K.Comes within 5-6 dB of capacity

Discretizing the constellation size results in negligible performance loss.

Constellations cannot be updated faster than 10s to 100s of symbol times: OK for most dopplers.

Introduction to Diversity

Basic IdeaSend same bits over independent

fading paths Independent fading paths obtained by

time, space, frequency, or polarization diversity

Combine paths to mitigate fading effects

Tb

tMultiple paths unlikely to fade simultaneously

Combining Techniques

Selection CombiningFading path with highest gain used

Maximal Ratio CombiningAll paths cophased and summed with

optimal weighting to maximize combiner output SNR

Equal Gain CombiningAll paths cophased and summed with

equal weighting

Array/Diversity gainArray 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.

OutageProbability

MRC and its Performance

With MRC, gS=Sgi for branch SNRs giOptimal technique to maximize output

SNRYields 20-40 dB performance gainsDistribution of gS hard to obtain

Standard average BER calculation

SSSS

MMMs

MMsss

dddpppP

dpppPdpPP

gggggggg

ggggggggg

...)()...()()...(...

)(...)()()...()()(

21211

**2*11

Integral hard to obtain in closed form and often diverges

MMx

s dddpppdxePM

gggggg

gg

...)()...()(2

... 2121)...(

2/

1

2

dxeQP xs

2/2

21)(

g

gRecall

MGF Approach Use alternate form of Q function

Define the MGF of gi as

Laplace transform of distributionOften simple closed form expressions

Rearranging order of integration, we get

dgPM

iis

5.

0 12sin

1 M

MMs dddpppdeP M gggggg

gg ...)()...()(... 2121

2/

0

)/(sin)...( 221

is

ii deps i gg g)()(0

M

g depends on modulation (,)

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

Main Points 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

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.

MIMO Systems and their Decomposition

MIMO (multiple-input multiple-output) systems have multiple transmit and receive antennas

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.

Beamforming Scalar codes with transmit precoding

1x

2x

tMxx

1v

tMv

• Transforms system into a SISO system with diversity.• Array and diversity gain• Greatly simplifies encoding and decoding.• Channel indicates the best direction to beamform• Need “sufficient” knowledge for optimality of beamforming

y=uHHvx+uHn

2v 1u

rMu

2u y

Optimality of Beamforming

Mean Information Covariance Information

Diversity vs. Multiplexing

Use antennas for multiplexing or diversity

Diversity/Multiplexing tradeoffs (Zheng/Tse)

Error Prone Low Pe

r)r)(M(M(r)d rt*

rSNRlog

R(SNR)lim SNR

dSNRlog

P log e

)(lim SNRSNR

Best usedependson the

application

How should antennas be used?

Use antennas for multiplexing:

Use antennas for diversity

High-RateQuantizer

ST CodeHigh Rate Decoder

Error Prone

Low Pe

Low-RateQuantizer

ST CodeHigh

DiversityDecoder

Depends on end-to-end metric: Solve by optimizing app. metric

MIMO Receiver Design

Optimal Receiver: Maximum likelihood: finds input symbol most likely

to have resulted in received vector Exponentially complex # of streams and

constellation size Decision-Feedback receiver

Uses triangular decomposition of channel matrix Allows sequential detection of symbol at each

received antenna, subtracting out previously detected symbols

Sphere Decoder: Only considers possibilities within a sphere of

received symbol.

Space-Time Processing: Encode/decode over time & space

Other MIMO Design Issues

Space-time coding: Map symbols to both space and time via

space-time block and convolutional codes.

For OFDM systems, codes are also mapped over frequency tones.

Adaptive techniques: Fast and accurate channel estimationAdapt the use of transmit/receive

antennas Adapting modulation and coding.

Limited feedback: Partial CSI introduces interference in

parallel decomp: can use interference cancellation at RX

TX codebook design for quantized channel

Main Points 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 antennasWith TX/RX channel knowledge, capacity

vs. outage is the capacity metric Beamforming provides diversity gain in

direction of dominent channel eigenvectors

Fundamental tradeoff between capacity increase and diversity gain: optimization depends on application

Main Points

MIMO RX design trades complexity for performanceML detector optimal; exponentially complexDF receivers prone to error propagationSphere decoders allow performance tradeoff

via radiusSpace-time processing (i.e. coding) used in

most systems

Adaptation requires fast/accurate channel estimation

Limited feedback introduces interference between streams: requires codebook design

ISI Countermeasures Equalization

Signal processing at receiver to eliminate ISI, must balance ISI removal with noise enhancement

Can be very complex at high data rates, and performs poorly in fast-changing channels

Not that common in state-of-the-art wireless systems

Multicarrier ModulationBreak data stream into lower-rate

substreams modulated onto narrowband flat-fading subchannels

Spread spectrumSuperimpose a fast (wideband)

spreading sequence on top of data sequence, allows resolution for combining or attenuation of multipath components.

Multicarrier Modulation

Breaks data into N substreams Substream modulated onto separate

carriersSubstream bandwidth is B/N for B total

bandwidthB/N<Bc implies flat fading on each

subcarrier (no ISI)

x

cos(2f0t)

x

cos(2fNt)

SR bps

R/N bps

R/N bps

QAMModulator

QAMModulator

Serial To

ParallelConverter

Overlapping Substreams

Can have completely separate subchannelsRequired passband bandwidth is B.

OFDM overlaps substreamsSubstreams (symbol time TN)

separated in RXMinimum substream separation is

BN/(1+).Total required bandwidth is B/2 (for

TN=1/BN)f0 fN-1

B/N

Fading Across Subcarriers

Leads to different BERSCompensation techniques

Frequency equalization (noise enhancement)

PrecodingCoding across subcarriersAdaptive loading (power and rate)

FFT Implementation of OFDM

Use IFFT at TX to modulate symbols on each subcarrier

Cyclic prefix makes linear convolution of channel circular, so no interference between FFT blocks in RX processing

Reverse structure (with FFT) at receiverx

cos(2fct)

R bps QAMModulator

Serial To

ParallelConverter

IFFT

X0

XN-1

x0

xN-1

Add cyclicprefix and

ParallelTo SerialConvert

D/A

TX

x

cos(2fct)

R bpsQAMModulatorFFT

Y0

YN-1

y0

yN-1

Remove cyclic

prefix andSerial toParallelConvert

A/DLPFParallelTo SerialConvert

RX

OFDM Design IssuesTiming/frequency offset:

Impacts subcarrier orthogonality; self-interference

Peak-to-Average Power Ratio (PAPR)Adding subcarrier signals creates large

signal peaks

Different fading across subcarriersSame mitigation techniques as in MCM:

Precoding to invert fading, coding across subcarriers, and adaptative loading over time most common

MIMO/OFDMApply OFDM across each spatial

dimensionCan adapt across space, time, and

frequency

Main Points ISI can be mitigated through

equalization, multicarrier modulation (MCM) or spread spectrum Today, equalizers often too complex or can’t

track channel.

MCM splits channel into NB flat fading subchannelsFading across subcarriers degrades

performance. Compensate through coding or adaptation

OFDM efficiently implemented using FFTs

OFDM challenges are PAPR, timing and frequency offset, and fading across subcarriers

Introduction to Spread Spectrum

Modulation that increases signal BWMitigates or coherently combines

ISI Mitigates narrowband

interference/jammingHides signal below noise (DSSS) or

makes it hard to track (FH)Also used as a multiple access

techniqueTwo types

Frequency Hopping: Narrowband signal hopped over wide

bandwidthDirection Sequence:

Modulated signal multiplied by faster chip sequence

Direct Sequence Spread Spectrum

Bit sequence modulated by chip sequence

Spreads bandwidth by large factor (K)

Despread by multiplying by sc(t) again (sc(t)=1)

Mitigates ISI and narrowband interference

s(t) sc(t)

Tb=KTc Tc

S(f)Sc(f)

1/Tb 1/Tc

S(f)*Sc(f)

2

ISI and Interference Rejection

Narrowband Interference Rejection (1/K)

Multipath Rejection (Autocorrelation rt

S(f) S(f)I(f)S(f)*Sc(f)

Info. Signal Receiver Input Despread Signal

I(f)*Sc(f)

S(f) S(f)S(f)*Sc(f)[d(t)+(t-t)]

Info. Signal Receiver Input Despread Signal

rS’(f)

Pseudorandom Sequences

Autocorrelation determines ISI rejectionIdeally equals delta function

Maximal Linear CodesNo DC componentLarge period (2n-1)TcLinear autocorrelationRecorrelates every periodShort code for acquisition, longer for

transmissionIn SS receiver, autocorrelation taken

over TbPoor cross correlation (bad for MAC)

1

-12n-1 Tc -Tc

SynchronizationAdjusts delay of sc(t-t) to hit

peak value of autocorrelation.Typically synchronize to LOS

component

Complicated by noise, interference, and MP

Synchronization offset of Dt leads to signal attenuation by r(Dt)

1

-12n-1 Tc -Tc

DtrDt)

RAKE Receiver Multibranch receiver

Branches synchronized to different MP components

These components can be coherently combinedUse SC, MRC, or EGC

x

x

sc(t)

sc(t-iTc)

xsc(t-NTc)

Demod

Demod

Demod

y(t)

DiversityCombiner

dk̂

Main Points In DSSS, bit sequence modulated by

chip sequence

Spreads bandwidth by large factor (K) Despread by multiplying by sc(t) again

(sc(t)=1) Mitigates ISI and narrowband

interferenceISI mitigation a function of code

autocorrelation Must synchronize to incoming signal RAKE receiver used to combine

multiple paths

s(t) sc(t)

Tb=KTc Tc

S(f)Sc(f)

1/Tb 1/Tc

S(f)*Sc(f)

2

short course: wireless communications : lecture 2

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