Wireless Multiple Access Schemes in a Class of Frequency Selective Channels

with Uncertain Channel State Information

Christopher Steger

February 2, 2004

Outline

Introduction and MotivationProblem FormulationAnalysisSimulationsConclusions

Outline

Introduction and MotivationProblem FormulationAnalysisSimulationsConclusions

Introduction: What is 4G?

We know that we desire data rates far exceeding existing systems.

We know that our PHY layer design depends heavily on our choice of multiple access scheme.

We still don’t know what 4G will be.

How do we choose?

We determine that there are four basic candidates: OFDM TDMA MC-CDMA DS-CDMA

We contend that spectral efficiency is an essential metric.

f

t

t

t

OFDM

TDMA

CDMA

How do we measure?

Observe that spectral efficiency is proportional to mutual information.

Mutual information can be determined without fixing a particular bandwidth.

Fewer assumptions are better

*

*

(b/sym) ninformatio mutual),(

(s/sym) period symbol

(b/s/Hz)

efficiency spectral

CT

B

RTYSIT

B

RC

S

S

S

PREAMBLE DATA

How can we add realism?

Two important aspects are missing from previous analyses: Frequency selective

channels Estimation-based

channel state information.

Outline

Introduction and MotivationProblem Formulation

Channel Model System Models

AnalysisSimulationsConclusions

Problem Formulation

This is a first step in several directions.

We need to stay simple. The simplest frequency

selective channels. The simplest versions

of our multiple access schemes

Channel Model

The simplest multipath channel: 2 paths.

The simplest frequency domain channel: 2 subcarriers.

Discrete in time and frequency.

Block fading. f1 f2

h1 h2

DFT

Channel Model

We define channels in both time and frequency to assure fairness.

Fading is complex Rayleigh or Ricean.

We vary correlation in one domain by varying variances in the other.

22

22

,

21

22

22

,

21

21

21

21

21

21

21

tly...independen fade ),( ssubcarrier twoWhen the

tly...independen fade ),(multipath twoWhen the

ff

ffhh

hh

hhff

ff

hh

System Models

Simplest broadcast scenario: 2 users. Avoid giving any system an unfair advantage. All systems form channel estimates from a

preamble signal.

Frame of Length L Symbols

Preamble of Length L (1-)L Data Symbols

Common Assumptions

Gaussian signaling No feedback.

No power control. Fixed resource allocation.

Size and number of subcarriers is constant. Time slot and spreading code allocations are constant.

Nonlinear interference cancellation. “Genie-aided”

LMMSE equalization.

OFDM System

Two subcarrier OFDM is indistinguishable from FDMA.

Each user gets one subcarrier Flat fading. Frequency allocation is

independent of power allocation.

0 B/2 B

User 1 User 2

0 t 2t

OFDM Block Diagram

Estimate Channel

Equalize

User 1 Data

User 2 Data

Channel FFTDetect and

Decode

Output

IFFT

TDMA System

Each user receives half of the frame and the full bandwidth. Users can resolve both

multipath Time allocation is

independent of power allocation.

Nonlinear ISI cancellation. Cancel edge effects as

well.

s0 h1 s0 h2

s1 h1 s1 h2

s2 h1 s2 h2

Interval of Interest

TDMA Block Diagram

Estimate Channel

Equalize

User 1 Data

User 2 Data

ChannelISI

CancellationDetect and

Decode

Output

MC-CDMA System

Complex orthogonal spreading codes. Length 2 Spread over two

subcarriers. Both users use full

bandwidth and full frame. Each subcarrier is flat

fading Code allocation and

spreading length is independent of power allocation.

s1c11f1 s1c12f2

s2c21f1 s2c22f2

Full Bandwidth

Half Bandwidth

User 1

User 2

First Subcarrier

Second Subcarrier

MC-CDMA Block Diagram

Estimate Channel

FFT

Despread

Spread

Spread IFFT

IFFT

ChannelInterference Cancellation

Equalize

Detect and Decode

User 1 Data

User 2 Data

Output

DS-CDMA System

Complex, orthogonal spreading codes. Length 2

Synchronous transmission Users can resolve both

multipath components. Nonlinear interference

cancellation ISI Other user

Code assignment and spreading length are independent of power allocation.

s1c11h s1c12h

s2c21h s2c22h

Symbol Interval

Chip Interval

User 1

User 2

DS-CDMA ChannelInterval of Interest

s10 c11 h1 s10 c12 h1

User 2

Signal

User 1

Signal

s10 c11 h2 s10 c12 h2

s11 c11 h1 s11 c12 h1

s11 c11 h2 s11 c12 h2

s12 c11 h1 s12 c12 h1

s12 c11 h2 s12 c12 h2

s20 c21 h1 s20 c22 h1

s20 c21 h2 s20 c22 h2

s21 c21 h1 s21 c22 h1

s21 c21 h2

s22 c21 h1

s21 c22 h2

s22 c22 h1

s22 c21 h2 s22 c22 h2

DS-CDMA Block Diagram

Estimate Channel

Despread

Detect and Decode

User 1 Data

User 2 Data

Spread

Spread

ChannelInterference Cancellation

Equalize

Output

Outline

Introduction and MotivationProblem FormulationAnalysis

Sketch of Derivation Calculating Achievable Rate Regions Results

SimulationsConclusions

Analysis

We are deriving a lower bound on mutual information using a method developed by Medard in 2000.

It is a lower bound because it assumes that uncertain CSI yields an additional AWGN term.

The bound depends on the variance of our LMMSE equalizer.

HHHH

HHHNHSY

H

~cov

error estimation~

estimate channelchannel actual

~

~

Sketch of Derivation

First, we find the LMMSE equalizer [Anderson and Moore, Optimal Filtering].

Then we find the variance of the equalizer.

We lower bound our mutual information by finding the difference between the entropy of the signal and the entropy of Gaussian noise with variance equal to that of the equalizer.

121

1

log

,0,0

|,

cov

,,

S

S

TT

MAI

NhNh

YShShYSI

YS

YYEYSE

INHSY

Calculating Achievable Regions

To find average mutual information, take expectation over all channel states.

To define the region, find the average mutual information for all divisions of transmit power between the two users.

Results: Equations

IHHYSI

IFFYSI

hhhhYSI

ffYSI

TS

SCHCSCHC

NSCHCSCHCCDMADS

TSCNSCFSCFCDMAMC

nsh

IRIRsTDMA

nsf

IRsFDMA

ISIISIISIISIISIISI1

221111

221111

112211

1

~~

~~

1~~

222~

22

22

21

21

2

222~

21

21

2

log2

1,

log2

1,

14

log,

12

log,

Results: Achievable Rate Regions

Results: Achievable Rate Regions

Results: Achievable Rate Regions

Recall that in order to achieve

correlation in time we have

made one subcarrier much

stronger than the other.

Therefore, one FDMA user is

favored.

Outline

Introduction and MotivationProblem FormulationAnalysisSimulations

Methods Results

Conclusions

Simulations

Try an alternative evaluation method for our multiple access schemes.

Verify our analytical results. Verify that we have calculated lower

bounds. Assess the tightness of the bounds. Verify convergence to analytical results with

perfect CSI.

Methods

Perform actual channel estimation, interference cancellation and equalization.

Determine the SNR of the output.

Use that SNR to determine mutual information.

Average over many (10000) channel states. noise

signal

effectivenoise

effective

effectivesignal

effective

P

PSNR

NP

SSN

SP

S

SSS

2

2

ˆ

ˆ,

Simulation Block Diagram

Estimate Channel

Equalize

Generate Signal 1

Generate Signal 2

ChannelCancel

InterferenceProcess

Calculate SNR

Process

Process

Multiplex

Calculate Mutual Info

Generate Fading

Generate Noise

Simulation Results

Simulation Results

Simulation Results

Recall that in order to achieve

correlation in time we have

made one subcarrier much

stronger than the other.

Therefore, one FDMA user is

favored.

Outline

Introduction and MotivationProblem FormulationAnalysisSimulationsConclusions

Evaluating Schemes Our Tools

Conclusions: Evaluating Schemes

In several cases, we did not achieve a clear differentiation between schemes.

In the cases where we were able to see strong trends: TDMA and MC-CDMA often had nearly identical

performance. When FDMA performs well, DS-CDMA tends to do

badly. It makes a large difference whether fading is defined in

time or frequency. The difference between Ricean and Rayleigh fading is

also a strong indicator of performance. All 4 schemes were best and worst at least

once.

Conclusions: Tools

Our analytical solutions don’t scale well for future work.

The agreement between our analytical and simulation results is mutually validating.

Simulations scale much more easily to more challenging channels.

Lower bound analysis is not always accurate.

Simulations are the best method.