Communications through High Delay Spread x Bandwidth (HDB) Channels: Opportunities and Challenges M. Emami, F. Lee and A. Paulraj Stanford University October.

Communications through High Delay Spread x Bandwidth (HDB) Channels:

Opportunities and Challenges

M. Emami, F. Lee and A. Paulraj

Stanford University

October 18, 2004

AIM Workshop on Time-Reversal Communications in Richly Scattering Environments

Agenda

What is a HDB Channel and the “TR” Effect Experimental Data Characterization of Spatial Focusing Communications in HDB Channels Single User

Capacity Equalization

Multi User Capacity Equalization

Concluding Remarks

Rich Channel - HDSBW

What is a HDB Channel?

Delay

AmplitudeAmplitude

Delay

Amplitude

Delay

High Delay Spread Sparse Channel

Few resolved pathsFew resolved paths

Low Delay Spread

Many resolved paths

High Delay Spread Rich Channel

HDB Metric

The TR effect depends on the number of significant resolvable taps (N) in the channel response

Typically, N > 30 represents a good HDB channel

Time Reversal (TR) Experiment

x(t) = s(t) h*(-t)

s(t)

r(t) = s(t) h*(-t) h(t)

Tx Rxx(t) h(t) r(t)

Step 2

Tx h(t) Rx(t)

h(t)

Step 1

TR Effects

Spatial focusing Temporal focusing Channel hardening

Normalized Magnitude

Num

ber

of O

ccur

renc

es

Original Channel

After TR

Magnitude PDF of One Tap

Agenda

What is a HDB Channel and the “TR” Effect Experimental Data Characterization of Spatial Focusing Communications in HDB Channels Single User

Capacity Equalization

Multi User Capacity Equalization

Concluding Remarks

Experimental Evidence for TR Effects

Indoor (Intel/Stanford) Large office space with cubicles (40 x 60 yards) Bandwidth 2 to 8 GHz (UWB) Channel measured with fixed Tx and Rx in a grid

of .5m x .5m at (approx.) every 3 cm Outdoor (Nokia)

Bandwidth 100 MHz Underwater Acoustics

Indoor Wireless: Spatial Focusing Effect

NLOS Data

Distance in WavelengthP

ower

LOS Data

Distance in Wavelength

Pow

er

Spatial power profile strongly localized at intended receiver location

Indoor Wireless: Temporal Focusing Effect

Tap Index

Nor

mal

ized

Mag

nitu

de

Impulse Response after TR

Temporal power profile at intended receiver strongly localized in time

Side lobes double channel length

Tap Index

Channel Impulse Response

Nor

mal

ized

Mag

nitu

de

Outdoor Wireless: Temporal Focusing Effect

Tap Index

Nor

mal

ized

Mag

nitu

de

Impulse Response after TR

Tap Index

Channel Impulse Response

Nor

mal

ized

Mag

nitu

de

N 17 for this case

Underwater Acoustics

Distance

High N Low N

Tim

e (µ

s)

Agenda

What is a HDB Channel and the “TR” Effect Experimental Data Characterization of Spatial Focusing Communications in HDB Channels Single User

Capacity Equalization

Multi User Capacity Equalization

Concluding Remarks

Characterizing Spatial Focusing

Single Ring (SR) Model h(τ,R) is the channel from Tx to r = R r=0 represents center of circle

r=0Tx

rmd

N i.i.d. uniformly distributed scatterers

rM

1

2

Spatial Focusing Statistics

Space-time (S-T) random field generated by a one shot TR pulse offers multiple characterization

Influencing parameters N - HDB metric λ - wavelength BW - bandwidth Δθ = θ2 -θ1 (receive angle spread)

Define E{(R )} = [max {s(, R)}]2

where s(, R) = h*(-, 0) h(, R)

Spatial Focusing Statistics - Metrics

Long range spatial focusing:

3-dB contour of (R ) around Rx (Ga and Gx are the range and cross-range widths of contour)

)0()(lim ηηp || RR

5.0)(/)(

5.0)(/)(

0u

0u

DxxD

DaaD

G

G

One-Shot Results: Single Tx AntennaD

ista

nce

in W

avel

engt

h

Ga

Gx

N = 1

N = 100

Typical one-shot realizations of (R ) around target point

Distance in Wavelength

One-Shot Results: 5 Tx Antennas

Typical one-shot realizations of (R ) around target point

Distance in Wavelength

N=1 N = 100

Dis

tanc

e in

Wav

elen

gth

Spatial Focalization: E{(R)}

Distance in Wavelength Pulse Bandwidth (MHz)

Peak

Pow

er (

dB)

S-T Focalization: Empirical Relationships for SR Model

5.12.0

6.035.04.0

2sin

228.0

TRMS MBppE

105.0

3.12.01.0

2sin

262.0

TRMSa MBG

43

2

sin

162.0

43

2sin

217.0

105.0

2.01.0

105.0

2.12.01.0

TRMS

TRMS

x

MB

MB

G

Agenda

What is a HDB Channel and the “TR” Effect Experimental Data Communications in HDB Channels Single User

Capacity Equalization

Multi User Capacity Equalization

Concluding Remarks

What is a HDB Communication System?

A communication system that exploits the “TR effect” to improve performance factors.

The transmitter uses a pre-filter derived from the time reversed channel for transmission to the intended receiver.

Demod. /Decode

h()Encode /Mod.

))(( * hf

Tx Rx

Important Questions for HDB Communications

How is capacity affected by HDB channels in single and multi-user scenarios?

What are the key communication problems? Equalization for ISI Channel coding Can spatial focusing be preserved Are there any “LPI” or CCI reduction effects Design tradeoffs

Agenda

What is a HDB Channel and the “TR” Effect Experimental Data Communications in HDB Channels Single User

Capacity Equalization

Multi User Capacity Equalization

Concluding Remarks

Capacity of Single User HDB Channels

Capacity of a communication channel determines maximum rate of transmission per channel use.

HDB channels are frequency selective fading channels. They will suffer a capacity penalty w.r.t. AWGN channels at high SNR.

Optimum approach to maximizing capacity is water-filling (WF). TR is close to but not true WF.

Effect of HDB Channels on Capacity

TRfor )(

)(h

hp

)(tx )(u )(h )(ty

)(tn

)(p

TR rate:

Max. achievable rate:

d

h

HITR 22

4

2 ||||

|)(|1log

2

1

d

HEI

PdEWF 2

2

2)(

|)(|)(1log

2

1max

Tx power spectral density

Water-Filling

In order to obtain IWF , the input energy must satisfy the water-filling solution:

d

HI

HE WF 2

2

22

2 |)(|log

2

1

|)(|)(

2

2

|)(|

H

Capacity: TR vs. WF

Ergrodic capacity of TR is near optimal at low SNR Outage capacity decreases with increase in # of taps

Rate (bits/s/Hz)P

roba

bili

ty

Cumulative Distribution

SNR

Ave

rage

Rat

e (b

its/

s/H

z)

50 taps

Equalization Options for HDB Channels

Tx Equalization Rx Equalization

TR None

None LE / DFE / MLSE

LE None

TR LE

THP THP

LE – Linear Equalizer

DFE – Decision Feedback Equalizer

MLSE – Maximum Likelihood Sequence Estimator – Too complex (exponential)

THP – Tomlinson-Harashima Precoding

Tx Eq. Rx Eq.h()

Equalization

HDB = high Inter Symbol Interference Problem Modulation schemes can be used to “mitigate” ISI

problem. e.g. Spread spectrum, OFDM. We discuss Single carrier schemes where the ISI problem

is severest.

TR at Tx – No Receive Processing

This channel has a severe ISI problem.Power of main tap = Power in ISI taps. TR does not solve the ISI problem.

Mitigation: Rate back-off

)(tx )(u )(h )(ty

)(tn

h

h )(

ISI

Rate back-off (RB)

Rate back-off refers to signaling at symbol rate < 1/BW. This effectively sub-samples the channel, reducing the effective ISI while capturing full diversity

Normal Channel after TR Effective Channel with RB = 2

Peak

ISI

ISI vs. Rate back-off for TR

Assuming the channel taps are i.i.d. Gaussian, the ratio of peak to ISI power is related to rate back-off as follows:

Plot of γTR for No Rate back-off (RB = 1)

Theoretical

Intel Indoor Data

NRBISI

PeakTR as

Rx-Only Equalization: LE and DFE

sk'H(z)sk

nk

C(z)

1–B(z)

sk'F(z)H(z)sk

nk

LE

DFE

Performance Complexity

LE Poor

(Noise enhancement)

Time domain: O(n)

Frequency domain: O(log2n)

DFE Close to MLSE at high SNR

(Error propagation negligible)

Time domain: O(2n)

Frequency domain: O(n) + O(log2n)

Tx-Only Equalization: LE

Minimize mean square error (MSE) subject to power constraint:

is the delay of the equalizer and the channel is for removing the bias We investigate

]|[|min 2

1

kk

ggxyE

H

ks ku)(zG )(zH ky

kn

NoiseISI

PeakSNReff

TR vs. Tx-LE: Effect of Rate back-off

Rate back-off improves effective SNR

SN

Ref

f (d

B)

SNRMFB (dB)

RB=25

RB=5RB=2RB=1

Joint Tx & Rx Equalization: TR & LE

ks ku)( 1 zH )(zH ky

kn

)(zC

TR performs near-optimal WF while LE & rate back-off mitigate ISI

For further complexity reduction, only the largest 10 or 20 taps in impulse response after TR and rate back-off are used to design LE

TR & LE: Performance Results

(Full impulse response after TR contains 499 taps)

LE only uses largest 20 taps of impulse response after TR

LE only uses largest 10 taps of impulse response after TR

RBRBRB

RBRBRB

RB = Rate-back-off Factor

Joint Tx & Rx Equalization: THP

Modulo operator at transmitter limits average & peak power of xk

Better BER performance than DFE, especially at low SNR, since there is no error propagation

Capacity penalty of 0.255 bits/transmission at high SNR compared to DFE (shaping loss)

H(z)

1–B(z)

modsk

xk

nk

mod sk'F(z)

Effect of HDB on LE & THP

Effect of Equalization on Spatial Focusing

Rx-only equalization: No spatial focusing Tx-only equalization

TR: Shown previously (use as reference)

LE: Similar to TR with a small penalty

1

RBN

Np

Spatial Focusing: Simulation Results

100 i.i.d. Gaussian taps (N=100) We have that for both MMSE and TR

20 40 60 80 100

4

6

8

10

12

14

16

18

Rate Back-off

S to I Ratio vs Rate Back-off

TR

20 40 60 80 100

0

2

4

6

8

10

12

14

16

Rate Back-off

S to I Ratio vs Rate Back-off

MMSE

RBIS

TR vs. Tx-LE: Effect of Multiple Antennas

SN

Ref

f (d

B)

SNRMFB (dB)

Effective SNR increases with # of Tx antennas (MT)

Single-User MIMO Systems

The capacity for a frequency selective MIMO channel is given by:

λi is the energy of space-frequency mode i of the channel

)(1 x

)(2 x

)(Mx

)(H

)(1 ty

)(2 ty

)(tyM

+

+

+

)(tn

MN

ii

is

MN

FS M

E

NC

MN

ii

122 1logmax

1

1

Multi-User Systems

Assumption Each user has 1 antenna Base station (BS) has MT antennas

Key questions What is the effect of HDB on capacity regions? What are the appropriate equalization techniques for

HDB channels?

H()

User 1

User K

. . .BS

. . .

Capacity Regions of Multiple Access Channels

R1

R2

R1

R2

R1

R2

Flat

Single Antenna Multiple Antennas

No ISI

ISI

R1

R2

Flat

Broadcasting Channels

Dirty Paper Coding (DPC)

Examples of practical DPC schemes THP Trellis precoding Flexible precoding Lattice coding

w2nR

sn zn

ŵ(yn)ynxn(w,sn)

interference noise

Tx Equalization for Broacast Channels

kx1 1g 1h ky1+

kn1

1

kx2 2g 2h ky2+

kn2

2

+

TTT

kkkkgg

ggg

xyExyEH

][

]}|[|],|[|max{min

21

2222

2111

1

THP for Broadcast Channels

s1'mod

I - B

HF

sK'modn

x

y1

yK

. .

.

modsk

Element-Wise Operation

Feedback Filter (Triangular)

Channel (Flat or ISI)

Feedforward Filter

Joint (vector/matrix) processing at BS Individual (scalar) processing for each user

THP for Broadcast Channels

Equivalent to VBLAST at Rx No error propagation

Sources of capacity loss relative to optimum DPC Shaping loss induced by modulo operation Symbol-by-symbol encoding

Secure communication possible Difficult for one user to decode other users’ data based on

its own received signal

Performance Example: [2]

2-Tap ISI Channel with Equal Power, # of Users = 4

MT = 4

MT = 5

MT = 6

Simulation

Theoretical Approximation

References

[1] R. Schober and W. H. Gerstacker, “On the Distribution of Zeros of Mobile Channels with Application to GSM/EDGE,” IEEE JSAC, July 2001.

[2] L. U. Choi and R. D. Murch, “ A Pre-BLAST-DFE Technique for the Downlink of Frequency-Selective Fading MIMO Channels,” IEEE Trans. Commun., May 2004.

Publications of TR Group

[1] M. Emami, et al., “Predicted Time Reversal Performance in Wireless Communications Using Channel Measurements,” to appear in IEEE Commun. Letters.

[2] J. Hansen, et al., “Design Approach for a Time Reversal Test Bed for Radio Channels,” Special Session on MIMO Prototyping, 12th European Signal Processing Conference, Sept. 2004.

[3] C. Oestges, et al., “Time Reversal Techniques for Broadband Wireless Communications,” European Microwave Week, Oct. 2004. (Invited Paper)

[4] T. Strohmer, et al., “Application of Time Reversal with MMSE Equalizer to UWB Communications,” to appear in GLOBECOM’04.

[5] M. Emami, et al., “Matched Filtering with Rate Back-off for Low Complexity Communications in Very Large Delay Spread Channels,” to appear in Asilomar Conference on Signals, Systems, and Computers, Nov. 2004.