802.16.3 July 2000

Space-Time Codes and Signal Processing for Slow Fading Channels

IEEE 802.16 Presentation Submission Template (Rev. 8)D ocument Number :

IEEE 802.16.3p-00/11D ate Submitted:

2000-07-07Source:

Roger Hammons Voice: +1 301 428 2784Hughes Network Systems Fax: +1 301 428 275011717 Exploration Lane mailto: rhammons@hns.comGermantown, MD 20876 USA

V enue: IEEE 802.16.3 Session #8Base Document : The presentation provides an overview of recent advances in space-time codes and signal processing. Sincespace-time techniques have potentially large benefits for MMDS systems, it is recommended that 802.16.3invest igate their applications in the new standard under development.

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802.16.3 July 2000

Space-Time Codes and Signal ProcessingSpace-Time Codes and Signal Processingfor Slow Fading Channelsfor Slow Fading Channels

A. Roger Hammons Jr. and Hesham El Gamal

Hughes Network SystemsGermantown, Maryland USA

802.16.3 July 2000

Space-Time Modems Exploit “Hidden”Capacity of the Multipath Channel

• Space-time codes: Lt > Lr. Seek diversity through code design.• BLAST: Lr = Lt. Seek high throughput through signal processing.• Hybrid schemes: Also possible.

InfoSource

ChannelEncoder

SpatialFormatter ...

Ant 1

Ant 2

Ant Lt( )c u c c cL= =G 1 2; ; ;Κ

u

c1

c2

cL

c

Space-Time Encoder

InfoSink ...

12

Lr

Space-TimeDemod

FadingMultipath

uest Space-TimeDecoder

=

Lc

c

c

Μ2

1

c

Space-Time Codeword

802.16.3 July 2000

Space-Time Technology:Code Design and Signal Processing

AT&T Research has popularized“Space-Time Channel Codes”

(Tarokh, Seshadri, Calderbank)

Lucent has popularized“Layered Space-Time Architecture”

or “BLAST” (Foschini, Gans)• Primary objective: Increased diversity• Method: Channel coding performed

across antennas as well as time

• Primary objective: Increased throughput• Method: Independent spatial channels via

interference avoidance and cancellation

We investigated synergistic approaches that advance the state of the art in both space-time codes and space-time modems.

802.16.3 July 2000

Design Criteria for Space-Time Codes

Pairwise error probability for Rayleigh fading channel:

( )PE

Ns

r

c e→ ≤

−η4 0

where ( ) ( )( )( )

r f f

r

r

= − ←

= ←

rank

rank of baseband difference

geometric mean of eigenvalues

c e

η λ λ λ1 21Λ /

• Rank Criterion : Maximize diversity advantage r over alldistinct code word pairs c and e.

• Product Distance Criterion : Maximize coding advantageη over all distinct code word pairs c and e.

Design Criteria [Fitz (Ohio State Univ.), Tarokh (AT&T)]

802.16.3 July 2000

Space-Time Modulation Format Gives3GPP “Open Loop” Transmit Diversity

N_pilot N_data

Slot 1

N_pilot N_data

S1 S2

-S2* S1 *

QPSK Space-TimeFormatter

No DiversityData Pattern

Ant #1

Ant #2

QPSK Space-TimeFormatter

ChannelEncoder

RateMatching

ChannelInterleaver

DiversityAntenna Pilot

MUX

x

Pilot Symbols

Channelization spreading code

Data

Ant#1

Ant#2

Ant#1

Ant#2

Tx.Ant#1

Tx.Ant#2

x

Simplified Block Diagrams of 3GPP Transmitter with “Space-Time TransmitDiversity” (STTD)

Alamouti space-time

“block code”

802.16.3 July 2000

Handcrafted Trellis Codes AchievingFull Spatial Diversity are Known

Tarokh-Seshadri-Calderbank (TSC) 4-State Trellis Code for QPSK Modulation

00 01 02 03

10 11 12 13

20 21 22 23

30 31 32 33

ttt

ttt

abx

abx

+=

+= −−

2

2)2(

11)1(

Binary Formulation

D

zk

zk−1

Z4 Formulation

Achieves maximum 2-level spatial diversity.

802.16.3 July 2000

Handcrafted Trellis Codes AchievingFull Spatial Diversity are Known

00 01 02 03

20 21 22 23

22 23 20 21

12 13 10 11

10 11 12 13

30 31 32 33

32 33 30 31

02 03 00 01

Tarokh-Seshadri-Calderbank (TSC) 8-State Trellis Code for QPSK Modulation

tttt

tttt

abax

abax

++=

++=

−

−−−

22

22

2)2(

112)1(

Binary Formulation

Z4 Formulation

Achieves maximum 2-level spatial diversity.

2

zk−2Dzk D

zk−12

9802.16.3 July 2000

Binary Criteria Identify Full-DiversitySpace-Time Codes

• BPSK Binary Rank Criterion: Let C be a linear space-timecode with . Suppose that every non-zero binary code word ismatrix of full rank over the binary field F. Then, for BPSK transmission,the space-time code C satisfies the space-time rank criterion and achievesfull spatial diversity L.

• QPSK Binary Rank Criterion: Let C be a linear space-timecode over with . Suppose that, for every non-zero binary codeword , the row-based indicant or the column-based indicanthas full rank L over F. Then, for QPSK transmission, the space-time codeC satisfies the space-time rank criterion and achieves full spatial diversity L.

• Extensions to Higher-Order Modulation: Use multi-levelconstruction and apply binary rank criteria to the design of the constituentcodes at each level.

nL×Ln ≥ C∈c

4ZnL×

Ln ≥C∈c )(cΞ )(cΨ

802.16.3 July 2000

Concatenations of space-time codessatisfying binary rank criterion formfull-diversity space-time codes .

“Stacking” Constructions Yield NewFull-Diversity Space-Time Codes

Μ

1c

2c

Lc

C∈=ΜΜΜΜΟ Μ

Λ

ΛΛ

)( 1cT

)( 2cT

)( LcT

)(CT∈Μ

=ΜΜΜΜΟ Μ

Λ

ΛΛ

⇓Linear

transformationof full-rank

Full-Diversity Space-Time Code

Full-Diversity Space-Time Code

Transformation TheoremStacking Construction

C∈=ΜΜΜΜΟ Μ

Λ

ΛΛ

=)(xc

)(1 xT

)(2 xT

)(xTL

Μ

C satisfies BPSK binary rank criterioniff is non-singular unless .

LLTaTaTaT +++= Λ2211

021 ==== Laaa Λ

Multi-Stacking Construction

C∈ΛΛ

C

802.16.3 July 2000

Convolutional Codes with Optimal dfree

Yield Full-Diversity Space-Time CodesConnection PolynomialsL ν freed

2 2 5, 7 53 64, 74 64 46, 72 75 65, 57 86 554, 744 107 712, 476 108 561, 753 12

3 3 54, 64, 74 104 52, 66, 76 125 47, 53, 75 136 554, 624, 764 157 452, 662, 756 168 557, 663, 711 18

4 4 52, 56, 66, 76 165 53, 67, 71, 75 187 472, 572, 626, 736 228 463, 535, 733, 745 24

5 5 75, 71, 73, 65, 57 227 536, 466, 646, 562, 736 28

“Natural” space-time code associatedwith rate 1/L convolutional code:Multiplex L output coded bits in space(among antennas) rather than time.

Practical examples of our generalspace-time “Stacking Constructions.”

g0(D)

Tx.Ant#1

g1 (D)

gL-1 (D)

)(tx

)(0 ty

)(1 ty

)(1 tyL−

Tx.Ant#2

Tx.Ant#L

Convolutional Encoder

ΜΜΜ

802.16.3 July 2000

Performance of BPSK Space-TimeCodes with 4 Transmit Antennas

4 Transmit Antennas

0.01

0.1

1

0 2 4 6 8 10

SNR (dB)

FE

R

• Optimal dfree code is 3 dB better than the delay diversity scheme.• Optimal dfree code is 1 dB better than Fitz-Grimm zeroes symmetry code.

Optimal dfree (K=6)

Zeroes symmetry (K=6)

Delay diversity

802.16.3 July 2000

Performance of BPSK Space-TimeCodes with 5 Transmit Antennas

SNR (dB)

5 Transmit Antennas

0.01

0.1

1

0 2 4 6 8 10

FE

R

Optimal dfree (K=6)

Zeroes symmetry (K=6)

Delay diversity

• Optimal dfree code is 3 dB better than the delay diversity scheme.• Optimal dfree code is 2 dB better than Fitz-Grimm zeroes symmetry code.

802.16.3 July 2000

Performance of QPSK Space-TimeCodes in Quasi-Static Fading Channels

QPSK, 2 Tx., 2 Rx.

0.01

0.1

1

6 7 8 9 10 11

SNR (dB)

FE

R

New Code (16 state)

Tarokh's Code (16 state)

802.16.3 July 2000

Performance of 8-PSK Space-TimeCodes in Quasi-Static Fading Channels

8-PSK, 2 Tx., 2 Rx.

0.01

0.1

1

9 10 11 12 13 14

SNR (dB)

FE

R

New Code ( 8 state)

Tarokh's Code ( 8 state)

802.16.3 July 2000

Stacking Construction YieldsNew Codes for Space-Time Appliques

1.E-05

1.E-04

1.E-03

1.E-02

10 15 20 25 30 35

SNR dB

Dec

od

ed B

it E

rro

r R

ate

L=2, Alamouti, QPSKOrthogonal Design

L=3, Tarokh, 16-QAMOrthogonal Design

L=3, Hammons-El Gamal,QPSK 3x3 Stacking Construction

2 bps/Hz

802.16.3 July 2000

Foschini Showed that Outage CapacityIncreases Linearly When Lr Equals Lt

16 QAM 3 MHz5 xmt/5 rcv

antennas

30 Mbps = 3 . 5 . 4 . 1/2

Bit Rate = Bandwidth . Number of antennas . Bit rate/antenna . Coding rate

802.16.3 July 2000

Layered Space-Time Architectures

Definition: A layer is anassignment of space-timetransmission resources to acomponent channelencoder in which at mostone antenna is availableeach transmitted symbolinterval.

Properties:• No spatial interference

within a layer.• Decoding is performed

layer by layer.• Conventional channel

codes can be used.

One code word per diagonal layer

Spac

e-T

ime

Tra

nsm

itter

Diagonal Layering

Spac

e-T

ime

Tra

nsm

itter

One code word per horizontal layerHorizontal Layering

802.16.3 July 2000

Lucent’s BLAST TechnologySp

ace-

Tim

eT

rans

mitt

er

1. Subtract interferencefrom previously decoded layers

2. Project away from interferencefrom undecoded layers

Two steps to decode a given layer :

Potential Limitations of BLAST Signal Processing• Requires equal number of transmit and receive antennas• Spatial diversity varies within a code word• Errors can propagate both spatially and temporally• Limited ability to interleave for temporal diversity• Loss in throughput due to diagonal layering

One code wordper diagonal layer

802.16.3 July 2000

Hughes Offers ThreadedSpace-Time Architecture

Characteristics of Threaded Space-Time Architecture• Generalized layering exploits spatial and temporal diversity • Threaded space-time channel codes ensure full-diversity• Receiver uses new, efficient, multi-user detection techniques

– Soft-decision feedback reduces spatial error propagation.– Iterative MMSE processing results in a symmetrical performance.

Spac

e-T

ime

Tra

nsm

itter

One code word per “thread”Threaded Layering

Thread = Layer whose temporal span is maximal for each antenna

802.16.3 July 2000

Iterative MMSE Space-Time Receiver

receivedsignal

MatchedFilter Bank

SISOMMSEMulti-User

Detector

ChannelEstimation

Deinter-leaver 1

SISODecoder 1

Interleaver 1

Μ Μ

Deinter-leaver n

SISODecoder n

Interleaver n

Μ Μ

ΜΛ

Λ

• Iterative multi-user detection (MUD) is one key to threaded space-time architecture.• Threaded channel codes, based on space-time principles, are optimized for MUD.

802.16.3 July 2000

Threaded Space-Time Code Designfor Quasi-static Fading Channels

Theorem (Threaded Stacking Construction):Let L be a layer of spatial span n. Given binary matrices of dimension ,let C be the binary code of dimension k consisting of all code words ,where denotes an arbitrary k-tuple of information bits. Let fL denote the spatial modulatorhaving the property that the modulated symbols are transmitted in the symbol intervalsof L that are assigned to antenna j.

Then, as the space-time code in a communication system with n transmit antennas and m receiveantennas, the space-time code C consisting of C and fL achieves spatial diversity dm in a quasi-static fading channel if and only if d is the largest integer such that have theproperty that

nMMM ,,, 21 Κ λ×k( ) nxxxxg MMM ||| 21 Λ=

x( )jxMµ

nMMM ,,, 21 Κ

[ ] .over rank of is

:1,,,,

2211

2121

FMMMM

F

kaaa

dnaaaaaa

nn

nn

ΛΛΚ

=+−=+++∈∀

802.16.3 July 2000

Threaded-STC Yields Bigger Bang thanthe BLAST Technology

At 1% FER, advantage is more than 3 dB.

BPSK, 2bits/sec/HZ, 4 Tx., 4 Rx.

0.001

0.01

0.1

1

0 2 4 6 8

SNR (dB)

FE

R

Threaded S-T Modem

Blast Modem

802.16.3 July 2000

Threaded Space-Time OutperformsAT&T’s Group Suppression Approach

At 1% FER, advantage is more than 4 dB.

QPSK, 4bits/sec/hz, 4Tx., 4Rx.

0.001

0.01

0.1

1

0 2 4 6 8 10 12 14

SNR (dB)

FE

R

HNS S-T Modem

AT&T S-T Modem

802.16.3 July 2000

Conclusions

• MMDS must contend with slow fadingchannels

• Space-time technology offers potentiallylarge gains in this environment

• 802.16.3 should be aggressive in study andadoption of best space-time solutions

802.16.3 July 2000

References

Journal Papers• Hammons and El Gamal, “On the theory of space-time codes for PSK constellations,” IEEE

Transactions on Information Theory, March 2000.• El Gamal and Hammons, “A new approach to layered space-time signal processing and code

design,” accepted for publication (pending revision) in IEEE Transactions on Information Theory.Conference Papers• Hammons and El Gamal, “Space-Time Codes: New Design Criteria and General Constructions

(Invited Paper),'' Sixth Annual Workshop on Smart Antennas in Wireless Mobile Communications,Stanford University, 1999.

• El Gamal and Hammons, “On the Design of Space-Time Codes,'' In Proceedings of the IEEE 1999Information Theory Workshop, Metsovo, Greece.

• El Gamal and Hammons, “Binary Design Criteria for Space-Time Codes,'' In Proceedings of Thirty-Seventh Annual Allerton Conference on Communication, Control, and Computing, University ofIllinois, Urbana-Champaign, 1999.

• El Gamal and Hammons, “A New Space-Time Architecture and Signal Processing,''In Proceedingsof Thirty-Seventh Annual Allerton Conference on Communication, Control, and Computing,University of Illinois, Urbana-Champaign, 1999.

• El Gamal and Hammons, “Space-Time Coding for the Block Fading Channel,'‘ In Proceedings ofCISS'2000, Princeton University.

• Hammons and El Gamal, “Further Results in the Algebraic Design of Space-Time Codes,'' InProceedings of IEEE 2000 International Symposium on Information Theory, Sorrento, Italy.