Space-Time Codes and Signal Processing for Slow Fading … · 802.16.3 July 2000 Space-Time Codes...
Transcript of Space-Time Codes and Signal Processing for Slow Fading … · 802.16.3 July 2000 Space-Time Codes...
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: [email protected], 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.