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Performance Evaluation of Multi-Layered Space Frequency Time Codes for MIMO-OFDM
Systems
Dr. Samir Al-GhadhbanAssistant Prof. EE Dept, KFUPM, Saudi
Arabiahttp://faculty.kfupm.edu.sa/ee/samir
NCTT-MCP08Aug, 2008
NCTT-MCP08 Alghadhban 2
Outline
• Background and motivation• IQ-Space Frequency Time codes• Multi-Layered STBC vs VBLAST• Multi-Layered SFT Codes
NCTT-MCP08 Alghadhban 3
Introduction: Multiple Input Multiple Output (MIMO) Channels
• A MIMO channel is a wireless link between MTtransmit and MR receive antennas.
• MIMO channels boost the information capacity of wireless systems by order of magnitude [Telater95][Foschini98].
Tx RxScatterers
1
2
MT
1
2
MR
11 1
1
( ) ( )( )
( ) ( )
T
R R T
M
M M M
h t h tt
h t h t
=
H…
NCTT-MCP08 Alghadhban 4
Introduction: Open Loop MIMO Communication Systems
Spatial Multiplexing
Transmit Diversity
D-BLAST [Fos96] V-BLAST [Wal99]Trellis Coding [Tar98]Block Coding [Ala98][Tar99a]
Differential Block Coding [Tar00]
Open Loop MIMOCommunication Systems
STBCG1
STBC Combiner and
DetectorB1 1B
MIMO Fading Channel
V-BLAST Detector
B1
BK
1B
MIMO Fading Channel
B2
BK-1
2B
1KB
−
KB
NCTT-MCP08 Alghadhban 5
Multi-layered STBC is a single user system that consists of K parallel STBC
STBCG1
STBCGK
SGINC Detector
B1
BK
1B
KB
MIMO Fading Channel
• It combines spatial multiplexing with transmit diversity.
• It is a V-BLAST system with STBC on each layer.
NCTT-MCP08 Alghadhban 6
How does MLSTBC compare to V-BLAST and STBC?
STBCG1
STBCGK
SGINC Detector
B1
BK
1B
KB
MIMO Fading Channel
V-BLAST Detector
B1
BK
1B
MIMO Fading Channel
B2
BK-1
2B
1KB
−
KB
STBCG1
STBC Combiner and
DetectorB1 1B
MIMO Fading Channel
V-BLAST STBC
MLSTBC
NCTT-MCP08 Alghadhban 7
Comparison of MLSTBC and V-BLAST over 4x4 MIMO-OFDM, Nc=64 and L=4
0 10 20 30 40 5010-5
10-4
10-3
10-2
10-1
100
Es/N0
OFD
M S
ER
V-BLAST-OFDM BPSK1/2 rate STBC-OFDM 256QAMMLSTBC-OFDM QPSK
0 10 20 30 40 5010-5
10-4
10-3
10-2
10-1
100
Es/N0
OFD
M S
ER
V-BLAST-OFDM QPSKMLSTBC-OFDM 16QAM
0 10 20 30 40 5010-6
10-5
10-4
10-3
10-2
10-1
100
Es/N0
OFD
M S
ER
V-BLAST-OFDM 16QAMMLSTBC-OFDM 256QAM
NCTT-MCP08 Alghadhban 8
Motivation
• Pervious work on MLSTBC over MIMO-OFDM systems didn’t take advantage of the available frequency diversity.
• Our Goal is to design MLSTBC system that takes full frequency diversity advantage over MIMO-OFDM channels.
• The solution is to add space frequency time (SFT) codes at each layer.
NCTT-MCP08 Alghadhban 9
Design criteria of SFT codes
• The maximum diversity available in MIMO-OFDM systems is MTLMR [Ben Lu 2000].
• The design criterion is to maximize the minimum effective length and break up channel correlation in frequency domain by interleaving.
• To achieve this diversity, the minimum effective length of the SFT code should be equal to at least MTL, which needs large number of states for practical values.
• For example, at MT=2 and L=3, we need 1024 states. And at L=4, we need 16384 states
NCTT-MCP08 Alghadhban 10
Design criteria of SFT codes
• Our goal is to simplify the design and reduce the number of states required to achieve the full spatial and frequency diversity.
• Our approach is based on concatenating trellis coded modulation (TCM) and space time block codes (STBC). [Lateif 2003]
• Spatial diversity is guaranteed by STBC and frequency diversity is provided by TCM.
• We further reduce the number of states of TCM by using IQ-TCM [AlSemari 97].
NCTT-MCP08 Alghadhban 11
IQ-TCM [AlSemari97]
• The minimum effective length of TCM is upper bounded by:
min / 1l v k≤ +
Where v is the number of memory elements and k is the number of inputs.
• Thus, when k is reduced by a half, lmin at most doubles and this is the reason behind the diversity increase of IQ-TCM.
I-TCM rate 1/2
Q-TCM rate 1/2 j
+ InI-Dec
Q-Dec
× De
[ ] -3 1 1 3Is ∈ −
[ ] -3 1 1 3Qs ∈ −
{ }16-QAMs∈ h
h*
Is
Qs
1 bps/Hz
1 bps/Hz
In: InterleaverDe: De-interleaver
3 -1
-1 3
1 -3
-3 1
-1 3
3 -1
-3 1
1 -3
-3 -1 1 3
4-AM Signal Set
2 bps/Hz IQ-16QAM-TCM
8-states 4AM-TCM
NCTT-MCP08 Alghadhban 12
2 bps/Hz Comparison
I-TCM rate 1/2
Q-TCM rate 1/2 j
+ InI-Dec
Q-Dec
× De
[ ] -3 1 1 3Is ∈ −
[ ] -3 1 1 3Qs ∈ −
{ }16-QAMs∈ h
h*
Is
Qs
1 bps/Hz
1 bps/Hz
In: InterleaverDe: De-interleaver
3 -1
-1 3
1 -3
-3 1
-1 3
3 -1
-3 1
1 -3
-3 -1 1 3
4-AM Signal Set
2 bps/Hz IQ-16QAM-TCM
8-states 4AM-TCM
• 8-states 8PSK-TCM:v=3, k=2 lmin=2
• 8-states IQ-16QAM-TCM:v=3, k=1 lmin=4
min / 1l v k≤ +
NCTT-MCP08 Alghadhban 13
IQ-SFT
IFFT
12
Nc
1,1
1,21
1, cN
ss
s
=
s
2,1
2,2
2
2,
*
**
*Nc
s
s
s
− −
− = −
s P/S CP
IFFT
122,1
2,22
2, cN
ss
s
=
s
1,1
1,2
1
1,
*
**
*Nc
s
s
s
=
s P/S CP
Time 1
Time 2
I-TCM
Q-TCM j
+ In
I-TCM
Q-TCM j
+ In
STBC
In= InterleaverCP= Cyclic Prefix
P/S= Parallel to Serial converter
Nc
1,Ib
1,Qb
2,Ib
2,Qb
1,Is
1,Qs
2,Is
2,Qs
1s
2s
FFT
12
Nc
2
22
2
1,1
1,21
1,
t
tt
tL
yy
y
=
YS/PRem
CP
Time 1Time 21
11
1
1,1
1,21
1,
t
tt
tL
yy
y
=
Y
STBC Combiner at
each subcarrier
De
I-Dec
Q-Dec
(Re)
(Im)
I-Dec
Q-Dec
(Re)
(Im)
1s
2s
Encoder
Decoder
Alamouti STBC Code
NCTT-MCP08 Alghadhban 14
Advantages of concatenated IQ-TCM-STBC at 2bps/Hz
644096671088647321024419430461625626214458641638444161024324642
IQ-16QAM-STBC8PSK-STBCTarokh STTC QPSK
L
Minimum number of states to achieve full diversity (MTLMR)
FCS Length
NCTT-MCP08 Alghadhban 15
The discrete received signal over T time slots at the ith subcarrier is
1,
2,1, 2, ,
,
i i i i
i
ii i K i i
K i
= +
= +
Y H S VSS
H H H V
S
Sk,i is the kth STBC at the ithlayer.Hk,iis the MR×NG MIMO matrix from group k to the receiver at the ith subcarrier.
MR: total number of receive antennasNG: number of transmit antennas per groupMT: total number of transmit antennas
IQ-SFT
G1
Multi-Layered IQ-SFT Decoder
IQ-SFTGK
OFDMDemodulator
OFDMDemodulator
NCTT-MCP08 Alghadhban 16
Due to the short code length of STBC, the received signals over T slots are rearranged into a vector
STBCG1
STBCGK
SGINC Detector
B1
BK
1B
KB
MIMO Fading Channel
xk is the symbols of the kth layer.
is the MIMO matrix from group k to the receiver.
1
21 2
ˆ
ˆ ˆ ˆK
K
= +
= +
y Hx ηxx
H H H η
x
ˆkH GM T N⋅ ×
NCTT-MCP08 Alghadhban 17
Serial Group Interference Nulling and Cancellation (SGINC)
• Group interference nulling: Based on an ordering criterion, assume that the first detected group is the kth group. Then, the algorithm calculates the orthonormal bases of the null space of:
1 1 1ˆ ˆ ˆ ˆ
k k k K− + = H H H HH
• Denote the orthonormal bases of the null space of by , then the received signal for the ith group after nulling is:
kH kN
k k k k k= = +y y H x ηNWhere is the post-processing channel matrix.kH
NCTT-MCP08 Alghadhban 18
SGINC
• STBC Combiner: • IQ-SFT Decoder• Group interference cancellation: After Decoding the kth
Layer, its contribution is subtracted from the received signal and the processing is repeated serially for each group.
• Ordering:– MaxMin FN– MaxAverage FN– Blind power allocation
• Number of receive antennas should be greater than or equal to number of layers.
Hk k k=x H y
NCTT-MCP08 Alghadhban 19
Serial Interference cancellation/ decoding algorithm
8 9 10 11 12 13 14 15 16 17 1810-5
10-4
10-3
10-2
10-1
100
K= 4, MR= 4, L= 4 paths, Nc=64 and W= 4 at 8bps/Hz
SNR
BE
R
Hard nullingNo orderingMaxAverage Pre-FNMaxMin Pre-FNMaxAverage Post-FNMaxMin Post-FNBlind Power allocation
2dB
2dB
8 9 10 11 12 13 14 15 16 17 1810-7
10-6
10-5
10-4
10-3
10-2
10-1
100 K= 4, MR= 4, L= 4 paths, Nc=64 and W= 4 at 8bps/Hz
Es/N0
BE
R
0 iteration
1
2 3 4
5 Perfect Cancellation
Parallel Interference Cancellation/ Decoding Algorithm
3dB
6dB
NCTT-MCP08 Alghadhban 20
Comparison
8 9 10 11 12 13 14 15 16 17 1810-5
10-4
10-3
10-2
10-1
100 K= 4, MR= 4, L= 4 paths, Nc=64 and W= 4 at 8bps/Hz
Es/N0
BE
RUncoded MLSTBC-OFDMSerial: power allocationParallel: four iterations
3dB
1dBFD = 4
No FD
NCTT-MCP08 Alghadhban 21
Conclusion
• Multi-layered Space frequency time codes were designed and evaluated over MIMO-OFDM channels.
• The code design is simplified with IQ-TCM. • Serial and parallel algorithms were proposed
and evaluated for MIMO-OFDM systems.
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