Download - Adct Lecture 28 Space Time Codes
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Space Time Codes
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A MIMO SYSTEM
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System Model
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System Model MIMO system with NT transmit and NR receive antennas
: received vector
: quasi-static channel matrix
: transmitted vector
: white Gaussian noise vector
RTR
T
NNN
N
hh
hh
1
111
)(
)(1
kr
kr
RN
)(
)(1
kx
kx
TN
)(
)(1
kn
kn
RN
)()()( kkk nxHr H
)(kr
)(kn)(kx Why Space Time coding ?
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Space-Time Coding
What is Space-Time coding? Coding schemes allow for the adjusting and optimization of
joint encoding across space and time in order to maximize the reliability of a wireless link.
Space-Time codes allow us to achieve this goal by exploiting Spatial diversity in order to provide coding and diversity gains
over an uncoded wireless link
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1. Space-Time Block Codes: These codes are transmitted using an orthogonal block structure which enables simple decoding at the receiver.
2. Space-Time Trellis Codes: These are convolutional codes extended to the case of multiple transmit and receive antennas.
Space-Time Coding
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Space-Time Block Codes achieve maximum possible diversity advantage but no coding gain and bandwidth expansion
advantage: simplicity
Space-Time Trellis Codes (STTC) joint design of error control coding, Modulation, transmit
and receive diversity
complexity coding gain, spectral efficiency,
and diversity improvement
Space-Time Coding
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Maximizing diversity with Space-Time Codes
Space–Time Trellis Codes (STTC) offer better performance at the cost of increased complexity
Complex decoding (vector version of the Viterbi algorithm) —increases exponentially with the transmission rate
Full diversity. Coding gain Space–Time Block Codes (STBC)
Simple maximum–likelihood (ML) decoding based on linear processing Full diversity. Minimal or no coding gain
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Space-Time Trellis Coding
0
1
2
3
Aim : To realize joint encoding, modulation and diversity across space and time .
Design : 4-QAM / QPSK4 – state2 – Transmit antennas
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Example of a 2 transmit space-time trellis code with 4 states
(4-PSK constellations, spectral efficiency of 2bps/Hz)
Space-Time Trellis Coding
Input Bits 00‘0’
01‘1’
10‘2’
11‘3’
State 0Output forAntenna1,Antenna2
00 01 02 03
State 1Output forAntenna1,Antenna2
10 11 12 13
State 2Output forAntenna1,Antenna2
20 21 22 23
State 3Output forAntenna1,Antenna2
30 31 32 32
State #
0
1
2
3
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Example Assume initial state : 00 state 0
Input stream : 0 3 0 1 2 0 3 2 0 1 0 0
Tx. Ant. 1 : 0 0 3 0 1 2 0 3 2 0 1 0 Tx. Ant. 2 : 0 3 0 1 2 0 3 2 0 1 0 0
Delay diversity ?
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Example - Delay diversity code, QPSK modulation
Code rate ½ , 2 Tx antennas
Encoder structure:Example: x = 1 3 2 0 1 c1 = 1 3 2 0 1
c2 = 0 1 3 2 0
Input x ∈ ℤ4
outputantenna 1
outputantenna 2D
c1
c2
1 symbol delayState
0 0
1
2
0/00
1/10
2/20
3/30
0/00
1/10
2/20
3
3/30
0/01
1/11
2/21
3/31
0/02
1/12
2/22
3/32
0/03
1/13
2/23
3/33
transition label: x /c 1c2
3
2
1
0
3
2
1
0
3
2
1
0
3
2
1
0
2/23
0/02
1/10
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Example -Space-time ring TCM code4-state trellis, code rate ½ (and n=2)
Encoder structure:
c1x
D c2+ +
3
1 2 3 1 1
input seq.
output seq.
1 2 3 1 1
1 3 0 3 0
t0 t1
2 1
0 0 0 0 0
0 1 3 0 1
0 2 2 0 2
0 3 1 0 3
1 0 1 1 1
1 1 0 1 2
1 2 3 1 3
1 3 2 1 0
2 0 2 2 2
2 1 1 2 3
2 2 0 2 0
2 3 3 2 1
3 0 3 3 3
3 1 2 3 0
3 2 1 3 1
3 3 0 3 2
input
St St+1
c1 c2
input
St St+1
c1 c2
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Example -Space-time ring TCM code4-state trellis, code rate ½ (and n=2)
0 0
1
2
0/00
1/11
2/22
3/33
0/00
1/11
2/22
3
3/33
1/12
2/23
3/30
0/01
2/20
3/31
0/02
1/13
3/32
0/03
1/10
2/21 3
2
1
0
3
2
1
0
3
2
1
0
3
2
1
0
3/30
1/13 1/10
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Space Time Trellis Decoding
For the 2 Tx antennas system the metric is reduced to:
m (rj ( l ), ci ( l ) / h ij ( l ) )
= [ rj( l ) - {h 1j ( l ) c1( l ) + h 2j ( l ) c2( l ) } ] 2
l = 1j = 1
L m
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Space Time Trellis Decoding
State
survivor path
0 0
1
2
3
0/00
1/11
2/22
3/33
22.378
1.0917
21.437
41.135
0/00
1/12
0
1
2
Transitionmetrics
12.071+22.378=34.449
22.952+1.0917=24.044
Accumulatedmetrics
2/23
3
7.8235+21.437=29.2602
4.5824+41.137=45.7176
1.0917+10.1054=11.1971 survivor
222211222
2211111 )1()1()1()1()1()1()1()1()1()1( cgcgrcgcgr
received1st antenna
CSItransition
signals
received2nd antenna
CSI transitionsignals =
branchlabels
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Simulation Results for Trellis Codes2 Tx, 1Rx, 4PSK codes: 2 Tx, 2Rx, 4PSK codes:
Increase in number of states → increases coding gain
Increase in number of receive antennas → increases diversity gain
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Space-Time Block Codes
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Encoding and Transmission :
Decoding: Linearly combine received symbols Perform Maximum Likelihood (ML) detection
Diversity order of 2NR guaranteed
Space-Time Block Code Alamouti Codes
c1c2c3c4c5
Tx1
Tx2
-c2* c1
c1* c2
The received symbols : 021100 )( nchchtrr
1*11
*201 )( nchchTtrr
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STBC for Tx. Ant > 2
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Simulation Results for Alamouti Scheme
Increase in number of receive antennas → increases diversity order
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Comparison of Alamouti and Trellis
Space–Time Trellis codes perform better than Alamouti scheme.
Alamouti code is lot simpler to decode than trellis codes
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Capacity increase in MIMO
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Scope of MIMO MIMO channels offer multiplexing gain, diversity
gain, power gain (array gain) and a co–channel interference cancellation gain
Tradeoff between diversity gain and multiplexing gain: Careful balancing between those gains is required
Space-Time Coding: Space-Time block codes (STBC) and Space-Time Trellis Codes Easy to combine with error control codes
MIMO systems offer a solution choice for future generation wireless networks
Distributed MIMO: Cooperative wireless networks