Multipe-Symbol Sphere Decoding for Space-Time Modulation
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Transcript of Multipe-Symbol Sphere Decoding for Space-Time Modulation
Multipe-Symbol Sphere Decoding for Space-
Time Modulation
Vincent HagMarch 7th 2005
Why MIMO?
• Limited radio resources• Need for higher data rate (3G services and beyond)
Make the best possible use of the spectrum in order to further increase throughput as well as user-capacity
MIMO antennas is a key technology
Why Multiple-Symbol Detection?
N received symbols are jointly processed to estimate N-1 symbols
Better evaluation of the channel statistics yields improved performances
Why Non-coherent Detection?
Phase estimation difficult or costly
Develop (de)modulation techniques that do not require CSI
Extend DPSK to MIMO systems
Problem Formulation
Performance(exploit space and time dimensions)
Complexity
(exponential in space and time dimensions)
Need for fast-algorithm based detection
Talk Outline
Transmission
Channel Model
Reception: Sphere Decoder
Simulation Results
Conclusions and Further Works
Transmission
Non-coherent Detection Differential Transmission
Diagonal codes (= extension of DPSK signals to STC)
Differential Encoding
klV
0 0
1k k k
l l
l l l
S VS V S
Code matrices are differentially encoded such as
Diagonal Codes
11tNu u
12
2
0 0
0 0 time
0 0
space
k
k
Nt
lj u
L
l
j u
L
Ve
e
Channel Model
• AWGN• Rayleigh fading• Multi-channel action:
1 1 1 10 0
0 0
0 0N N N N
R S H W
R S H W
Communication link
Catch-up slide
fast detection scheme
MIMO systems
Multiple-Symbol Sphere Decoding
for
Space-Time Modulation
Talk Outline
Transmission
Channel Model
Reception: Sphere Decoder
Simulation Results
Conclusions and further Works
Reception: Metric
Metric:
2
arg max Pr |
arg min
N
N
MLS C
MLS C
S R S
S US
ML decision rule:
Sphere Decoding: Concept
Fix and examine signals such that
2 2US
S
Search of signals lying inside a sphere of radius instead of the whole space
Sphere Decoding
i N?2 2 2
NN N N NU S d S
2
11 1 120
0 0
N
NN N
U U S
U S
with U upper triangular
NS 1SS can be determined component-wise,
starting from and tracking up to
Sphere Decoding
1i N
?22 2 2
1 1 1 1 1 1N N N N N N N N Nd U S U S d S
2
11 1 120
0 0
N
NN N
U U S
U S
Sphere Decoding
choose that minimizes to keep it as small as possible:
Partial distance criterion:
2
2 21
1
N
i i ii i ij jj i
d d U S U S
2
1
arg mini
N
i ii i ij jS C
j i
S U S U S
iS id
Sphere Decoding
1i
S
radius updated to U S
Then, restart the sphere decoding algorithm with the new radius value
Sphere Decoding
• Phase ambiguities:
1NS fix and start sphere decoding at
• Search strategy:
Zigzag procedure: hypothetical symbols(examined for the ith component) are ordered according monotically increasing distance
1i N
iS
id
Zigzag for 8-PSK constellation
Representation in a tree
DFDD
Attractive low-complexity algorithm performing differential detection
Linear predictor making decision onbased on and
klV
-( -1), , k k NR R ( 1, , 2)k ilV i N
Talk Outline
Transmission Channel ModelReception: Sphere DecoderSimulation ResultsConclusions and further Works
Simulation Results
• Simulation setup
• BER performances
• Computational Complexity
• BER vs. Complexity
Simulation Setup
• bit/channel use,
• Spatially independent Rayleigh continuous fading channels
• Detect at least 1000 bit errors to assess the BER at any SNR
• Number of multiplications as a measure of the complexity
2R 0.03dB T
BER performances
Error floor removed
Single Antenna System
BER performances
MSDSDvs
DFDD
3tN
BER performances
Mismacth of the Doppler rate
4dB shiftRobust?
Computational Complexity
Average Number of Real Multiplicationsdone to estimate a 10-length sequence
Computational Complexity
( ) log ( )c NE N ANMB
BER vs Complexity
Restrict the number of multiplications for practical reasons
BER vs Complexity
Conclusion
• SD outperforms DFDD, a good low-complexity algorithms
• Excellent performance versus complexity trade-off:
• ML performances
• But orders of magnitudes below that of brute-force search (ML detection)
• Gains in power efficiency almost for free
Further Works
• Investigate other STC, possibly with other search strategy for PDP
• Take interference into account
Questions?