super-orthogonal space- time bpsk trellis code design for 4 transmit antennas in fast fading...
TRANSCRIPT
Super-Orthogonal Space-Super-Orthogonal Space-Time BPSK Trellis CodeTime BPSK Trellis Code Design for 4 Transmit Design for 4 Transmit AntennasAntennas in Fast Fading in Fast Fading ChannelsChannels
Asli Birol Asli Birol Yildiz Technical University,Istanbul,Turkey
Ümit AygölüÜmit AygölüIstanbul Technical University, Istanbul,Turkey
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Outline
Introduction to Space-Time CodesIntroduction to Space-Time Codes Design Criteria for Fast Fading ChannelsDesign Criteria for Fast Fading Channels Super-Orthogonal Space-Time Trellis CodesSuper-Orthogonal Space-Time Trellis Codes Code Design for Fast Fading ChannelCode Design for Fast Fading Channel Simulation ResultsSimulation Results ConclusionConclusion
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Wireless CommunicationWireless Communication
Recent trends in wireless communication Rapid growth in the number of wireless subscribers Increasing demand for multimedia applications
Wireless channel impairments FadingFading Limited BandwidthLimited Bandwidth Dynamism (random access, mobility)Dynamism (random access, mobility) Limited power (at least on one end) Limited power (at least on one end) InterferenceInterference
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Diversity TechniquesDiversity Techniques
Diversity: Primary technique used to improve performance on
a fading channel.
Main idea is to provide the receiver with multiple versions of the same transmit signal over independent channels.
How to create independent channels needed for diversity?
Frequency Diversity Time Diversity Space Diversity
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Why Transmit Diversity?Why Transmit Diversity?
In downlink, Receive diversity is difficult to implement Requires multiple antennas and additional processing at the
mobile station Not suitable due to size and battery power limitation at mobile
Put additional processing and complexity at the base station => Transmit Diversity
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Transmit DiversityTransmit Diversity
Close loop transmit diversity Requires feedback of channel from the receiver to the
transmitter
Open loop transmit diversity No need for feedback ex: Delay diversity
an ancestor of space-time trellis codes. Main idea: Transmission of same information from transmit
antennas simultaneously with different delays
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Space-Time Coding (STC)Space-Time Coding (STC)
Significance: First systematic treatment of coding for achieving (open-loop) transmit diversity
Objective: To achieve full M×N diversity without channel knowledge at transmitter and to maximize coding gain as a secondary criteria
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Design Criteria for Fast Fading ChannelsDesign Criteria for Fast Fading Channels
transmitted symbol sequence
erroneously decided symbol sequence
pairwise error probability
nlll
nn ccccccccc 212
22
121
21
11c
nlll
nn eeeeeeeee 212
22
121
21
11e
),( 0
2
4)(
ec
ecect
ms
tt N
EP
n
i
it
ittt ec
1
22ec
),( ec
ect
tt2
(c,e) : the set of time instances that c and e differ l : number of elements in (c,e)
: sum-product distance
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Design Criteria for Fast Fading ChannelsDesign Criteria for Fast Fading Channels
maximize the minimum l parallel transitions between any state pair are avoided. the shortest error event path will have two steps
maximize the minimum sum-product distance via computer program
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Design CriteriaDesign Criteria
Quasi-Static Fading Fast Fading
Diversity Gain Rank Criteria Effective Code Length
Coding Gain Determinant Criteria Sum-Product Distance
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Space Time Space Time CCodeodess
ST Trellis Code : Full diversity as well as coding gain. No systematic code design method.
ST Block Code (OSTBC):
Full diversity, simple decoding. No coding gain.
TCM + OSTBC Rate loss
SOSTTC Motivation : find a systematic design method for space time code
to achieve full diversity, more coding gain, and no rate loss.
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Super-Orthogonal ST Trellis CodesSuper-Orthogonal ST Trellis Codes
OSTBC does not use all orthogonal matrice, use all of them to do TCM
Ex. 2 transmit antennas, BPSK
*
1*2
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xx
xx
*1
*2
21
xx
xx
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Super-Orthogonal ST Trellis CodesSuper-Orthogonal ST Trellis Codes
A super-orthogonal code is defined as
an extension of orthogonal design code does not extend the constellation alphabet of the
transmitted signals does expand the number of available orthogonal
matrices.
*1
*2
2121 ),,(
xex
xexθxxC
j
j
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Super-Orthogonal ST Trellis CodesSuper-Orthogonal ST Trellis Codes
The coding procedure can be departed into 2
step: set partitioning for super-orthogonal code construct trellis code using the super-orthogonal code
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Orthogonal Designs
Full-rate orthogonal designs with complex symbols are impossible for more than two transmit antennas. Alamouti’s scheme
a full-rate N×N real orthogonal design only exists for N=2,4,8.
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Orthogonal Designs
example of a 4×4 real orthogonal design :
1234
2143
3412
4321
4321
xxx-x-
x-xxx-
xx-xx-
xxxx
)x,x,x,C(x
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Orthogonal Designs
To expand the number of orthogonal matrices phase rotations can be used as follows:
In general, for N transmit antennas, N-1rotations can be used.
13jθ22jθ
31jθ4
23jθ12jθ
41jθ3
33jθ42jθ
11jθ2
43jθ32jθ
21jθ1
3214321
xexex-ex-
x-exexex-
xex-exex-
xexexex
)θ,θ,θ,x,x,x,C(x
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Code Design
i {0, } , i=1,2,3. Set partitioning based on sum-product distance. Best result is obtained using (1,2,3)=(0,0,0) and
(1,2,3)=(,,). the orthogonal matrices are denoted by
i=1,2 represents (1,2,3) = (0,0,0) and (1,2,3) = (,,), respectively
j= 1,2,…,16 denotes all realizations of the binary codeword x1x2x3x4 as
0000, 1111, 0011, 1100, 0101, 1010, 0110, 1001, 0001, 1110, 0010, 1101, 0100, 1011, 1111, 1000, respectively, which are mapped to the BPSK symbols by the rule 0-1, 11
ijc
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16-state BPSK SOSTTC16-state BPSK SOSTTC
Space-time symbol wise Hamming distance =8
Sum-product distance = 32
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Simulation ResultsSimulation Results
Properties of the system considered
4 transmit and 1 receive antenna 130 symbol/frame from each transmit antenna fast fading channel the signals received from different transmit antennas
experience independent fading
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Simulation ResultsSimulation Results
For the case of 4 transmit antennas, any BPSK SOSTTC designed according to fast fading channel criteria is not available in the literature.
Reference Code 1 2-state BPSK SOSTTC designed according to quasi-
static fading channel criteria for four transmit antennas Reference Code 2
4-state BPSK SOSTTC designed for two transmit antennas regarding fast fading channel criteria
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Simulation ResultsSimulation Results
performances of proposed 16-state BPSK SOSTTC and reference codes on Rayleigh fast fading channels
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ConclusionConclusion a new BPSK SOSTTC designed for four transmit antennas in
fast fading channels is proposed. The new code provides full rate, full diversity, and high coding
gain. Comparison of Coding gain : SOSTTC > STTC > STBC Simulation results confirm that the proposed code offer a
better performance compared to their counterparts given in the literature.
The research is restricted to BPSK scheme, since full-rate complex orthogonal designs for four transmit antennas does not exist.
Allowing a decrease in rate or using quasiorthogonal transmission matrices, the research can be expanded to complex constellation schemes.
