Space Time Block Codes Poornima Nookala. Outline Motivation Revisit MRRC Two transmit and one...
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Transcript of Space Time Block Codes Poornima Nookala. Outline Motivation Revisit MRRC Two transmit and one...
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Space Time Block Codes
Poornima Nookala
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Outline• Motivation
• Revisit MRRC
• Two transmit and one Receiver scheme
• Two Transmit and Two receiver scheme
• Performance of Alamouti’s Scheme
• Basics of STBC
• Design of codes
• Capacity of STBC
• Outage Capacity
• Applications
• Performance of STBC in Powerline and satellite Communication
• Advantages• Implementation Issues
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MOTIVATION
• Mobile units are small, hence not optimal for receiver diversity
• Decoding complexity limited by the Processor
• Need for efficient open loop system
• Simple encoding and decoding algorithms
• Limited Power
• Need for transmit diversity at base station
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Revisit- MRRCReceived Signal:
Si will be selected iff:
Combiner:
[1]
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Alamouti’s Scheme
Three functions:
• The encoding and transmission sequence
• Combining sequence
• Maximum likelihood decision region
[1]
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Alamouti’s Scheme
Time Antenna 0 Antenna 1
t S0 S1
t+T -S1* S0
*
1. Encoding : For two branch transmission scheme
Assume fading is constant for two consecutive symbol periods
Received signal is given byReceived signal is given by
[1]
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Alamouti’s Scheme – Combining Sequence & Maximum likelihood Detection
2. Combining Sequences
Solving
3. Maximum likelihood detection is used to find the most probable symbols
(a)
(b)
[1]
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Alamouti’s scheme- 2Tx & 2 RxReceived signals
Combiner
Solving
[1]
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Alamouti’s scheme- Performance
BER comparison of coherent BPSK with MRRC and STBC In Rayleigh fading [1]
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STBC
• STBC is the generalized scheme developed by Alamouti to an arbitrary number of tx antennas
• Encoding is represented by matrix
is linear combination of symbols
(repetition code)
• Code Rate – If the block encodes k symbols, code rate = k/T
• The decoding is same as Alamouti’s scheme
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STBC
• No coding scheme included here, contrary to Space time trellis code (STTCs) which provides both coding as well as diversity gain.
• Orthogonal designs are used to construct STBC satisfying:
AiTAk+ Ak
TAi = [0],
AiTAi = I
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Properties of Orthogonal Designs
There are two attractions in providing transmit diversity via orthogonal designs:
• There is no loss in bandwidth, in the sense that orthogonal designs provide maximum possible transmission rate at full diversity
• There is an extremely simple maximum- likelihood decoding algorithm which uses linear combination at the receiver.
[2]
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Higher Order STBC for complex Constellations• Three Transmit antennas
,
• Four Transmit antennas
,
[2]
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Higher order STBC
• Its proved that no code for more than 2 transmit antennas can achieve full rate.
• For more than two antennas the maximum rate that can be achieved is ¾
• Alamouti’s scheme is a special form of STBC which provides full diversity and rate
• Quasi – Orthogonal codes – rate 1, but not orthogonal
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Performance of STBC
Bit error probability versus SNR for space–time block codes at 3 bits/s/Hz; one receive antenna.
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Capacity of STBC• The block capacity for the channel is given by
• The STBC capacity in bits per channel is
• The difference in the capacity (ie) capacity loss:
Where P is the SNR
[2]
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Capacity
• Space time block codes are optimal with respect to capacity when:
Code rate is oneChannel rank is one
[2]
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Capacity
Capacity difference increases in SNR and number of antennas [2]
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Outage Capacity
5%-outage capacity as a function of the average SNR at the receiver(before decoding) for some uncorrelated MIMO ricean fading channels with
different number of antennas, code rates (R) and ricean-K factors (K). [4]
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Some Potential Applications
• 802.11n(hybrid scheme – STBC/SMX)
• UTRA (Alamouti’s scheme)
• Powerline Communication(PLC)
• Satellite communication
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Performance of STBC in PLC• Channel is assumed to be frequency selective,
multipath fading with AWCN
BER performance of PLC using BPSK
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Performance of STBC in Satellite Communication
• Satellite channel for urban channel is modeled as combination Rayleigh and log normal process in presence of AWGN
BER performance of satellite channel using BPSK modulation
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Advantages of STBC
• Can achieve full diversity with linear processing at the receiver.
• Open loop transmit diversity technique
• Simple encoding and decoding
• No bandwidth expansion
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Issues
• Sensitivity to channel estimation error
• Delay Effects
• Antenna Configurations
• Soft failures
[1]
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References[1] S. M. Alamouti, “A simple transmitter diversity scheme for wireless communications,” IEEE J.
Select. Areas Commun., vol. 16, pp. 1451–1458, Oct. 1998.
[2] V. Tarokh, H. Jafarkhani, and A. R. Calderbank, “Space-time block codes from orthogonal
designs,” IEEE Trans. Inform. Theory, vol. 45, pp. 1456–1467, July 1999.[3] S. Sandhu and A. Paulraj, “Space-time block codes: A capacity perspective,” IEEE Commun.
Lett., vol. 4, pp. 384–386, Dec. 2000.
[4] Jes´us P´erez, Jes´us Ib´a˜nez, Luis Vielva, and Ignacio Santamar´ıa, “Closed-form Approximation for the Outage Capacity of Orthogonal STBC”, IEEE COMMUN LETTERS, VOL. 9, NO. 11, NOVEMBER 2005
[5] Anna Papaioannou, George D. Papadopoulos, and Fotini-NioviPavlidou, “Performance of Space-Time Block Coding in Powerline and Satellite Communications”, IEEE JOURNAL OF COMMUNICATION AND INFORMATION SYSTEMS, VOL. 20, NO. 3, 2005
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Questions ?Questions ?