1. Space Time Coding and Channel Estimation
By Orhan GAZI
11/7/2018
Space Time Coding and Channel Estimation by Orhan Gazi

2. Space Time Coding and Channel Estimation by Orhan Gazi
Outline
Spatial Multiplexing
Space Time Coding
MIMO Channel Capacity
MIMO channel estimation
Our aim
11/7/2018
Space Time Coding and Channel Estimation by Orhan Gazi

3. Space Time Coding and Channel Estimation by Orhan Gazi
Spatial Multiplexing
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Space Time Coding and Channel Estimation by Orhan Gazi

4. Space Time Coding and Channel Estimation by Orhan Gazi
Data is divided into data streams
Each stream is sent with an antenna
Multiplexing gain is maximum
The received symbols are decoded using different techniques
Maximum Likelihood (ML) receiver
Minimum Mean Square Error receiver
ZF receiver
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Space Time Coding and Channel Estimation by Orhan Gazi

5. Space Time Coding and Channel Estimation by Orhan Gazi
Spatial Multiplexing
Maximum multiplexing gain
Maximum data transmission
What about the system performance?
- What about BER vs SNR graph
- Is it the best one?
11/7/2018
Space Time Coding and Channel Estimation by Orhan Gazi

6. Space Time Coding and Channel Estimation by Orhan Gazi
NO !!
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Space Time Coding and Channel Estimation by Orhan Gazi

7. For a better system performance
Increase diversity
Increase coding gain
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Space Time Coding and Channel Estimation by Orhan Gazi

8. Space Time Coding and Channel Estimation by Orhan Gazi
Diversity
Spatial Diversity
- Transmit diversity
- Receive diversity
Path Diversity
- Time diversity
- Frequency Diversity
- Polarization Diversity
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Space Time Coding and Channel Estimation by Orhan Gazi

9. Space Time Coding and Channel Estimation by Orhan Gazi
Spatial Diversity
More than one transmit antenna at the transmit side
- Transmit diversity
More than one receive antenna at the receiver side
Receive diversity
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Space Time Coding and Channel Estimation by Orhan Gazi

10. Space Time Coding and Channel Estimation by Orhan Gazi
Correlation occurs if antennas are spaced at a distance d which is smaller than the half transmit wavelength.
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Space Time Coding and Channel Estimation by Orhan Gazi

11. Space Time Coding and Channel Estimation by Orhan Gazi
Path Diversity
Frequency diversity
Different frequencies are used to send the same symbol
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Space Time Coding and Channel Estimation by Orhan Gazi

12. Space Time Coding and Channel Estimation by Orhan Gazi
Delay Diversity
Symbol and its delayed version are transmitted
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Space Time Coding and Channel Estimation by Orhan Gazi

13. Polarization Diversity
Antenna polarization is employed for diversity
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Space Time Coding and Channel Estimation by Orhan Gazi

14. How is the effect of diversity gain on the performance
Diversity increases the slope
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Space Time Coding and Channel Estimation by Orhan Gazi

15. Space Time Coding and Channel Estimation by Orhan Gazi
Space Time Block Code
Alamouti discovered space time block codes
-He used 2 transmit antennas instead of one single antenna.
-1 receive antenna is employed at the receiver side
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Space Time Coding and Channel Estimation by Orhan Gazi

16. Alamouti transmit system
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Space Time Coding and Channel Estimation by Orhan Gazi

17. Comparison with the classical one transmit two receive antenna case
Slopes are the same
3dB loss in performance due to the power division between two transmit antennas
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Space Time Coding and Channel Estimation by Orhan Gazi

18. Following Studies after Alamouti
Tarokh worked on Space Time Codes
Alamouti code only gives diversity gain
Tarokh generalized Alamouti’s work for any number of transmit and receive antennas.
Designed space time codes for real and complex signals.
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Space Time Coding and Channel Estimation by Orhan Gazi

19. Tarokh discoveries on STBC
For real signals full rate space time codes exist for only 2,4 and 8 transmit antennas.
If transmission rate is not full, then is possible to construct space-time block codes for any number transmit antennas
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Space Time Coding and Channel Estimation by Orhan Gazi

20. Space Time Coding and Channel Estimation by Orhan Gazi
for complex signals
Full rate space time code exists for only two transmitter antenna case
Rate ¾ complex orthogonal codes exists for 3 or 4 transmit antennas.
Rate ½ complex orthogonal codes exists for any number of transmit antennas
If Tx >4 then it is not possible to find a code with rate >1/2
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Space Time Coding and Channel Estimation by Orhan Gazi

21. Examples ¾ complex orthogonal codes
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Space Time Coding and Channel Estimation by Orhan Gazi

22. Space Time Trellis Codes
Tarokh also designed space time trellis codes
Space time trellis codes provides
Diversity gain
Coding gain
Slope increases ( Diversity Gain), curve shifts to left (Coding Gain)
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Space Time Coding and Channel Estimation by Orhan Gazi

23. Space Time Coding and Channel Estimation by Orhan Gazi
11/7/2018
Space Time Coding and Channel Estimation by Orhan Gazi

24. Space Time Coding and Channel Estimation by Orhan Gazi
Any Space Code Design
Although Tarokh worked on STBC and STTC, his ideas can be generalized for any space time code design.
While designing space time code we should try to maximize the diversity and coding gain
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Space Time Coding and Channel Estimation by Orhan Gazi

25. Space Time Code Design Criteria
The transmitted code matrix is C
The received code matrix is C’
Error matrix E=(C-C’)(C-C’)T
M is the number of receive antennas
r is the rank of E
is the eigenvalues of E
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Space Time Coding and Channel Estimation by Orhan Gazi

26. Space Time Coding and Channel Estimation by Orhan Gazi
Is called diversity gain
Is called coding gain
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Space Time Coding and Channel Estimation by Orhan Gazi

27. Space Time Coding and Channel Estimation by Orhan Gazi
Rank Criterion
To achieve maximum diversity the error matrix E must have full rank for any pair of distinct code words C and C’
Determinant Criterion
- For the maximization of the coding gain the determinant of the error matrix must be maximized for a given target diversity order
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Space Time Coding and Channel Estimation by Orhan Gazi

28. Space Time Coding and Channel Estimation by Orhan Gazi
Multi Input Multi Output Communication System
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Space Time Coding and Channel Estimation by Orhan Gazi

29. Space Time Coding and Channel Estimation by Orhan Gazi
N the number of transmit antennas
M the number of receive antennas
H the channel matrix between transmitter and receiver.
S is the transmitted symbol data matrix
Y is the received symbol data matrix
Y=HS+N
N is AWGN
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Space Time Coding and Channel Estimation by Orhan Gazi

30. Space Time Coding and Channel Estimation by Orhan Gazi
Ex N=3 M=4
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Space Time Coding and Channel Estimation by Orhan Gazi

31. Space Time Coding and Channel Estimation by Orhan Gazi
MIMO Channel Capacity
When channel knowledge is available at the receiver
r is the rank of the channel and is are the positive eigenvalues of the HHT
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Space Time Coding and Channel Estimation by Orhan Gazi

32. Space Time Coding and Channel Estimation by Orhan Gazi
When N=M, the channel capacity is given as
TheMIMO channel capacity is N times SISO channel capacity
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Space Time Coding and Channel Estimation by Orhan Gazi

33. When channel knowledge is available at the transmitter side
r is the rank of the channel matrix H
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Space Time Coding and Channel Estimation by Orhan Gazi

34. Space Time Coding and Channel Estimation by Orhan Gazi
This idea is called water pouring
Allocate power according to channel eigenvalues
Give more power to larger eigenvalues
Capacity is greater than the NO CSI at the transmitter but only at the receiver case.
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Space Time Coding and Channel Estimation by Orhan Gazi

35. Space Time Coding and Channel Estimation by Orhan Gazi
The mentioned formulas are for static flat fading channels.
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Space Time Coding and Channel Estimation by Orhan Gazi

36. Space Time Coding and Channel Estimation by Orhan Gazi
What about random channels
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Space Time Coding and Channel Estimation by Orhan Gazi

37. Space Time Coding and Channel Estimation by Orhan Gazi
For random channels
Ergodic Capacity
Outage probability
Outage Capacity
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Space Time Coding and Channel Estimation by Orhan Gazi

38. Space Time Coding and Channel Estimation by Orhan Gazi
Ergodic capacity is the expected value of the capacity over the distribution of the channel elements
Outage probability is the probability that given a transmission rate R and transmit power constraint the channel capacity cannot support reliable communication
Given an outage probability, the maximum information rate that can be supported by the communication channel is called the outage capacity of the channel
P{C<Cout}=Pout
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Space Time Coding and Channel Estimation by Orhan Gazi

39. MIMO Channel Estimation Methods
*Blind *
*Training Based*
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Space Time Coding and Channel Estimation by Orhan Gazi

40. Practical systems use training based channel estimation
Ex: GSM frame structure
Figure taken from* Tapio Mikael, Channel Estimation, Ms Thesis,Goteborg Sweden
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Space Time Coding and Channel Estimation by Orhan Gazi

41. Space Time Coding and Channel Estimation by Orhan Gazi
Complete System
11/7/2018
Space Time Coding and Channel Estimation by Orhan Gazi

42. Channel Matrix Estimation
Using the received signal matrix and knowing the transmitted training signal matrix, the MIMO channel matrix can be found with maximum likelihood method or minimum mean square error method
Y is the received signal matrix, S is the sent training matrix
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Space Time Coding and Channel Estimation by Orhan Gazi

43. Space Time Coding and Channel Estimation by Orhan Gazi
Another approach to estimate the channel is to transform the received data linearly so as to minimize the estimation error and it is given as
Y is the received signal matrix, S is the transmitted training signal matrix, is the average signal to noise ratio, I is the identity matrix
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Space Time Coding and Channel Estimation by Orhan Gazi

44. Pilot Insertion methods
Figure taken from Tapio Mikael, Channel Estimatio, Ms Thesis, Goteborg Sweden
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Space Time Coding and Channel Estimation by Orhan Gazi

45. Space Time Coding and Channel Estimation by Orhan Gazi
Our Initial Goal
Using superimposed channel estimation technique and space time code design principles, a better MIMO communication system is to be designed
11/7/2018
Space Time Coding and Channel Estimation by Orhan Gazi