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Space Time Coding and Channel Estimation

Space Time Coding and Channel Estimation. By Orhan GAZI. Outline. Spatial Multiplexing Space Time Coding MIMO Channel Capacity MIMO channel estimation Our aim. Spatial Multiplexing. Data is divided into data streams Each stream is sent with an antenna Multiplexing gain is maximum

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Space Time Coding and Channel Estimation

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  1. Space Time Coding and Channel Estimation By Orhan GAZI Space Time Coding and Channel Estimation by Orhan Gazi

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

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

  4. 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 Space Time Coding and Channel Estimation by Orhan Gazi

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

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

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

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

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

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

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

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

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

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

  15. 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 Space Time Coding and Channel Estimation by Orhan Gazi

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

  20. 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 Space Time Coding and Channel Estimation by Orhan Gazi

  21. Examples¾ complex orthogonal codes 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) Space Time Coding and Channel Estimation by Orhan Gazi

  23. Space Time Coding and Channel Estimation by Orhan Gazi

  24. 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 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 Space Time Coding and Channel Estimation by Orhan Gazi

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

  27. 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 Space Time Coding and Channel Estimation by Orhan Gazi

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

  29. 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 Space Time Coding and Channel Estimation by Orhan Gazi

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

  31. 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 Space Time Coding and Channel Estimation by Orhan Gazi

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

  34. 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. Space Time Coding and Channel Estimation by Orhan Gazi

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

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

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

  38. 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 Space Time Coding and Channel Estimation by Orhan Gazi

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

  41. Complete System 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 Space Time Coding and Channel Estimation by Orhan Gazi

  43. 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 Space Time Coding and Channel Estimation by Orhan Gazi

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

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

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