1. 16.548 Coding and Information Theory Lecture 15: Space Time Coding and MIMO:

2. Credits

3. Wireless Channels

4. Signal Level in Wireless Transmission

5. Classification of Wireless Channels

6. Space time Fading, narrow beam

7. Space Time Fading: Wide Beam

8. Introduction to the MIMO Channel

9. Capacity of MIMO Channels

11. Single Input- Single Output systems (SISO) x(t): transmitted signal y(t): received signal g(t): channel transfer function n(t): noise (AWGN, 2) g y(t) = g •x(t) + n(t) y(t) x(t) Signal to noise ratio : Capacity : C = log2(1+)

12. Single Input- Multiple Output (SIMO) Multiple Input- Single Output (MISO) • Principle of diversity systems (transmitter/ receiver) • +: Higher average signal to noise ratio Robustness • - : Process of diminishing return Benefit reduces in the presence of correlation • Maximal ratio combining > Equal gain combining > Selection combining

13. 1 N Idea behind diversity systems • Use more than one copy of the same signal • If one copy is in a fade, it is unlikely that all the others will be too. • C1xN>C1x1 • C1xN more robust than C1x1

14. Background of Diversity Techniques • Variety of Diversity techniques are proposed to combat Time-Varying Multipath fading channel in wireless communication • Time Diversity • Frequency Diversity • Space Diversity (mostly multiple receive antennas) • Main intuitions of Diversity: • Probability of all the signals suffer fading is less then probability of single signal suffer fading • Provide the receiver a multiple versions of the same Tx signals over independent channels • Time Diversity • Use different time slots separated by an interval longer than the coherence time of the channel. • Example: Channel coding + interleaving • Short Coming: Introduce large delays when the channel is in slow fading

15. Diversity Techniques • Improve the performance in a fading environment • Space Diversity • Spacing is important! (coherent distance) • Polarization Diversity • Using antennas with different polarizations for reception/transmission. • Frequency Diversity • RAKE receiver, OFDM, equalization, and etc. • Not effective over frequency-flat channel. • Time Diversity • Using channel coding and interleaving. • Not effective over slow fading channels.

16. RX Diversity in Wireless

17. Receive Diversity

18. Selection and Switch Diversity

19. Linear Diversity

20. Receive Diversity Performance

21. Transmit Diversity

22. Transmit Diversity with Feedback

23. TX diversity with frequency weighting

24. TX Diversity with antenna hopping

25. TX Diversity with channel coding

26. Transmit diversity via delay diversity

27. Transmit Diversity Options

28. MIMO Wireless Communications: Combining TX and RX Diversity • Transmission over Multiple Input Multiple Output (MIMO) radio channels • Advantages: Improved Space Diversity and Channel Capacity • Disadvantages: More complex, more radio stations and required channel estimation

29. MIMO Model T: Time index W: Noise • Matrix Representation • For a fixed T

30. Part II: Space Time Coding

31. 1 M 1 N H Multiple Input- Multiple Output systems (MIMO) H11 HN1 H1M HNM • Average gain • Average signal to noise ratio

32. Shannon capacity K= rank(H): what is its range of values? Parameters that affect the system capacity • Signal to noise ratio  • Distribution of eigenvalues (u)of H

33. Interpretation I: The parallel channels approach • “Proof” of capacity formula • Singular value decomposition of H: H = S·U·VH • S, V: unitary matrices (VHV=I, SSH =I) U : = diag(uk), uk singular values of H • V/ S: input/output eigenvectors of H • Any input along vi will be multiplied by ui and will appear as an output along si

34. Vector analysis of the signals 1. The input vector x gets projected onto the vi’s 2. Each projection gets multiplied by a different gain ui. 3. Each appears along a different si. u1 <x,v1> · v1 <x,v1> u1s1 u2 <x,v2> u2s2 <x,v2> · v2 uK <x,vK> uKsK <x,vK> · vK

35. Capacity = sum of capacities • The channel has been decomposed into K parallel subchannels • Total capacity = sum of the subchannel capacities • All transmitters send the same power: Ex=Ek

36. (si)1 (si)N 1 N Interpretation II: The directional approach • Singular value decomposition of H: H = S·U·VH • Eigenvectors correspond to spatial directions (beamforming) 1 M

37. Example of directional interpretation

39. Space-Time Coding • What is Space-Time Coding? • Space diversity at antenna • Time diversity to introduce redundant data • Alamouti-Scheme • Simple yet very effective • Space diversity at transmitter end • Orthogonal block code design

40. Space Time Coded Modulation

41. Space Time Channel Model

43. STC Error Analysis

44. STC Error Analysis

47. STC Design Criteria

49. STC 4-PSK Example

50. STC 8-PSK Example