1. 12- OFDM with Multiple Antennas

2. Multiple Antenna Systems (MIMO) TX RX Transmit Antennas Receive Antennas Different paths Two cases: 1.Array Gain: if all paths are strongly correlated to which other the SNR can be increased by array processing; 2.Diversity Gain: if all paths are uncorrelated, the effect of channel fading can be attenuated by diversity combining

3. Recall the Chi-Square distribution: 1. Real Case. Let Then with 2. Complex Case. Let Then with

4. Receive Diversity: TX RX Transmit Antennas Receive Antennas Different paths Noise PSD Energy per symbol

5. Assume we know the channels at the receiver. Then we can decode the signal as signal noise and the Signal to Nose Ratio

6. Now there are two possibilities: 1. Channels strongly correlated. Assume they are all the same for simplicity In the Wireless case the channels are random, therefore is a random variable Then and assuming

7. better on average … … but with deep fades! From the properties of the Chi-Square distribution: Define the coefficient of variation In this case we say that there is no diversity.

8. 2. Channels Completely Uncorrelated. Since: with Diversity of order

9. Example: overall receiver gain with receiver diversity.

10. Transmitter Diversity TXRX Transmit Antennas Receive Antennas Different paths Total energy equally distributed on transmit antennas Equivalent to one channel, with no benefit.

11. However there is a gain if we use Space Time Coding (2x1 Alamouti) Take the case of Transmitter diversity with two antennas TXRX Given two sequences code them within the two antennas as follows time antennas

12. This can be written as: To decode, notice that Use a Wiener Filter to estimate “s”: with

13. It is like having two independent channels Apart from the factor ½, it has the same SNR as the receive diversity of order 2.

14. TX RX 2x2 MIMO with Space Time Coding (2x2 Alamouti)

15. Same transmitting sequence as in the 2x1 case: Received sequences: antennas time

16. Write it in matrix form:

17. Combined as to obtain

18. After simple algebra: with diversity 4 This yields an SNR

19. WiMax Implementation Base Station Subscriber Station Down Link (DL): BS -> SS Transmit Diversity Uplink (UL): SS->BS Receive Diversity

20. Down Link: Transmit Diversity Use Alamouti Space Time Coding: Error Coding Data in M-QAMbuffer Block to be transmitted STC IFFTTX IFFTTX Space Time Coding time Transmitter:

21. Error Correction Data out M-QAMSTD FFT Receiver: with Space Time Decoding: For each subcarrier k compute: 2 S/PP/S 2

22. Preamble, Synchronization and Channel Estimation with Transmit Diversity (DL) The two antennas transmit two preambles at the same time, using different sets of subcarriers 128 64 CP 128 64 CP 128 EVEN subcarriers ODD subcarriers ++ + - time frequency

23. Both preambles have a symmetry: received signal from the two antennas Problems: time synchronization estimation of both channels

24. Symmetry is preserved even after the channel spreading: 128 64 CP 128 64 CP 128 ++ + -

25. One possibility: use symmetry of the preambles The two preambles can be easily separated

26. MIMO Channel Simulation Take the general 2x2 channel Rayleigh Correlation at the receiver Correlation at the transmitter