12- OFDM with Multiple Antennas

1. 12- OFDM with Multiple Antennas

2. Multiple Antenna Systems (MIMO) TX RX Receive Antennas Transmit Antennas Different paths • Two cases: • Array Gain: if all paths are strongly correlated to which other the SNR can be increased by array processing; • 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: RX TX 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. In the Wireless case the channels are random, therefore is a random variable Now there are two possibilities: 1. Channels strongly correlated. Assume they are all the same for simplicity Then assuming and

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

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

9. Example: overall receiver gain with receiver diversity.

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

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

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

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

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

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

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

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 EVEN subcarriers CP 128 + + 64 128 128 CP 128 + ODD subcarriers - 64 128 128 frequency time

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: CP 128 + + 64 128 128 CP 128 + - 64 128 128

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 Rayleigh Correlation at the transmitter Correlation at the receiver