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12- OFDM with Multiple Antennas. 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;
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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
Recall the Chi-Square distribution: 1. Real Case. Let Then with 2. Complex Case. Let Then with
Receive Diversity: RX TX Transmit Antennas Receive Antennas Different paths Noise PSD Energy per symbol
Assume we know the channels at the receiver. Then we can decode the signal as signal noise and the Signal to Nose Ratio
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
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.
2. Channels Completely Uncorrelated. Since: Diversity of order with
Transmitter Diversity TX RX Transmit Antennas Receive Antennas Different paths Equivalent to one channel, with no benefit. Total energy equally distributed on transmit antennas
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
This can be written as: To decode, notice that Use a Wiener Filter to estimate “s”: with
It is like having two independent channels Apart from the factor ½, it has the same SNR as the receive diversity of order 2.
Same transmitting sequence as in the 2x1 case: antennas time Received sequences:
Combined as to obtain
After simple algebra: with diversity 4 This yields an SNR
WiMax Implementation Subscriber Station Base Station Down Link (DL): BS -> SS Transmit Diversity Uplink (UL): SS->BS Receive Diversity
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
Receiver: Data out P/S S/P Error Correction FFT M-QAM STD 2 2 Space Time Decoding: For each subcarrier k compute: with
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
Both preambles have a symmetry: received signal from the two antennas • Problems: • time synchronization • estimation of both channels
Symmetry is preserved even after the channel spreading: CP 128 + + 64 128 128 CP 128 + - 64 128 128
One possibility: use symmetry of the preambles The two preambles can be easily separated
MIMO Channel Simulation Take the general 2x2 channel Rayleigh Rayleigh Correlation at the transmitter Correlation at the receiver