12 OFDM with Multiple Antennas Multiple Antenna Systems

12 - OFDM with Multiple Antennas

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

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

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

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

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

Example: overall receiver gain with receiver diversity.

Transmitter Diversity TX RX Transmit Antennas Different paths Receive Antennas 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 (2 x 1 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.

2 x 2 MIMO with Space Time Coding (2 x 2 Alamouti) TX RX

Same transmitting sequence as in the 2 x 1 case: antennas time Received sequences:

Write it in matrix form:

Combined as to obtain

After simple algebra: with diversity 4 This yields an SNR

Wi. Max 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 Data in Error Coding M-QAM buffer STC IFFT Block to be transmitted TX TX Space Time Coding time

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

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 CP 128 + 64 128 time ODD subcarriers 128 frequency

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 CP 128 + 64 128

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

MIMO Channel Simulation Take the general 2 x 2 channel Rayleigh Correlation at the transmitter Correlation at the receiver