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Alamouti Code/OSTBC (Orthogonal Space Time Block Code)

 

OSTBC stands for Orthogonal Space Time Block Code. As it's name implies, it is a special kind of STBC in which the each column of the STBC code (matrix) is orthogonal to each other. Alamouti Code is a typical example of OSTBC. It is named as Alamouti Code, named after the person who invented this method.

 

It is a special kind of technique that is used to transmit signal through multiple antenna. You may ask why we need any special kind of technique ? Isn't it simple like just transmitting the exactly the same data through all the antenna at every symbol timing in case of Diversity ? or just transmitting the different stream of data through each antenna at every symbol timing in case of MIMO ?

Many people think like this and just looking at the final result in terms of throughput you can say that. However, if you look into the very details of transmitted data at each symbol timing, it is not as simple as you might think.

 

For example, let's think of an example of using 2 Tx antenna and 1 Rx antenna and transmitting data using Alamouti Code. I can be illulstrated as follows. First, look at the illustration and see how much detailed story you can make on your own.

 

 

This is my interpretation of the illustration shown above.

    i) At higher layer, the exactly same pair of data is transmitted via two Tx antenna twice over two symbol period.

    ii) But the transmitted data at the physical antenna has a little different form at each symbol timing. At symbol time t1, the higher layer data is transmitted to each antenna as it is without any modification. but at symbol time t2, the same higher data go through a mathematical changes and also mapping between higher layer data and Tx antenna also changes.

    iii) The reciever does not process the data at every symbol. It wait until it recieves two received symbols and combine them in special way and decode each separate transmitted data by using special mathematical process.

Then you may ask 'Why they go through this kind of strange looking and complicated process in stead of simpling transmitting the same data twice or same duplicated data through each antenna ?'

If the radio channel (signal path) is ideal and there is no noise, fading, interference, just transmitting the duplicated data would be OK. Actually if the channel is ideal as it is, you don't even need to transmit the duplicated data since you can guarantee that the transmitted data will be received without any problem and reciever will always successfully decode the transmitted data.

Alamouti invented this method and it is one of the most widely used technique even now (especially in Tx Diversity situation) because it can greatly increase the reliability of recovering the received data in any kind of channel condition.

 

Then you may ask another question "How can you show (prove) this kind of method can increase the success rate of received data recovery ?".

Now you have to go through all the detailed mathematical process to understand this. If you don't like the math like me :), or does not need that much of the details, you can skip this part and just think 'we use this kind of techniques because it is better in many ways'.

 

Now let's begin with the math part.