Space–time block code: Difference between revisions

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Diversity criterion: Proper use of dots in TeX.
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An STBC is usually represented by a [[matrix (mathematics)|matrix]]. Each row represents a time slot and each column represents one antenna's transmissions over time.
 
: <math>
\mboxtext{time-slots}
\begin{matrix}
\mboxtext{transmit antennas}\\
\left \downarrow
\overrightarrow{
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\end{matrix}
</math>
 
Here, <math>s_{ij}</math> is the [[modulation|modulated]] symbol to be transmitted in time slot <math>i</math> from antenna <math>j</math>. There are to be <math>T</math> time slots and <math>n_T</math> transmit antennas as well as <math>n_R</math> receive antennas. This block is usually considered to be of 'length' <math>T</math>
 
The [[code rate]] of an STBC measures how many symbols per time slot it transmits on average over the course of one block.<ref name="stbc" /> If a block encodes <math>k</math> symbols, the code-rate is
 
: <math>r = \frac{k}{T}. </math>.
 
Only one standard STBC can achieve full-rate (rate 1) — [[#Alamouti's code|Alamouti's code]].