Orthogonal space time block codes

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waz_mac

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Hello

Alamouti scheme (amongst others) is said to be an orthogonal STBC. What I don't understand is the "orthogonal" part. WHAT exactly is orthogonal? Can somebody show me mathematically how it is orthogonal? I've tried using the orthogonal matrix definition (matrix times its transpose = identity matrix) with no luck.
 

Orthogonal means that they don't affect each other. When you decode using one code, all other orthogonal codes present before the decoding cancel out, so they don't have any effect on the result after decoding.
 

I understand that orthogonality allows the symbols to be uniquely decoded (i.e. they dont interfere with each other) but how do you tell if a scheme is orthogonal or not?

How would you show that [x1 x2; -x2* x1*] is an orthogonal scheme?
 

Orthogonality means that the dot product is zero.
[x1 x2] is orthogonal to [ -x2* x1*] because x1(-x2*) + x2(x1*) = 0
 

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