Let us assume we have $16$ symbols to transmit. We can represent these $16$ symbols by $16$ unique signals and transmit. If at the receiver we can identify these $16$ signals correctly, we have identified the symbols transmitted correctly. I have used
qammod([0:15],16,0) in MATLAB and got the output that is attached here.
>> a = qammod([0:15],16,0); a' ans = -3.0000 - 3.0000i -3.0000 - 1.0000i -3.0000 + 1.0000i -3.0000 + 3.0000i -1.0000 - 3.0000i -1.0000 - 1.0000i -1.0000 + 1.0000i -1.0000 + 3.0000i 1.0000 - 3.0000i 1.0000 - 1.0000i 1.0000 + 1.0000i 1.0000 + 3.0000i 3.0000 - 3.0000i 3.0000 - 1.0000i 3.0000 + 1.0000i 3.0000 + 3.0000i
$0,1,\ldots,15$ represent the $16$ symbols. $16$ represents the number of symbols or the number of unique signals - sinusoids with different amplitudes and phases - to be transmitted. $0$ represents the offset phase.
Now I want to interpret the output. I actually got $16$ complex numbers.
- What do they represent?
- What are the magnitude, phase, real part and imaginary part of these complex numbers that they represent? I guess they represent the parameters of sinusoidal signals.
- In both the real and imaginary parts we see $-1, -3 , 1$ and $3$. We do not see $-2, 0$ and $2$. Why?