Questions on the transmission of 16QAM modulation

Hello everyone,

i have a problem with 16QAM transmission policy
I think my problem is that I don´t understand correctly the transmission of 16QAM. I am currently working on a 16QAM transmission in Matlab and have made nearly everything on the Transmitter side.
So I generated a bit stream, seperated in I and Q stream and assigned amplitudes. Afterwards I convoluted this stream with a root raised cosine filter and multiplied this signal with a cosine / sine and added it like this:

x_b = xI*cos(2*pi*f*T)+j*xQ*sin(2*pi*f*T)
whereas:
xb = Basebandsignal
xI = Inphase component
xQ = Quadrature component

So my question now is: How can I modulate this basebandsignal on a carrier frequency so I can transmit it over a speaker or on even higher frequencies in optical fibers? I cannot transmit a complex valued signal ...

Thanks for your help

Re: 16QAM modulation

Hi,
to transmit your signal you have to multiply it by:

exp(j*2*pi*fc*t) where fc is the carrier frequency

then take the real part and transmit it. To recover Real and Imag parts at the receiver side, just multiply the incoming signal by:

exp(-j*2*pi*fc*t)

Re: 16QAM modulation

Thanks for your help! hmm but normally the inphase component is multiplied with a cosine and the Quadrature comp. with a sine and then added up ... so you say I should add I and Q comp. up and multiply it with exp(2*pi*fc*t)? (Transmitter side)

Re: 16QAM modulation

Sorry, but probably I didn't understand your question. If what you indicated with "f" is the carrier frequency you want to send on-air then you can simply forward to the antenna the signal:

s(t) = xI*cos(2*pi*f*t) - xQ*sin(2*pi*f*t)

where xI and xQ are the pulse-shaped baseband signals.
In the previous answer I was referring to an up (or down) conversion.

Re: 16QAM modulation

Yes exactly! I have the same! So my last question is:
On the Receiver side I have only to multiply the received signal with exp(-2*pi*fc*t) and split it up into imaginary and real part to get Q btw. I stream?

Re: 16QAM modulation

No. You just have to multiply again by cos(2*pi*f*t) and -sin(2*pi*f*t) to recover real and imaginary parts. After multiplication you must apply a lowpass filter in order to remove the 2*f frequency modulation products.

Re: 16QAM modulation

hmm ok thats the same as multiplying with exp(2*pi*fc*t) and then splittin up into real and imaginary part ...

ok i transmitted xI*cos(2*pi*fc*t)-xQ*sin(2*pi*fc*t)

so at the receiver I get for example for the I-Component:
xI*cos(2*pi*fc*t)^2-xQ*sin(2*pi*fc*t)*cos(2*pi*fc*t)
where the last part sin(...)*cos(....) is hopefully reduced respectively surpressed by the LPF (3rd order I want to implement)

But that looks not really like the signal I transmitted ...
Thanks again

Re: 16QAM modulation

calling x = 2*pi*f*T, applying simple trigonometry you will have:

I line
XI*cos(x)^2 = XI*1/2*[1+cos(2*x)]
XQ*sin(x)*cos(x) = XQ*1/2*sin(2*x)

Q line
XI*sin(x)*cos(x) = XI*1/2*sin(2*x)
XQ*sin(x)^2 = XQ*1/2*[1-cos(2*x)]

so by means of a low pass filter you can easily remove the "2*x" frequency components, restoring the original signal (divided by 2)

Re: 16QAM modulation

ahh thanks now i get it