DAC in QPSK modulation

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Could you clarify your question? What are your channels? Do you understand the single-channel case?
 

In QPSK modulation, there are two channels- the inphase and quadrature channel. After the binary bits are transformed into parallel bits they enter the two channels where they are multiplied by cos and sin signal in each channel respectively by two mixers.

My question is whether the binary bits after serial to parallel are applied to DAC before they are mulitplied by cos and sin in each channel by the two mixers.
 

Okay, I find your description of channels a bit strange, but I see what you are talking about*. I haven't thought about this issue before, so I am not 100% sure. The answer may be implementation-specific (i.e. it is up to the designer). Or, it may "always" be better to do the mixing in the analogue domain.

Perhaps you could do some web searches for wireless transmitter designs. For example, I found this one [link] which converts to analogue before (1) filtering (to remove Nyquist images caused by the digital sampling) and then (2) mixing and (3) summing. This seems like a sensible design to me. (It might be possible to do the analogue filtering after mixing and summing, but this may be difficult in practice, I'm not sure).

Now, I don't want to introduce extra confusion, but it is not true that binary bits get mixed. Even in the case of QPSK, we have to decide how the bits map to symbols. For example, with Gray coding, we would map every pair of bits as:

Code:
bit n-1  |  bit n  |  symbol
    0    |     0   |  1 + 0j
    0    |     1   |  0 + 1j
    1    |     0   |  0 - 1j
    1    |     1   | -1 + 0j

Then, we need to upsample (i.e. zero-pad), then low-pass filter (probably in the digital domain) to remove the resulting out-of-band components. The reasons for this are very important, but will take more time to explain. Please ask me if you need to know about this.

*The reason I find your description of "channels" strange is because, in my experience of modern wireless communications, we are always talking about complex baseband signals. A single complex channel therefore comprises the real ("in-phase") and imaginary ("quadrature") parts. "Multi-channel" then normally refers to multiple logical and/or physical channels.
 

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