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I'm designing a basic transmitter and receiver using QPSK in baseband. So the pulse shaping filter I'm using at transmitter is Raised cosine with interpolation of 2. So I'm transmitting 2 samples / symbol. My question is that on the receiver side I am using same Raised cosine filter as matched filter, so should I have to that filter with decimation or interpolation ?

PS: I'm designing this on lab view .

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  • $\begingroup$ removing the unrelated tags! $\endgroup$
    – Marcus Müller
    Commented Jul 12 at 10:14

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should I have to that filter with decimation or interpolation ?

Probably: neither!

  • Decimation: if you decimate by 2, you get 1 sample per symbol. Which is perfect, and exactly what you want! Small problem: that only works if you already have exactly aligned your receiver in time with the transmitter. In your simulated baseband system, you can have a transmission delay, for example of 0.7373 samples; just as in reality, transmitters and receivers are apart from each other an arbitrary distance, so the signal travels for an unknown time. Now, if you just filter with the matched filter and throw out half the samples, you'd never hit close to the maxima of you pulse shape (and that means you lose data very easily, because you get less signal energy). You need to recover timing first before going down to 1 symbol per sample. Recovering timing at 1 sample per symbol is hard. You'll want more.
  1. interpolation: don't know what sense that would make.

So, you're at the point where you need to add timing recovery to your system. That's fine – and that's typically where you use your matched filter. Depending on the kind of timing recovery you build, you will inherently already decimate to 1 sample per symbol, or do it afterwards.

remark: it's a bit unusual to use a raised cosine as pulse-shaping and matched filter. Are you sure you don't want to use a root raised cosine filter? That would, together with itself as matched filter, potentially fulfill Nyquist criteria.

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  • $\begingroup$ Thanks Marcus, I got your point and by decimation of 2 my constellation is good. and also the point of not going to 1 samples per symbol before timing recovery. I have to see the effect of raised cosine and root raised cosine both. I might have to increase my interpolation for good timing recovery ? $\endgroup$
    – Muhammad Umar
    Commented Jul 12 at 10:54
  • $\begingroup$ No, you don't really have to. The amount of information about timing in the signal stays the same – what you can do is making the impulse response of pulse and matched filter longer, to get better SNR in the timing estimation; but that has quickly diminishing returns. $\endgroup$
    – Marcus Müller
    Commented Jul 12 at 11:19
  • $\begingroup$ can you guide me about phase offset recovery and frequency offset recovery. My next step is that but I'm bit confused about that like how to implement that I have added the phase offset and frequency offset but I'm having trouble designing PLL which can track both $\endgroup$
    – Muhammad Umar
    Commented Jul 15 at 5:20
  • $\begingroup$ then don't both at once! Build one that can only track a phase offset first. Show that it works when you slowly change the phase of your channel. When that's done, ask yourself what a frequency offset is in terms of changing phase over time. $\endgroup$
    – Marcus Müller
    Commented Jul 15 at 8:51
  • $\begingroup$ ok, one question I have IQ data at input so do I have to take the hilbert transform before phase detection step ? $\endgroup$
    – Muhammad Umar
    Commented Jul 15 at 11:35

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