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I can't find this answer anywhere. I have a couple satellite modem manuals and they refer to digital filtering functions that they do, but they say almost nothing about their sample rate. I always thought, without considering it too much, that all the modems I've worked with were only sampling at a rate high enough to extract the bits--something close to the symbol rate. But if so, how then do they do digital filtering, and how would they be able to display the spectrum, like most of them will do? I believe you must have enough samples to re-create the waveform in order to do those things; I just didn't think all these modems were doing that.

And if all these normal modems implementing digital filtering do sample at the Nyquist rate+, I'm not really seeing the distinction between traditional IF and digital IF, since the first thing the modems are doing is sampling high enough to effectively have a digital IF.

Thanks. There's a lot I don't know, and wish I'd learned 20 years ago.

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All modems sample at higher than the symbol rate up until timing recovery is resolved, at which point the received waveform can de down-sampled to 1 sample per symbol.

As for a digital IF: digital IF means the waveform is centered on some higher frequency, higher than its occupied bandwidth, and can be represented completely as a real signal. In contrast to this is a complex baseband signal, in which case it would be two datapaths that are sampled representing the in-phase (I) and quadrature (Q) components of the complex baseband waveform. When a digital IF is used, a digital down-conversion is required to translate the IF signal to the complex I and Q baseband signal. Both cases are sampled higher than the symbol rate in order for the receiver to resolve carrier and timing offsets and perform optimum matched filtering; meeting the Nyquist requirements as a minimum plus some additional margin for realizable filtering.

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  • $\begingroup$ I appreciate this gentlemen. This constitutes the first technical question I've asked online, ever. In the last ten years I've come to appreciate that maybe the most valuable thing about paid classes at a university was having access to someone that could answer questions. Rather than having to go searching for them on your own for days and years. I don't quite follow the complex baseband, vs simply baseband. $\endgroup$
    – Blue42
    Commented Apr 21 at 4:15
  • $\begingroup$ @Blue42 I hear your confusion with "complex baseband" etc and the need to have someone to answer questions. I teach online classes where I go through all that in detail if you want the 15 hour answer combined with live Q&A with me. One is starting this week and there is still a chance to jump in: it's called "DSP for Wireless Communications" and you can sign up here: ieeeboston.org/courses $\endgroup$ Commented Apr 21 at 12:25
  • $\begingroup$ I just got approval from my manager and put the request into the company for the class. $\endgroup$
    – Blue42
    Commented Apr 22 at 22:36
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To extend on what Dan said (his answer is right! This is just too much for a comment):

If you wanted to sample at exact symbol rate, you would have to continuously adjust the clock of the ADC to be precisely the symbol rate – and to sample at exactly the symbol "instants" (imagine you'd have the exact right frequency, but sampled always in the middle between symbols).

That would necessitate either a DAC controlled by your digital clock and timing recovery logic, influencing a control loop, which introduces jitter/noise and quantization, or analog timing and clock recovery circuitry, which is harder, more power hungry and vastly more complex than doing it digitally, if at all possible, for many systems. While classically, especially geosynchronous satellite modems were intentionally PSK-based, which made PLLs quite feasible, you pay a price in data rate or synchronization robustness if you restrict yourself to things that can be solved with variations of Costas loops. I've been told that very high-rate modems do still use analog PLLs / FLLs to achieve basic synchronization with the carrier, but there's another layer of finer synchronization following in the digital domain.

Either way, adding a DAC or analog circuitry that can detect, track and correct phase and frequency errors is additional cost. If you can achieve the same by oversampling a bit – why not do that? Especially if you don't want to track a single stationary satellite with a large-gain antenna pointed at it, but multiple satellites at once in LEO/MEO orbits, you'd need slightly more than your "payload" bandwidth, anyways, because you need to account for that bandwidth being Doppler'ed out of nominal frequency, anyways.

Another aspect here is the complexity and cost of oversampling, but: sometimes, that's not too terrible; in fact, chances are that the ADC in your modem would be based on an ADC architecture (often, a delta-sigma converter) that makes a trade-off between bit depth and sample rate, anyways. Going for a higher sample rate at reduced bit depth is a technical feasibility in these, and the reduced effective numbers of bits (due to reduced noise shaping, lower quantization) could be offset by the processing gain in the digital filters later on.

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  • $\begingroup$ I thought that pretty much all digital receivers were coherent, at least for any PSK, so that they recover the carrier and use it to correlate with the input to determine how much cos and how much sin is in each symbol. But are you saying that by sampling at a high enough rate to recreate the waveform, you then don't have to synchronize or use coherent detection? $\endgroup$
    – Blue42
    Commented Apr 21 at 4:57
  • $\begingroup$ no, that's not what I'm saying. $\endgroup$ Commented Apr 21 at 9:30
  • $\begingroup$ I don't understand this statement then: "...adding a DAC or analog circuitry that can detect, track and correct phase and frequency errors is additional cost. If you can achieve the same by oversampling a bit – why not do that?" I took this to mean that each separate function: detecting, tracking, correcting phase and frequency errors were functions that oversampling could achieve, instead of analog circuits achieving them. And I thought this tied to your description about PLL's being an outgoing technique. It's not important. I'm just trying to put things together. $\endgroup$
    – Blue42
    Commented Apr 22 at 22:29
  • $\begingroup$ no, oversampling alone doesn't do that; you need to oversample enough for your frequency synchronization (on the digital signal) to be possible; depending on the kind of signal, you often prefer to do frequency synchronization after the timing recovery, and if you decide to put the frequency recovery into the analog domain, you then inherently have to also do the timing recovery in analog. And that's another can of worms – something that is pretty easy in digital domain, like looking for and correlating with a known preamble, is pretty hard in analog domain. $\endgroup$ Commented Apr 23 at 10:28

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