I've been studying the modulation schemes used in NB-IoT communication, with a particular focus on energy efficiency. I've noticed that QPSK (Quadrature Phase Shift Keying) is used in multi-tone transmission, while π/4-QPSK is often used in single-tone transmission (https://scdn.rohde-schwarz.com/ur/pws/dl_downloads/dl_application/application_notes/1ma296/1MA296_2e_NB-IoT_Measurements.pdf or https://digibug.ugr.es/bitstream/handle/10481/56821/67983.pdf table 3.7 and 3.8). I'm curious about the reasons behind this choice of modulation schemes.

  • Why is QPSK preferred for multi-tone transmission in NB-IoT, especially considering that π/4-QPSK is used for single-tone transmission?
  • What are the advantages and trade-offs of using QPSK over π/4-QPSK in multi-tone transmission for NB-IoT devices?
  • Are there specific technical or practical considerations (energy efficiency, throughput or coverage for example) that make QPSK a more suitable choice than π/4-QPSK, particularly in good coverage conditions?

I would appreciate any insights or explanations regarding the modulation choices for these two NB-IoT transmission scenarios. Thank you!


1 Answer 1


It's hard to know what the actual reasons for these things are; 4G is design by committee (both for the better, and the worse), so that technical, commercial, and compatibility interests all intermingle.

We can still reason about things on a technical level:

$\pi/4$-QPSK has mainly the advantage that the direct path between two consecutive symbols never goes through the origin; that means that the dynamic range needed to represent such paths is less large, which in turn is advantageous in highly efficient power amplifiers (PAs), because they need to be linear across a smaller range.

There's a couple of issues with applying this claim to a fourth-generation narrowband waveform:

  • We don't linearly interpolate between symbols; so, by applying appropriate pulse shaping, the amount of times we're crossing close to zero can be drastically reduced. Note that you can't achieve that with Nyquist criterion-fulfilling filters, but these are typically not used (RRC is "half" such a filter, for example).
    • conversely, also, with pulse-shaping filters longer than 2 symbol periods, the offset helps very little against zero "flybys"
  • Reduced PA linearity is less of an issue in modern transmitters: digital predistortion is pretty much standard; for example, I know of a sigfox transceiver family whose DACs are non-uniform in amplitude steps.
  • Technical advantages of the last 50 years have made amplifiers better, so that the more extreme cases, where significant OOB emissions were caused by the nonlinear behaviour of PAs, are less of a concern to begin with.

Generally applicable downsides, but which weigh heavy in a cellular context, include the fact it's harder to synchronize the phase of such a constellation, with increased chances of phase slipping, which in general isn't great for SER; this might or might not be a problem in the NB-IoT use case, since I assume that frames are rather short, typically.

Thus, my suspicion is that π​/​4​-​QPSK has been accepted into the standard based on the lobbying of a standardization group member who had ready-to-use solutions (or an essential patent) for it, and the rest of the group did not care enough (it's not like anything in single-carrier π​/​4​-​QPSK is exciting, and the downsides are very benign).

For multi-carrier waveforms, 4G already has an abundance of OFDM configurations and modulators used on that. Also, in a multicarrier scheme, even the hypothetical advantages in terms of dynamic range of π​/​4​-​QPSK disappear completely, so they just stuck with the more common QPSK.

  • $\begingroup$ Agree that "it's not like anything in single-carrier π​/​4​-​QPSK is exciting, and the downsides are very benign". However, I think that as this π​/​4​-​QPSK is intended for uplink, it is technically reasonable in the senses of maximizing UE power efficiency and leaving the burden of RX processing for base stations. $\endgroup$
    – AlexTP
    Commented Sep 18, 2023 at 22:15
  • $\begingroup$ Also, where could I find the information about "sigfox transceiver family whose DACs are non-uniform in amplitude steps"? Thanks. $\endgroup$
    – AlexTP
    Commented Sep 18, 2023 at 22:16
  • $\begingroup$ @AlexTP sadly, not employed there anymore, so can't just walk up to a closet and look in right now, but: started with py... let me check publications $\endgroup$ Commented Sep 19, 2023 at 6:05
  • $\begingroup$ @AlexTP might have been de.farnell.com/pycom/lopy4/iot-entwboard-sigfox-lora-wifi/dp/… that we burdened a student with :) was a research assistant back in the day, and that research was public. $\endgroup$ Commented Sep 19, 2023 at 6:11
  • $\begingroup$ Could you please explain (or just slip some keywords or papers) for this "harder to synchronize the phase of such a constellation, with increased chances of phase slipping,"? The only thing I find is $\pi/4$-QPSK is easier to demodulate than OQPSK maaz.ihmc.us/rid=1224197201492_276366100_5982/L5.pdf $\endgroup$
    – Rokai
    Commented Mar 8 at 13:54

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