Superimposed Pilots?

The concept of superimposed pilots is (at least 15 years) old, but clever and intriguing. The idea is to add pilot and data samples together, instead of separating them in time and/or frequency, before modulating with waveforms. More recently, the authors of this paper argued that in massive MIMO, based on certain simulations supported by asymptotic analysis, superimposed pilots provide superior performance and that there are strong reasons for superimposed pilots to make their way to practical use.

Until recently, a more rigorous analysis was unavailable. Some weeks ago the authors of this paper argued, that all things considered, the use of superimposed pilots does not offer any appreciable gains for practically interesting use cases. The analysis was based on a capacity-bounding approach for finite numbers of antennas and finite channel coherence, but it assumed the most basic form of signal processing for detection and decoding.

There still remains some hope of seeing improvements, by implementing more advanced signal processing, like zero-forcing, multicell MMSE decoding, or iterative decoding algorithms, perhaps involving “turbo” information exchange between the demodulator, channel estimation, and detector. It will be interesting to follow future work by these two groups of authors to understand how large improvements (if any) superimposed pilots eventually can give.

There are, at least, two general lessons to learn here. First, that performance predictions based on asymptotics can be misleading in practically relevant cases. (I have discussed this issue before.) The best way to perform analysis is to use rigorous capacity lower bounds, or possibly, in isolated cases of interest, link-level simulations with channel coding (for which, as it turns out, capacity bounds are a very good proxy). Second, more concretely, that while it may be tempting, to superimpose-squeeze multiple symbols into the same time-frequency-space resource, once all sources of impairments (channel estimation errors, interference) are accurately accounted for, the gains tend to evaporate. (It is for the same reason that NOMA offers no substantial gains in MIMO systems – a topic that I may return to at a later time.)

11 thoughts on “Superimposed Pilots?”

  1. Hi, I Stumbled upon this site after much searching, sorry if the question is not directly relevant to the post.

    The general conclusion from everywhere I read is that FDD – Massive MIMO doesn’t work, or at least not anywhere near the performance leap in TDD. 128 x 128 TDD has already been tested with carrier around the world since early this year. China and Huawei seems to be pushing this further and faster then everyone else.
    Meanwhile we only have 32×32 FDD testing right now, and performance / results are not comparable to 32×32 in TDD cases.

    It also seems we have no clear solution to the problem in sight, it will requires handset with 3GPP Rel14 support to be used, compared to Rel 9 for TDD.

    Which means, all of a sudden the 30% of the Carrier Operator around the world uses TDD have leapfrog all the other FDD operator in capacity and performance? Assuming everything else being equal.

    It also seems there will be a lot more regulation problem if any operator suddenly wanted to use TDD since spectrum are auctioned by TDD and FDD, they cant switched from one to another.

    Am I correct in all the assumption above? Because this paint a pretty grim future to me.

    1. Not really sure. If there are multiple actors (operators) in an area it doesn’t seem easy to convert a network from FDD to TDD operation because they would all have to be synchronized to avoid interference problems. But yes, looking only at the information theory and physics, TDD is superior to FDD. This has been elaborated on at many places, by us and by others.

  2. Yet another insightful post from Prof. Larsson. Thank You Sir.
    Can you please further elaborate why NOMA doesn’t offer much substantial gain in MIMO networks?

    1. Thank you for your comment. The issue is again, the accuracy of the channel state information required. We have a recent paper that discusses some aspects of this, H. V. Cheng, E. Björnson and E. G. Larsson, “Performance analysis of NOMA in training based multiuser MIMO systems,” accepted to the IEEE Transactions on Wireless Communications, that may be of some interest.

  3. Thank you for your points.
    What about time-shifted pilots? Are there strong reasons for time-shifted pilots to make their way to practical use due to the interference between pilots and datas?

    1. This issue is discussed on p. 94 in our book Fundamentals of Massive MIMO, and in some research papers. Pilot interference is harmful no matter what the interfering signal consists of (pilots, or data). But if pilots are transmitted with full power (as in the canonical model in the book), then pilot interference may be somewhat worse than data interference, since data normally is subject to careful power control.

    1. Yes, that is what you do when using superimposed pilots. Check the references in the blog post for further details.

  4. I am looking for some information discussing on the coverage improvement brought by Massive MIMO. but it seems not the focus until now. But from a commercial deployment, coverage could be the first important issue concerned by all the operator. Do you have any idea on that?

    1. Massive MIMO greatly improves coverage at the cell edge, even with the most basic signal processing. The main reason is the coherent beamforming (array) gain. The interference suppression facilitated by beamforming also helps.

      Several case studies quantify this: for example, chapter 6 in our book “Fundamentals of Massive MIMO” (Cambridge University Press 2016), and several examples in Emil Bjornson’s book “Massive MIMO Networks” (Now publishers, 2018).

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