Finally, a new modulation scheme in WLAN 802.11ay: NUC-QAM

Since the beginning of WLAN standards, we have always seen various physical layer techniques being introduced regularly to drive more throughput or to make way for efficient spectrum e.g., OFDM in 802.11a-1999, MIMO in 802.11n-2009, MU-MIMO in 802.11ac - 2013, OFDMA in 11ax D7.0 (To be ratified), OFDM was the fundamental revolution using standard modulations schemes across sub-carriers from BPSK-QAM, even when other features like MIMO/MU-MIMO/OFDMA are being added these base modulation schemes remained same, though we have seen QAM trying to map/pack more bits (256QAM, 1024QAM, etc) the core modulation schemes remained same until 802.11ay (to be ratified).

All of these modulation schemes as based on a uniform constellation scheme (both PSK and QAM), where all the symbols are uniformly separated in I and Q phases typically looking like a square/rectangular shape, See the below diagram from [1] showing PSK and QAM constellations.

802.11ay introduced an optional new scheme using NUC (Non-Uniform Constellation) based 64QAM referred to as 64NUC which improves the channel capacity esp. for Low SNRs. But before we discuss that, let us see the pros and cons of Uniform QAM (Simply referred to as QAM).

Uniform QAM

QAM scheme offers higher data rates compared to PSK, but with the extra complexity of decoding not only phase as in PSK but also amplitude (each phase has multiple amplitudes). See below a nice GIF from [3] for 16QAM to see how the constellation diagram helps understand how (de)modulation works, there are a number of receiver schemes as to how to demodulate the signal (LRR, MLR, MMSE, ZD, etc) each with own accuracy and complexity. As you can see, the distance between symbols are uniform in both I and Q phases.

This was the preferred scheme for many years, but due to recent technological advancements, research was done to evaluate this mapping efficiency i.e., how close it is to Shannon's channel capacity or simply Shannon limit, then it was found that there is still scope to improve the efficiency by using a non-uniform constellation. From [4] see the results for various QAM order modulation compared against the Shannon limit, as we can see there is still scope for improvement, do not only focus on the maximum ranges but even for a given SNR, the performance varies.

As per Shannon, the best capacity can be achieved when signals are received using a gaussian distribution (think of Bell curve) but here QAM symbols are mapped using the square-shaped constellations, leaving the scope for improvement but with the tradeoff of complex receive circuitry. So, there was more research done in order to use non-uniform constellation's which are closer to the Gaussian distribution to close the gap to Shannon's limit. That is the main idea behind NUC (Non-Uniform Constellation), "Broadcast" technologies like DVB/ATSC driven the innovation on this first, now 802.11ay is adopting these techniques.

NUC-QAM

Let us discuss the general concepts of NUC before we delve into 802.11ay specifics. We use simulation results from [4] to visualize and compare.

As we are talking about an optimization problem any solution cannot be generally applicable, these NUC symbols/points are specifically tailored for a given SNR and a Channel Model (AWGN, Rayleigh, etc.). But typically as the rate control algorithm already has knowledge of which modulation schemes to use for a given SNR, this should not be complicated to incorporate NUC into them.

There are two basic NUC models to be used, depending on the complexity introduced in the receiver (constellation de-mapper) and the number of dimensions the distance needs to be calculated (for only real - 1D, for both real and imaginary - 2D)

One dimensional Non-Uniform Constellation QAM (1D NUC-QAM or NUC)

We still keep the QAM property of rectangular/square shape (the number of parameters to optimize is limited by this choice) but relax the uniformity property i.e., the distance between points in a single I/Q is non-uniform, this has the advantage of keeping the receiver simpler (I and Q can be de-mapped independently, so, the same de-mapper as Uniform QAM). As we are still using the square shape we can leverage that property into calculating the euclidean distance from a received point to the constellation to see which symbols it maps to using only a 1D de-mapper (See "1D-demapping" in chapter 2 [4] for details)

Here, we use the term degrees of freedom (DoF) to represent the number of points we try to optimize for that SNR (not all points are optimized) i.e., it indicates how much we can play around to get close to Shannon's limit, so, the more the DoF closer we are, DoF is given by the formula (√ M /2 ?1), where M is the number of constellation symbols per-quadrant. Though 802.11ay proposes 64NUC, we use 16NUC below as it is simpler to explain and demonstrate.

For e.g. if for Uniform 16-QAM we have {?3, ?1, +1, +3} in each quadrant, for 16NUQAM we will have {?a1, ?1, +1, +a1} (DoF=√16/2 -1 =1, so, only one variable to play with), if a1=3 then it is 16QAM. See the figure from [4] to see how different values of a1 compare to 3, in the left graph (3dB SNR) a1=2.25 we get the maximum channel capacity, and for the right graph (10dB SNR) a=3.34, but this is achieved using multiple iterations. To summarise, see the below box.

16QAM: {?3, ?1, +1, +3} at any SNR

16NUC-QAM: {?2.25, ?1, +1, +2.25} at 3dB SNR

16NUC-QAM: {?3.34, ?1, +1, +3.34} at 10dB SNR

And as we go to higher-order modulations we have more DoF and hence the optimization cost will increase but they will be closer to the Shannon limit. See below figure from [4] for some constellations for 64-15dB, 256-20dB, 1024-25dB for a combination of AWGN, and i.i.d Rayleigh channel models.

Two dimensional Non-Uniform QAM (2D NUC-QAM or NUC) 

Though we are now closer to Shannon's limit with 1D-NUC, at lower SNR's we still lag behind, see below figure from [4], for higher SNRs 1D-NUC is still optimal but for lower SNR's 1D-NUC is suboptimal. Now, we drop the property of keeping the rectangular/square shape, this gives us the flexibility of finding the perfect symbols or points in the constellation closer to the Gaussian distribution of Shannon's limit but unlike with 1D-NUC, the number of optimization parameters and iterations increases drastically and also as now we cannot separate a given symbol into I and Q hence the receiver complexity (2D de-mapper) is also increased, but this scheme performs well at lower SNRs and provides higher channel capacity. We can reduce the optimization complexity by using symmetry across quadrants, map the bits into the first quadrant of the constellation and then mirror across the I and Q axes, this greatly reduces the DoF. 802.11ay also uses this symmetry.

As we now use two real points to represent a symbol (separately in I and Q), it becomes a 2D problem, so, each choice of coordinates is now a sector, so, DoF freedom is now defined as (2M/S ? 1), S is the number of sectors. Without going into derivation details, now the constellation looks like in the below figure from [4] for 16-5dB, 64-10dB, 256-15dB for a combination of AWGN, and i.i.d Rayleigh channel models.

To compare both the schemes see this figure from [4], observe that 2D NUC for medium SNRs gets you close to the Shannon limit and distribution looks Gaussian.

And as a final comparison between all three schemes again from [4] is shown below, even though the same 6 bits are transmitted, using a NUC mapping gives a good performance esp. for higher-order modulation and some SNRs esp. 2D-NUC.

802.11ay

802.11ay proposes to use π/2-64-NUC* modulation, simulations showed that using NUC esp. for higher-order modulations like 64QAM improved the performance esp. in presence of phase noise [7, 8]. And moreover using NUC improves performance greatly when channel bonding is in use. 11ay proposes a pre-calculated optimal symbols constellation as can be seen below using 2D-NUC (complex coordinates of these points are in [7, 8]), for < 256QAM the de-mapper complexity of 2D-NUC is also reasonable, hence 2D was used for its advantages. Compared to 64QAM you can see the difference in the layout of the symbols, it kinds looks like a "diamond constellation".

The formula to map incoming 6 bits into this constellation is given by the below complex equation, which is then rotated by 90 degrees (π/2). Observe that the coordinates are separate for I and Q indicating it is 2D-NUC, and from the coordinate values, it is optimized for channel capacity.

MCSs 17-21 are used to represent either 64QAM or 64NUC as the same 6 bits are transmitted the data rates are not changed, selection of modulation scheme Uniform of Non-Uniform is based on "NUC Applied" bit in EDMG-Header-A (SU)/B (MU) and is applicable for both OFDM and SC.

* NUC rotated by 90 degrees, the reason for rotation is given in section 3.2 in [4], not discussing here as it's already a lengthy article.

Hope this gives an introduction to NUC whose details are scarce in 802.11ay standard. Make sure your VSA is upgraded to support this before venturing out testing 802.11ay PHY. Please leave your comments if any.

References

1. https://www.researchgate.net/publication/221911850_Adaptative_Rate_Issues_in_the_WLAN_Environment (Only for "constellation diagram")
2. https://arxiv.org/pdf/1804.01048.pdf (Till Section 3)
3. https://en.wikipedia.org/wiki/Quadrature_amplitude_modulation
4. https://riunet.upv.es/bitstream/handle/10251/84743/Fuentes%20-%20Non-Uniform%20Constellations%20for%20Next-Generation%20Digital%20Terrestrial%20Broadcast%20Systems.pdf?sequence=1 (Till 3.1.3)
5. 802.11ay Draft 6.0
6. https://mentor.ieee.org/802.11/dcn/16/11-16-0955-00-00ay-non-uniform-constellation-of-hom-for-sc-in-11ay.pptx
7. https://mentor.ieee.org/802.11/dcn/15/11-15-0601-00-00ay-non-uniform-constellations-for-64qam.pptx
8. https://mentor.ieee.org/802.11/dcn/16/11-16-0072-00-00ay-performance-of-non-uniform-constellations-in-presence-of-phase-noise.pptx

Acknowledgments

Not much information is available with regards to NUC on the internet. As you can see my primary source of information apart from IEEE discussions, is [4] a Ph.D. thesis by @manuel-fuentes, so special thanks to him for a very good material with excellent simulations and graphs which I have copied here, these graphs enable to visualize esp. for a MAC layer guy like me :).