# [Bloat] [Starlink] [Cake] [Make-wifi-fast] [Cerowrt-devel] Due Aug 2: Internet Quality workshop CFP for the internet architecture board

Dick Roy dickroy at alum.mit.edu
Tue Aug 10 13:56:37 EDT 2021

```You can approximate the H-matrix as containing only complex numbers or
complex frequency responses as below, however the truth is that in the real
world, in general, the entries in the H-matrix are Green's functions, aka
impulse response functions derivable from Maxwell's equations and all the
surrounding boundary conditions (and yes they are time-varying) which give
the output (at the receiver) due to an input impulse (from the transmitter).
"You bang on the box and see what comes out!"  For "narrowband", nearly
"time-invariant" systems, these complex transfer functions can be
approximated by complex numbers  For non-narrowband, yet still (slowly)
time-varying systems, the H-matrix can be approximated (as shown below) by a
time-invariant transfer (Green's) function whose Fourier transform (aka the
spectrum) can be calculated (and plotted as shown below . although as noted
the phase is missing!)  Each point in the spectral domain is actually a
complex number (amplitude and phase as a function of frequency if you will)
again as noted below.  FWIW, the understanding that the ability to quickly
and accurately obtain estimates of the entries of the H-matrix (aka the
spectral response) under these "almost time-invariant" assumptions is
crucially important to achieving anything near channel capacity is what
makes the choice of an OFDM PHY "optimal" (aka really good . and there is
the issue of "water-pouring", but that's another story for another day).

That said, it is really important to remember that a (relatively) stationary
STA and AP does NOT mean that the channel is time-invariant.  It's not.  The
magnitude of the variations depend on how fast the environment around them
is changing (remember Maxwell's equations and the boundary conditions)!
This really matters in the vehicular (aka transportation) environment.  The
ability of a pedestrian in a cross-walk to connect to an AP in the
Starbuck's on the other side of the street depends on how many cars are in
the vicinity and how fast they are moving!

As for using expensive phase-shifters cabled together to make Butler
matrices at \$2.5k per pop, I guess I'm in the wrong business:^)))))

RR

_____

From: Bob McMahon [mailto:bob.mcmahon at broadcom.com]
Sent: Tuesday, August 10, 2021 10:07 AM
To: dickroy at alum.mit.edu
Cc: Rodney W. Grimes; Cake List; Make-Wifi-fast;
starlink at lists.bufferbloat.net; codel; cerowrt-devel; bloat
Subject: Re: [Starlink] [Cake] [Make-wifi-fast] [Cerowrt-devel] Due Aug 2:
Internet Quality workshop CFP for the internet architecture board

The slides show that for WiFi every transmission produces a complex
frequency response, aka the h-matrix. This is valid for that one
transmission only.  The slides show an amplitude plot for a 3 radio device
hence the 9 elements per the h-matrix. It's assumed that the WiFi STA/AP is
stationary such that doppler effects aren't a consideration. WiFi isn't a
car trying to connect to a cell tower.  The plot doesn't show the phase
effects but they are included as the output of the channel estimate is a
complex frequency response. Each RX produces the h-matrix ahead of the MAC.
These may not be symmetric in the real world but that's ok as transmission
and reception is one way only, i.e. the treating them as repcripocol and the
matrix as hollows symmetric isn't going to be a "test blocker" as the goal
is to be able to use software and programmable devices to change them in
near real time. The current approach used by many using butler matrices to
\$2.5K per each butler.

GiOTjolvKbP4NugcE-vw1Q3vk9Z7R04YA1k3kQMvyiR5RhcHOjbXbsRMfjLBY-RYML2tFxovzMpT
www5UZiu0Xgxzhi8fFru_g>
Bob

On Tue, Aug 10, 2021 at 9:13 AM Dick Roy <dickroy at alum.mit.edu> wrote:

Well, I hesitate to drag this out, however Maxwell's equations and the
invariance of the laws of physics ensure that all path loss matrices are
reciprocal.  What that means is that at any for any given set of fixed
boundary conditions (nothing moving/changing!), the propagation loss between
any two points in the domain is the same in both directions. The
"multipathing" in one direction is the same in the other because the
two-parameter (angle1,angle2) scattering cross sections of all objects
(remember they are fixed here) are independent of the ordering of the
angles.

Very importantly, path loss is NOT the same as the link loss (aka link
budget) which involves tx power and rx noise figure (and in the case of
smart antennas, there is a link per spatial stream and how those links are
managed/controlled really matters, but let's just keep it simple for this
discussion) and these generally are different on both ends of a link for a
variety of reasons. The other very important issue is that of the
""measurement plane", or "where tx power and rx noise figure are being
measured/referenced to and how well the interface at that plane is
"matched".  We generally assume that the matching is perfect, however it
never is. All of these effects contribute to the link loss which determines
the strength of the signal coming out of the receiver (not the receive
antenna, the receiver) for a given signal strength coming out of the
transmitter (not the transmit antenna, the tx output port).

In the real world, things change.  Sources and sinks move as do many of the
objects around them.  This creates a time-varying RF environment, and now
the path loss matrix is a function of time and a few others things, so it
matters WHEN something is transmitted, and WHEN it is received, and the two
WHEN's are generally separated by "the speed of light" which is a ft/ns
roughly. As important is the fact that it's no longer really a path loss
matrix containing a single scalar because among other things, the time
varying environment induces change in the transmitted waveform on its way to
the receiver most commonly referred to as the Doppler effect which means
there is a frequency translation/shift for each (multi-)path of which there
are in general an uncountably infinite number because this is a continuous
world in which we live (the space quantization experiment being conducted in
the central US aside:^)). As a consequence of these physical laws, the
entries in the path loss matrix become complex functions of a number of
variables including time. These functions are quite often characterized in
terms of Doppler and delay-spread, terms used to describe in just a few
parameters the amount of "distortion" a complex function causes.

Hope this helps ... probably a bit more than you really wanted to know as
queuing theorists, but ...

-----Original Message-----
Rodney W. Grimes
Sent: Tuesday, August 10, 2021 7:10 AM
To: Bob McMahon
Cc: Cake List; Make-Wifi-fast; starlink at lists.bufferbloat.net;
codel at lists.bufferbloat.net; cerowrt-devel; bloat
Subject: Re: [Starlink] [Cake] [Make-wifi-fast] [Cerowrt-devel] Due Aug 2:
Internet Quality workshop CFP for the internet architecture board

> The distance matrix defines signal attenuations/loss between pairs.  It's
> straightforward to create a distance matrix that has hidden nodes because
> all "signal  loss" between pairs is defined.  Let's say a 120dB
attenuation
> path will cause a node to be hidden as an example.
>
>      A    B     C    D
> A   -   35   120   65
> B         -      65   65
> C               -       65
> D                         -
>
> So in the above, AC are hidden from each other but nobody else is. It does
> assume symmetry between pairs but that's typically true.

That is not correct, symmetry in the RF world, especially wifi, is rare
due to topology issues.  A high transmitter, A,  and a low receiver, B,
has a good path A - > B, but a very weak path B -> A.   Multipathing
is another major issue that causes assymtry.

>
> The RF device takes these distance matrices as settings and calculates the
> five branch tree values (as demonstrated in the video). There are
> limitations to solutions though but I've found those not to be an issue to
> date. I've been able to produce hidden nodes quite readily. Add the phase
> shifters and spatial stream powers can also be affected, but this isn't
> shown in this simple example.
>
> Bob
>
> On Mon, Aug 2, 2021 at 8:12 PM David Lang <david at lang.hm> wrote:
>
> > I guess it depends on what you are intending to test. If you are not
going
> > to
> > tinker with any of the over-the-air settings (including the number of
> > packets
> > transmitted in one aggregate), the details of what happen over the air
> > don't
> > matter much.
> >
> > But if you are going to be doing any tinkering with what is getting
sent,
> > and
> > you ignore the hidden transmitter type problems, you will create a
> > solution that
> > seems to work really well in the lab and falls on it's face out in the
> > wild
> > where spectrum overload and hidden transmitters are the norm (at least
in
> > urban
> > areas), not rare corner cases.
> >
> > you don't need to include them in every test, but you need to have a way
> > to
> > configure your lab to include them before you consider any
> > settings/algorithm
> > ready to try in the wild.
> >
> > David Lang
> >
> > On Mon, 2 Aug 2021, Bob McMahon wrote:
> >
> > > We find four nodes, a primary BSS and an adjunct one quite good for
lots
> > of
> > > testing.  The six nodes allows for a primary BSS and two adjacent
ones.
> > We
> > > want to minimize complexity to necessary and sufficient.
> > >
> > > The challenge we find is having variability (e.g. montecarlos) that's
> > > reproducible and has relevant information. Basically, the distance
> > matrices
> > > have h-matrices as their elements. Our chips can provide these
> > h-matrices.
> > >
> > > The parts for solid state programmable attenuators and phase shifters
> > > aren't very expensive. A device that supports a five branch tree and
2x2
> > > MIMO seems a very good starting point.
> > >
> > > Bob
> > >
> > > On Mon, Aug 2, 2021 at 4:55 PM Ben Greear <greearb at candelatech.com>
> > wrote:
> > >
> > >> On 8/2/21 4:16 PM, David Lang wrote:
> > >>> If you are going to setup a test environment for wifi, you need to
> > >> include the ability to make a fe cases that only happen with RF, not
> > with
> > >> wired networks and
> > >>> are commonly overlooked
> > >>>
> > >>> 1. station A can hear station B and C but they cannot hear each
other
> > >>> 2. station A can hear station B but station B cannot hear station A
3.
> > >> station A can hear that station B is transmitting, but not with a
strong
> > >> enough signal to
> > >>> decode the signal (yes in theory you can work around interference,
but
> > >> in practice interference is still a real thing)
> > >>>
> > >>> David Lang
> > >>>
> > >>
> > >> To add to this, I think you need lots of different station devices,
> > >> different capabilities (/n, /ac, /ax, etc)
> > >> different numbers of spatial streams, and different distances from
the
> > >> the capabilities may be sufficient while keeping all stations at same
> > >> distance.  This assumes you are not
> > >> actually testing the wifi rate-ctrl alg. itself, so different
throughput
> > >> levels for different stations would be enough.
> > >>
> > >> So, a good station emulator setup (and/or pile of real stations) and
a
> > few
> > >> RF chambers and
> > >> programmable attenuators and you can test that setup...
> > >>
> > >>  From upload perspective, I guess same setup would do the job.
> > >> Queuing/fairness might depend a bit more on the
> > >> station devices, emulated or otherwise, but I guess a clever AP could
> > >> enforce fairness in upstream direction
> > >> too by implementing per-sta queues.
> > >>
> > >> Thanks,
> > >> Ben
> > >>
> > >> --
> > >> Ben Greear <greearb at candelatech.com>
> > >> Candela Technologies Inc  http://www.candelatech.com
> > >>
> > >
> > >
> >
>
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