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<p class=MsoNormal><font size=2 color=navy face=Arial><span style='font-size:
10.0pt;font-family:Arial;color:navy'>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). <o:p></o:p></span></font></p>
<p class=MsoNormal><font size=2 color=navy face=Arial><span style='font-size:
10.0pt;font-family:Arial;color:navy'><o:p> </o:p></span></font></p>
<p class=MsoNormal><font size=2 color=navy face=Arial><span style='font-size:
10.0pt;font-family:Arial;color:navy'>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!<o:p></o:p></span></font></p>
<p class=MsoNormal><font size=2 color=navy face=Arial><span style='font-size:
10.0pt;font-family:Arial;color:navy'><o:p> </o:p></span></font></p>
<p class=MsoNormal><font size=2 color=navy face=Arial><span style='font-size:
10.0pt;font-family:Arial;color:navy'>As for using expensive phase-shifters cabled
together to make <st1:City w:st="on"><st1:place w:st="on">Butler</st1:place></st1:City>
matrices at $2.5k per pop, I guess I’m in the wrong business:^)))))<o:p></o:p></span></font></p>
<p class=MsoNormal><font size=2 color=navy face=Arial><span style='font-size:
10.0pt;font-family:Arial;color:navy'><o:p> </o:p></span></font></p>
<p class=MsoNormal><font size=2 color=navy face=Arial><span style='font-size:
10.0pt;font-family:Arial;color:navy'>RR<o:p></o:p></span></font></p>
<p class=MsoNormal><font size=2 color=navy face=Arial><span style='font-size:
10.0pt;font-family:Arial;color:navy'><o:p> </o:p></span></font></p>
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face="Times New Roman"><span style='font-size:12.0pt'>
<hr size=3 width="100%" align=center tabindex=-1>
</span></font></div>
<p class=MsoNormal><b><font size=2 face=Tahoma><span style='font-size:10.0pt;
font-family:Tahoma;font-weight:bold'>From:</span></font></b><font size=2
face=Tahoma><span style='font-size:10.0pt;font-family:Tahoma'> Bob McMahon
[mailto:bob.mcmahon@broadcom.com] <br>
<b><span style='font-weight:bold'>Sent:</span></b> Tuesday, August 10, 2021
10:07 AM<br>
<b><span style='font-weight:bold'>To:</span></b> <st1:PersonName w:st="on">dickroy@alum.mit.edu</st1:PersonName><br>
<b><span style='font-weight:bold'>Cc:</span></b> Rodney W. Grimes; Cake List;
Make-Wifi-fast; starlink@lists.bufferbloat.net; codel; cerowrt-devel; bloat<br>
<b><span style='font-weight:bold'>Subject:</span></b> Re: [Starlink] [Cake] [Make-wifi-fast]
[Cerowrt-devel] Due Aug 2: Internet Quality workshop CFP for the internet
architecture board</span></font><o:p></o:p></p>
</div>
<p class=MsoNormal><font size=3 face="Times New Roman"><span style='font-size:
12.0pt'><o:p> </o:p></span></font></p>
<div>
<p class=MsoNormal style='margin-bottom:12.0pt'><font size=3
face="Times New Roman"><span style='font-size:12.0pt'>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 produce
off-diagonal effects is woefully inadequate. And we're paying about
$2.5K per each butler.<br>
<span id=gmail-docs-internal-guid-c23f4170-7fff-947a-4651-888888f0a88e><img
width=1200 height=900 id="_x0000_i1025"
src="https://lh3.googleusercontent.com/WqWMFHFPo3ltkxkpoyvgPxgdFxmnZpVvpw0NcCTFhGiOTjolvKbP4NugcE-vw1Q3vk9Z7R04YA1k3kQMvyiR5RhcHOjbXbsRMfjLBY-RYML2tFxovzMpTwww5UZiu0Xgxzhi8fFru_g"><br>
</span>Bob<o:p></o:p></span></font></p>
</div>
<p class=MsoNormal><font size=3 face="Times New Roman"><span style='font-size:
12.0pt'><o:p> </o:p></span></font></p>
<div>
<div>
<p class=MsoNormal><font size=3 face="Times New Roman"><span style='font-size:
12.0pt'>On Tue, Aug 10, 2021 at 9:13 AM Dick <st1:City w:st="on"><st1:place
w:st="on">Roy</st1:place></st1:City> <<a href="mailto:dickroy@alum.mit.edu">dickroy@alum.mit.edu</a>>
wrote:<o:p></o:p></span></font></p>
</div>
<blockquote style='border:none;border-left:solid #CCCCCC 1.0pt;padding:0in 0in 0in 6.0pt;
margin-left:4.8pt;margin-right:0in'>
<p class=MsoNormal style='margin-bottom:12.0pt'><font size=3
face="Times New Roman"><span style='font-size:12.0pt'>Well, I hesitate to drag
this out, however Maxwell's equations and the<br>
invariance of the laws of physics ensure that all path loss matrices are<br>
reciprocal. What that means is that at any for any given set of fixed<br>
boundary conditions (nothing moving/changing!), the propagation loss between<br>
any two points in the domain is the same in both directions. The<br>
"multipathing" in one direction is the same in the other because the<br>
two-parameter (angle1,angle2) scattering cross sections of all objects<br>
(remember they are fixed here) are independent of the ordering of the<br>
angles. <br>
<br>
Very importantly, path loss is NOT the same as the link loss (aka link<br>
budget) which involves tx power and rx noise figure (and in the case of<br>
smart antennas, there is a link per spatial stream and how those links are<br>
managed/controlled really matters, but let's just keep it simple for this<br>
discussion) and these generally are different on both ends of a link for a<br>
variety of reasons. The other very important issue is that of the<br>
""measurement plane", or "where tx power and rx noise
figure are being<br>
measured/referenced to and how well the interface at that plane is<br>
"matched". We generally assume that the matching is perfect,
however it<br>
never is. All of these effects contribute to the link loss which determines<br>
the strength of the signal coming out of the receiver (not the receive<br>
antenna, the receiver) for a given signal strength coming out of the<br>
transmitter (not the transmit antenna, the tx output port). <br>
<br>
In the real world, things change. Sources and sinks move as do many of
the<br>
objects around them. This creates a time-varying RF environment, and now<br>
the path loss matrix is a function of time and a few others things, so it<br>
matters WHEN something is transmitted, and WHEN it is received, and the two<br>
WHEN's are generally separated by "the speed of light" which is a
ft/ns<br>
roughly. As important is the fact that it's no longer really a path loss<br>
matrix containing a single scalar because among other things, the time<br>
varying environment induces change in the transmitted waveform on its way to<br>
the receiver most commonly referred to as the Doppler effect which means<br>
there is a frequency translation/shift for each (multi-)path of which there<br>
are in general an uncountably infinite number because this is a continuous<br>
world in which we live (the space quantization experiment being conducted in<br>
the central <st1:country-region w:st="on"><st1:place w:st="on">US</st1:place></st1:country-region>
aside:^)). As a consequence of these physical laws, the<br>
entries in the path loss matrix become complex functions of a number of<br>
variables including time. These functions are quite often characterized in<br>
terms of Doppler and delay-spread, terms used to describe in just a few<br>
parameters the amount of "distortion" a complex function causes. <br>
<br>
Hope this helps ... probably a bit more than you really wanted to know as<br>
queuing theorists, but ...<br>
<br>
-----Original Message-----<br>
From: Starlink [mailto:<a href="mailto:starlink-bounces@lists.bufferbloat.net"
target="_blank">starlink-bounces@lists.bufferbloat.net</a>] On Behalf Of<br>
Rodney W. Grimes<br>
Sent: Tuesday, August 10, 2021 7:10 AM<br>
To: Bob McMahon<br>
Cc: Cake List; Make-Wifi-fast; <a href="mailto:starlink@lists.bufferbloat.net"
target="_blank">starlink@lists.bufferbloat.net</a>;<br>
<a href="mailto:codel@lists.bufferbloat.net" target="_blank">codel@lists.bufferbloat.net</a>;
cerowrt-devel; bloat<br>
Subject: Re: [Starlink] [Cake] [Make-wifi-fast] [Cerowrt-devel] Due Aug 2:<br>
Internet Quality workshop CFP for the internet architecture board<br>
<br>
> The distance matrix defines signal attenuations/loss between pairs.
It's<br>
> straightforward to create a distance matrix that has hidden nodes because<br>
> all "signal loss" between pairs is defined. Let's
say a 120dB<br>
attenuation<br>
> path will cause a node to be hidden as an example.<br>
> <br>
> A B C D<br>
> A - 35 120 65<br>
> B - 65 65<br>
> C -
65<br>
> D
-<br>
> <br>
> So in the above, AC are hidden from each other but nobody else is. It does<br>
> assume symmetry between pairs but that's typically true.<br>
<br>
That is not correct, symmetry in the RF world, especially wifi, is rare<br>
due to topology issues. A high transmitter, A, and a low receiver,
B,<br>
has a good path A - > B, but a very weak path B -> A.
Multipathing<br>
is another major issue that causes assymtry.<br>
<br>
> <br>
> The RF device takes these distance matrices as settings and calculates the<br>
> five branch tree values (as demonstrated in the video). There are<br>
> limitations to solutions though but I've found those not to be an issue to<br>
> date. I've been able to produce hidden nodes quite readily. Add the phase<br>
> shifters and spatial stream powers can also be affected, but this isn't<br>
> shown in this simple example.<br>
> <br>
> Bob<br>
> <br>
> On Mon, Aug 2, 2021 at 8:12 PM David Lang <<a
href="mailto:david@lang.hm" target="_blank">david@lang.hm</a>> wrote:<br>
> <br>
> > I guess it depends on what you are intending to test. If you are not<br>
going<br>
> > to<br>
> > tinker with any of the over-the-air settings (including the number of<br>
> > packets<br>
> > transmitted in one aggregate), the details of what happen over the
air<br>
> > don't<br>
> > matter much.<br>
> ><br>
> > But if you are going to be doing any tinkering with what is getting<br>
sent,<br>
> > and<br>
> > you ignore the hidden transmitter type problems, you will create a<br>
> > solution that<br>
> > seems to work really well in the lab and falls on it's face out in
the<br>
> > wild<br>
> > where spectrum overload and hidden transmitters are the norm (at
least<br>
in<br>
> > urban<br>
> > areas), not rare corner cases.<br>
> ><br>
> > you don't need to include them in every test, but you need to have a
way<br>
> > to<br>
> > configure your lab to include them before you consider any<br>
> > settings/algorithm<br>
> > ready to try in the wild.<br>
> ><br>
> > David Lang<br>
> ><br>
> > On Mon, 2 Aug 2021, Bob McMahon wrote:<br>
> ><br>
> > > We find four nodes, a primary BSS and an adjunct one quite good
for<br>
lots<br>
> > of<br>
> > > testing. The six nodes allows for a primary BSS and two
adjacent<br>
ones.<br>
> > We<br>
> > > want to minimize complexity to necessary and sufficient.<br>
> > ><br>
> > > The challenge we find is having variability (e.g. montecarlos)
that's<br>
> > > reproducible and has relevant information. Basically, the
distance<br>
> > matrices<br>
> > > have h-matrices as their elements. Our chips can provide these<br>
> > h-matrices.<br>
> > ><br>
> > > The parts for solid state programmable attenuators and phase
shifters<br>
> > > aren't very expensive. A device that supports a five branch tree
and<br>
2x2<br>
> > > MIMO seems a very good starting point.<br>
> > ><br>
> > > Bob<br>
> > ><br>
> > > On Mon, Aug 2, 2021 at 4:55 PM Ben Greear <<a
href="mailto:greearb@candelatech.com" target="_blank">greearb@candelatech.com</a>><br>
> > wrote:<br>
> > ><br>
> > >> On 8/2/21 4:16 PM, David Lang wrote:<br>
> > >>> If you are going to setup a test environment for wifi,
you need to<br>
> > >> include the ability to make a fe cases that only happen with
RF, not<br>
> > with<br>
> > >> wired networks and<br>
> > >>> are commonly overlooked<br>
> > >>><br>
> > >>> 1. station A can hear station B and C but they cannot
hear each<br>
other<br>
> > >>> 2. station A can hear station B but station B cannot
hear station A<br>
3.<br>
> > >> station A can hear that station B is transmitting, but not
with a<br>
strong<br>
> > >> enough signal to<br>
> > >>> decode the signal (yes in theory you can work around
interference,<br>
but<br>
> > >> in practice interference is still a real thing)<br>
> > >>><br>
> > >>> David Lang<br>
> > >>><br>
> > >><br>
> > >> To add to this, I think you need lots of different station
devices,<br>
> > >> different capabilities (/n, /ac, /ax, etc)<br>
> > >> different numbers of spatial streams, and different
distances from<br>
the<br>
> > >> AP. From download queueing perspective, changing<br>
> > >> the capabilities may be sufficient while keeping all
stations at same<br>
> > >> distance. This assumes you are not<br>
> > >> actually testing the wifi rate-ctrl alg. itself, so
different<br>
throughput<br>
> > >> levels for different stations would be enough.<br>
> > >><br>
> > >> So, a good station emulator setup (and/or pile of real
stations) and<br>
a<br>
> > few<br>
> > >> RF chambers and<br>
> > >> programmable attenuators and you can test that setup...<br>
> > >><br>
> > >> From upload perspective, I guess same setup would do
the job.<br>
> > >> Queuing/fairness might depend a bit more on the<br>
> > >> station devices, emulated or otherwise, but I guess a clever
AP could<br>
> > >> enforce fairness in upstream direction<br>
> > >> too by implementing per-sta queues.<br>
> > >><br>
> > >> Thanks,<br>
> > >> Ben<br>
> > >><br>
> > >> --<br>
> > >> Ben Greear <<a href="mailto:greearb@candelatech.com"
target="_blank">greearb@candelatech.com</a>><br>
> > >> Candela Technologies Inc <a
href="http://www.candelatech.com" target="_blank">http://www.candelatech.com</a><br>
> > >><br>
> > ><br>
> > ><br>
> ><br>
> <br>
> -- <br>
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