Welcome to Physics with CatSE. We’ll be using 4 methods not known to analysts (Such as TMF associates.) covering the D2D space race: -Math. -Physics. -Phased Array Antenna Simulator tools. & -Logic. To answer questions: Does size matter? And if so how? Pointy =scary? 🧶🐈‍⬛ 1/

Lets get a couple of benchmarks up. This is a Starlink v1 DTC satellite phased array. It’s on orbit. I counted the antenna elements. They are 1600 arranged 40x40. The lattice spacing is half wavelength ~3 inches. 2/

An array of 40 elements would be roughly 3.0 – 3.14 meters long, depending on whether it is optimized for the uplink or downlink frequency of PCS-G block. The way elements are arranged they stack a bit more narrow one way. And we can simulate the Starlink DTC beam. 3/

I used the full array to generate this edge beam at 25.9 degrees look angle. This corresponds to 58.4 degrees scan angle, Theta. If we add a circle for where earth is in yellow and a red circle for ten degree cutoff we see a lot of sidelobes hitting where emissions are prohibited.🚫 4/

We add advanced $ASTS proprietary and patented weighting AKA tapering on Starlinks v1, as a thought experiment. This requires controlling 1600 attenuators per beam. AND $ASTS patent. Such patents are more of a constrain than launch. If you use logic not feelings in analysis. 5/

The result of tapering the edge beam on Starlink v1 DTC was as could be expected a: Reduction of sidelobes. Reduction of main beam and grating lobe directivity. Gain dropped 33.85-31.40 =2,45 dB Where Starlink is at that drop cuts the link. So they’re not able to use ASTs patent would they ve allowed it. And will opt to spatially spam the planet with sidelobes instead. (Note the individual element gain of ~5dB is to be added to each to get full gain of the system.) 6/

Now lets do an edge beam of $ASTS BlueBird Block3. (Launching in 2027) They span the same spectrum bandwidth as Starlink DTC and is comparable in things like element spacing and frequency. But they are larger. 160x192 elements =30,720 12.88x15.456 m (199 sqm) 7/

We’ll apply a simple Hamming Taper. What it does is that it attenuates edge antennas to dampen sidelobes on wide scanning angles. It’s a RADAR technique that $ASTS miraculously got patented for communications applications. And we’re using the same Theta, scan angle as tge Starlink example. 58.4 degrees. 9/

This is the resulting -white knight -beam. I put Starlink -Black Ships - DTC beam next to it in two versions. One as is with sidelobes, and the other with hypothetical taper and blunter beam. Notice that $ASTS beam is ~10.5 dB more pointy. 10x more pointy. (TBC, dinner time) 10/

Let’s compare 72 $ASTS Block3 2GHz beams to 18 Starlink v1 DTC 2GHz beams. You might notice a smear of sidelobes in the Starlink plot. That type of self degradation creating high noise in its ovn bands is the reason Starlink never launched more V1 mini DTC. They immediately run into law of diminishing returns. And can not scale their current system. 🐾

And now physichs/math: The key performance metric of an direct to device satellite system is per Area Spectral Efficiency, ASE. We derive it from Shannons law of capacity (throughput). Rearrange that to show an efficiency metric (throuhput per bandwidth), known as Spectral Efficiency, SE Then lastly for Area spectral efficiency divide it with Area served.

And so on a single satellite to satellite comparison you get an larger increase in efficiency by increasing area. An outsized efficiency gain of fewer but larger arrays. In other words larger sats is better than many sats. That’s just RF physics!

Now lets examine mathematical how these components scale when increasing Antenna Area 🅰️ SNR, Signal to Noise ratio, increases with Gain, which increases proportional to 🅰️ ASE ∝ SNR ∝ 🅰️ 👍 n, Number of antennas on uncorrelated signal paths increases also proportional to 🅰️ as does number of beams per sat. ASE ∝ n ∝ 🅰️ 👍 And 1/Coverage Area means ASE also increases proportional to ASE ∝ 1/A We will not change coverage Area, although there is some positive correlation also here.

We can also compare the 19x larger satellites versus 19x more numerous satellites in an systems level equal total acerage of antenna comparison. Spoiler: Larger satellites win. And we haven’t even taken the sidelobes and grating lobes into account yet.

Here are 18 Starlink beams.

And so we get this. ASE on an individual satellite level scales proportional to A log A. And the magnitude of the improvement by simply going from 40x40 to ~175x175 an 19x aperture area increase thus corresponds to an ASE, efficiency, increase of 64 to 44x depending on your initial SNR assumption. The base 19x from the n factor and rest from the log SNR factor.

Great and interesting explanation. Thanks for so much input, so if I understand it in simple terms, due to the fact that the area is bigger the sidelobe is less of an effect resulting in higher gain (more pointy) and thus more SE?! Or am I missing the point completely?

You got that right. And you now have more understanding of these things than the most often quoted analyst in articles on AST the last 6 years.

Thanks Catse, I have understood all of the derivative from a mathematical POV and the physics how you explained. But what I did not understand is, why does v1 behave this way? Why does it cause these patterns and BB dont, even though the delta dB seem alike? Or am I wrong?

Delta dB differs. Because of size/area mainnly and in two ways. 1. Directly causing larger directivity of the main beam 2. Indirectly because AST has lots of area they can use some of it despite a certain directivity penalty to taper their array (attenuate edge elements) causing a disproportionate and much larger reduction in the sidelobes than in the very directive main beam. Which still remains sharp enough while the sidelobes dive down to natural background levels.

Hey CatSe, don't want to spam you, but I figured it out. Due to their size, as you said, the main beam in comparison to theta=/0 is way bigger allowing for more precise signals. While with starlink their 14dB noisefloor still "echos" in other areas around theta=0. = interference

Thanks for everything.

Here are all 8 edge beams activated simultaneously.

Now lets adjust phi to illustrate the sidelobe and grating lobe problem. Here are 4 different beams pointing in phi increments of 20 degrees different azimuth. Like pointing east to north-north-east.

$ASTS Hi CatSE, I just "attended" your Physics class. While I am a practicing engineer (civil engineer...with a focus on water and dirt) and understood some of the RF physics you presented, I immediately latched on to your image below and the dirt-like substance spewing from Elon's vehicle (is that a "tractor" beam...? :D). To me, this image says it all. Thanks for sharing this information!

Forget it. He never got a pass Euclidean geometry.

Four more for north to nort-west. See all these sidelobes? They spam bad radio signals.

I don't know how anyone could take Tim or Stu's "expertise" opinion on anything, when clearly the true expertise is right here with @CatSE___ApeX___ . All those guys do is spew FUD and bullsh!t opinions.

@Defiantclient2 Hi CatSE. Great analysis. I’m not the best at digesting this level of math, sorry if this question is already answered but how many simultaneous calls can each AST satellite handle?