Radio Link Budget
I am not a radio antenna designer. The following needs to be improved by a real radio engineer. I do have extensive background in timing and calibration of semiconductor testers, and know that with sufficient measurement, calibration, and characterization, timing signals can be generated with femtosecond accuracy and jitter. This level of timing correction is possible with large digital LSI circuits and lots of patience - it is not achievable with small scale integration, single ended signals, and open-loop control.
Thinsats are covered with dipole antennas, in-plane with other conducting items like heat sinks and solar cells. It is likely that the antennas will act like separate uncoupled dipoles, but perhaps the other conductive areas can be shaped to link the antennas and maximize directionality. THIS NEEDS FURTHER STUDY.
Thinsats do not have dish antennas. While this would greatly enhance gain, dishes are not agile.
With clever design, a thinsat will behave as if the approximately 15 cm "central disk" inside the electrochromic thrusters acts as a phased emitter. The 37 GHz uplink/downlink wavelength is 8mm. The gain is G = ( \pi D / \lambda )^2 = 3500 and the beam width in degrees is approximately BW = 70 \lambda / D = 3.7o; perpendicular to the thinsat, perhaps less off-axis.
Thinsats may originate downlink messages anywhere in the array, and the digital packets are broadcast and relayed between thinsats until all the satellites have the packet and its destination angles. At the appropriate time, carefully modulated I and Q signals are sent from each dipole on each thinsat, adding together to make the beam to the ground.
Assume a typical 100kg array of 32x32x32 version 3 thinats, with approximately 5 meters spacing. The gain of the entire array for transmit is 3500*sqrt(32768), or about 600K, or 58dB (power).
Assume the array produces a kilowatt of radio transmit energy (starting with 32KW of DC power to the transmitters and transmit phase computers). The link distance is 10,000 kilometers. The energy at the ground receiver is 600K times 1KW / ( 4pi * 1E14 m2 ) or 0.47 microwatts per square meter. Assuming a receiver temperature plus noise of 1000K ( ln(2)KT = 1e-20 Joules/bit ) , and an effective receive area of 0.1 m2, the power delivered to the receive antenna is about 47e-9 W and the bit rate can be 4700 gigabits per second.
However, we will be limited by modulation and bandwidth to a fraction of that, and there will be significant losses in the atmosphere for some paths (low elevation, clouds, scattering). So we might be limited to perhaps 10 Gb/s per beam, and perhaps 5 simultaneous beams to different ground receivers per array.
If the total population of server sky is 1E15 thinsats, in 30 million arrays (some of which are eclipsed), the total bandwidth to the ground might be 2E7*5E10 or 1E18 bits per second, an exabit per second. However, for ground receivers to angularly differentiate all these arrays might require some large antennas, and some moderate inclination thinsat orbits.
Because the thinsats are spaced more widely than a wavelength, there will be some energy splattered into grating lobes within a +/- 4o degree cone around the principal lobe (which will be 8 millidegrees wide, or about 200 meters north-south at 60 north ).
Since the receive signals are very small, it is impractical to attempt to combine signals from all the array receivers in all directions, and simultaneously attempt to do high receive bandwidth. So, individual thinsats will receive and combine signals independently. Assuming a 1 watt transmit signal from an effective 0.1 m2 antenna on the ground, the aperture angle is +/- 1.8o and the gain is 15000 and the receive power at 10,000 km is 12pW/m2 or 2.8E-13 watts per thinsat, about 28Mb/s . If each thinsat is listening to a 20Mb/s band with a +/-4 degree area, and the total bandwidth is 5Gb/s in each angular area, then the bandwidth of a whole server sky constellation pointed at the whole earth would be approximately:
(60/4)2 earth area over thinsat area
x (300/1.8) horizontal addressability
x (10/1.8) vertical addressability
or 1E15 bits per second, 1 petabit per second. Unless both the ground antennas and the receive antennas increase in size, it will be difficult to exceed this whole-system bit rate. However, large dishes (or arrays of correlated ground transmitters) can be used to send very narrowly focused signals to specific arrays, so bulk data transfers from a few ground sites can be made to specific arrays.
For narrow-band signals (radar returns at a specific angle, for example) the receive signals can be digitized and combined across an array.
In both directions, a beam will reach many receivers. While this is bad news for secret transmissions, it is great for broadcast. Thus, the same set of data can be sent to many thinsats or nearby arrays simultaneously.
I am NOT a radio engineer. I may have screwed up the above calculations big time. Also, I have no idea how much bandwidth will be provided by the International Telecommunications Union for server sky, or what the technological capabilities will be when server sky is widely deployed.