Radios for communication, interconnect, synchronization, radar, and orientation
As a new service, server sky will likely be allocated EHF frequencies for the downlink - in the 30GHz to 300GHz range. For now, let's assume a frequency of 38GHz and a wavelength of 8 millimeters. This wavelength is smaller than the size of a server-sat, so directional beams can be made with server-sat scale antennas. Each server-sat can direct radio energy into an angle of perhaps sin-1(0.1) or 6 degrees, for a ground spot of perhaps 600km.
However, the directionality of sever-sats comes from their ability to act as a phased array. Constructive and destructive interference between phase locked arrays of server-sats permits ground spots of a few tens of meters - better than cellular service and wimax. The wider the array, the smaller the ground spot, so for downlink at least, adding server-sats will improve spatial multiplexing bandwidth, with no practical limits on download bandwidth to billions of customers on earth.
A phased array works by adjusting the time delay of each server-sat radio so that the signals from each radio, located at a different distance from the receiver, all arrive at the receiver at same time. If each transmitter is emitting a pure sine wave, this can be accomplished by shifting the phase of the outgoing signal.
The easiest way to do this is to compute the path length from each transmitter to the ground receiver in wavelengths, take the fractional part, and conjugate it (that is, the negative fractional part becomes the phase of that transmitter). For a 10000km path, that can be accurately represented as a 30.10 bit fixed point number or a 64 bit IEEE754 floating point number.
If the system is linear, then the transmitter can emit the sum of many different phased signals pointing at many ground spots. An easy way to do this is to make the transmitter emit modulated I and Q signals (90 degrees apart), where each I and Q signal is the computed algebraic sum of many baseband or intermediate frequency signals representing different spatial channels. Modern VLSI integrated circuits can combine many data channels and compute the phased sums of them at high speed, while recomputing transmit angles to accommodate the movement of the orbiting array relative to the ground (angles will change 21 nanodegrees per microsecond). In this way, one phased array can communicate with many different ground spots.
However, traditional phased arrays have a problem called grating lobes. If the spacing of the transmitter nodes is wider than the wavelength of the sine wave source, then there are many ground spots and many angles that show a constructive interference maximum. These spatial lobes are called grating lobes, and resemble the off-axis lobes in an x-ray crystallography pattern. If the precise spacing of server-sats is 10 meters, there will be grating lobes at 0.046 degree spacings, or a ground spacing of 5.1 kilometers. Although the main ground spot of a large array of transmitters will be narrow, there will be many more than one.
The grating lobes near the main ground spot for a 10 meter spacing and an 8mm wavelength, 128 elements in a line. The peaks shown are actually the maximum of many peaks - the lobes have a fine structure.
There is a solution. Unlike a traditional phased array, the transmitters can be placed in an unevenly spaced (or even random) array, and the array spacing can be adjusted and optimized in real time. This destroys the exact periodicity of the array, and flattens the lobes into the noise floor. While the same amount of unwelcome power is splattered across the landscape, at least it is not focused into a few spots (the sidelobe power would only be reduced if the transmitting antennas were close enough to couple). If the randomly spaced elements are still phased for a maximum at the primary lobe, the power of that lobe is unaffected.
This is easiest to show (and compute) for a linear array, although the same procedure may be extended to a three dimensional array. Many different spacing algorithms is possible. Random dithering around a precision center seems to average out to produce grating lobes (just as thermal vibration smears but does not eliminate lobes in x-ray crystalography). However, a random walk distance algorithm, where a random amount is added to each spacing between transmitters, does a good job of smearing out grating lobes. The following graphs show the results of adding uniform random spacings of 0m, 1m, 2m, and 3m to the basic 10m spacing. The distance scale is varied from -1km/1km to -1000km/5000km.