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A phased array works by adjusting the time delay of each serversat 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.  A phased array works by adjusting the time delay of each serversat transmitter so that the signals from each transmitter, 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. 
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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.  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 10,000km path, that can be accurately represented as a 32.10 bit fixed point number or a 64 bit IEEE754 floating point number. 
Radios for communication, interconnect, synchronization, radar, and orientation
Serversat radios will have multiple lowpower outputs and communicate to many printedcircuit antennas and resonant impedance matchin structures. They will talk on multiple bands, for downlink, uplink, femtosecondprecision array timing, micronprecision serversat location and orientation within the array, and orientation to other arrays and to GPS and ground systems. Much of this accuracy will come from continuous monitoring and averaging, differential and quadrature analog signal processing, and the ultralow vibration and perturbation environment of a serversat in a completely predictable nanogee space environment.
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Timing precision and synchronization
In the late 1990s, Keith Lofstrom worked with Teradyne and Analog Devices to produce a timing interpolator system for a tester that produced timing edges with 1ps resolution within a 2ns time period. Measurements showed that the timing accuracy of each edge was less than the 8 femtoseconds of the measurement equipment. This was for single edges  an system that averages trillions of edges should be able to estimate system phasing to fractions of a femtosecond; at the speed of light, this is a small fraction of a micron. To achieve this, the measurement system must be well isolated from all noise sources, and all signals must be differential, with balanced power on all edges, balanced grounds and power signals to each circuit, etc. Vibration can generate errors, but the vibrations will be very small in a serversat (mostly related to transients caused by the LCD thrusters, and perhaps from nanometeor impact) and measurable. Thermal variations will occur as various electronic sections turn on and off, but these thermal variations can be characterized and extracted. Perhaps the largest source of unpredictable perturbations will be radio energy from other arrays coupling with signal runs on the serversat; this may require extra ground planes.
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Downlink communications
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 serversat, so directional beams can be made with serversat scale antennas. Each serversat 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 seversats comes from their ability to act as a phased array. Constructive and destructive interference between phase locked arrays of serversats 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 serversats 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 serversat transmitter so that the signals from each transmitter, 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 10,000km path, that can be accurately represented as a 32.10 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 offaxis lobes in an xray crystallography pattern. If the precise spacing of serversats 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 xray 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.
This is just a first pass test using this C program and gnuplot using a command file like this. A two dimensional extension and a three dimensional extension is needed (which will be very compute intensive), and it is likely that the proper nonrandom spacing algorithm (perhaps based on a windowed fourier transform) will produce a better spacing algorithm.
communication within an array
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communication between arrays
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radar  locating space debris
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orientation to other arrays, GPS, and ground stations
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