1 kW Signals At 10 A.U. From Earth

9008-001

9008-001a

The graph 9006-018 illustrates communications within the Solar System.  It shows the received signal levels for three different types of 1 kW beacon which have their transmitter powers confined to a 1 Hz bandwidth. The received signal is plotted on a spectral density basis. i.e., W/m².Hz.  The calculations are based on communications between the Earth and a deep space probe.   In this model, the transmitter is on Earth, i.e., 1 A.U. from the Sun, and the receiver is just beyond Saturn, i.e., about 10 A.U. from the Earth.  It is assumed that the Earth is in direct line-of-sight with the Sun, i.e., the Sun is directly behind or slightly to the side of the Earth as viewed near the vicinity of Saturn's orbit.

For the optical beacons, we initially assume that a light bucket (using an incoherent receiver) is used to collect the signal photons, i.e., the antennas are not diffraction limited, and hence the Sun is not resolved as a disk.  For a diffraction limited receiver, the Planck radiation is at the much lower level indicated by the three small horizontal arrows marked "Planck Limit".  In this situation, the antenna only "sees" part of the disk of the Sun, and hence only part of the radiation actually collected is imaged at the same point as the signal.

At 11 A.U. from the Sun, a 300 meter diameter diffraction limited microwave dish operating at 1.5 GHz would just be able to resolve the Sun's disk.  The Signal-To- Noise Ratio (SNR) would thus be about the same as indicated.

9008-001b

The 656 nm visible transmitter would appear as a -1 Magnitude star, so it would be about as bright as Sirius, the brightest star in the sky.  The naked eye can see to +6 Magnitude.  With the Sun in the background and the bandwidth confined to 1 Hz, an SNR of about 70 dB is possible.  This implies that an SNR of about 10 dB could be obtained in a 1 MHz bandwidth.  The Sun, from the orbit near Saturn, appears as a -22 Magnitude star.  If we remove the Sun from the line-of-sight, then the normalized SNR is limited by quantum shot noise only, and the SNR increases to about 130 dB.  In this situation, bandwidths of 10 GHz are possible with an SNR of approximately 30 dB.   This is an excellent SNR and would allow for error-free transmission at 10 Gbits/s.

Note that the SNRs of the optical systems quoted here are slightly larger (by about 3 dB) than we would expect from an incoherent optical receiver because the SNRs were calculated from the heterodyne CNR relationship.  We see that quite modest lasers and small telescopes can produce excellent communication data rates across our solar system.   This is the reason why NASA is very interested in optical communications for deep space probes.  If we assume that the alien planet is not resolved from its star when we get out to distances of many light years, we find that the quantum shot noise spectral density level is always higher than the Planckian starlight level in coherent optical receivers.

Copyright (c), 1996