CNR For NTSC/PAL F.M. Video Over 10 L.Y.
Graph 9010-014 illustrates how the CNR varies with effective optical bandwidth for an F.M. video system over a range of 10 light years. This graph is based or a normalized CNR = 34 dB re 1 Hz bandwidth for a 1 kW transmitter, so that a 1 GW transmitter will produce a normalized CNR = 94 dB re 1 Hz. The graph shows the carrier-to-noise ratio based on quantum noise considerations only, the carrier-to-noise ratio based on Planckian radiation only, and the effective CNR taking both noise sources into account. Planckian noise is equal to quantum noise at an I.F. bandwidth of 2.5 kHz. Because the "Planckian noise power" detected from the alien star is itself proportional to bandwidth, the effective CNR will drop very rapidly as the I.F. bandwidth is increased.
The CNR for a conventional C/Ku-Band TVRO (Television receive Only) satellite dish (10 ft. diameter) receiver is also shown for comparison purposes. At the standard I.F. bandwidth of 30 MHz, the CNR is about 12 dB, 5 dB above the 7 dB F.M. threshold.
For the extraterrestrial optical system, the CNR at this bandwidth without Planckian radiation present is about 19 dB. Hence, we can expect broadcast-quality reception. However, if the I.F. bandwidth is increased to 4.6 GHz, corresponding to an optical filter of 0.0066 nm bandpass, the CNR falls below zero dB.
If it is not possible to reject Planckian radiation from the alien star with a space-based telescope, then even in a 30 MHz I.F. bandwidth, the CNR is below -20 dB. Hence, the importance of increasing the rejection of Planckian starlight at these large bandwidths so that the CNR is not degraded.
For a 10 light year distant transmitter and planetary system, it may be possible to provide 40 to 50 dB rejection of Planckian radiation, and thus allow for a CNR above the F.M. threshold.