only natural noise (excluding spin modulation noise), the BER for 

 the DCS system is given by 



BER = 1/2 e -O-'^^^ N (2) 



where C/N is the CNR as a numeric (not in dB) and e = 2.71828. 

 This equation is derived from statistical communication theory. 

 Because of the spin modulation noise, the required CNR will be 

 somewhat higher than given by equation (2). 



Direct measurements on GOES A, B, and C show that a CNR of 14dB 

 on the DCS over natural noisfe is necessary to give a BER of 

 1 in 10~^. This CNR is greater than predicted by equation (2)^ 

 because it takes into account the spin modulation noise which 

 equation (2) does not consider. As mentioned earlier, it is 

 expected that the GOES-D, E, and F generation of satellites will 

 not have spin modulation noise. Lower CNR ' s , which are more in 

 agreement with equation (2), should be usable with these satellites. 



The user should bear in mind that a CNR of 14dB is necessary for 

 a BER of 1 in 10^. If the user requires more accurate data (higher 

 BER), then a higher CNR is necessary. This in turn will require 

 a larger and more expensive antenna and/or lower noise preamplifier. 



Conversely, if a lower error rate is acceptable, a lower CNR is 

 permissible, resulting in a more economical receiving system. 

 Users should, therefore, carefully analyze their BER requirements 

 to ensure that they obtain adequate accuracy at the lowest cost. 



As stated previously, the noise power at the receiver output will 

 be -]53dBm/100Hz and that a CNR of 14dB is necessary for a BER of 

 1 in 10^. Hence, a carrier level of -153dBm +14dB = -139dBm 

 is required. As a signal level of only -169.3dBm can be expected 

 the difference, -139dBm -(-169.3dBm) = 30.3dB, must be made up 

 by using an antenna with 30.3dB. This requires a paraboloidal 

 antenna with a diameter of 2.5 meters and assumes an aperture 

 efficiency of 55 percent, which is typical for antennas of this 

 type. 



If the DCS system is heavily loaded (100 channels transmitting), 

 the received signal per channel will be lOdB lower and an antenna 

 diameter of 3.16 times 2.5 meters = 7.9 meters will be necessary. 

 (Note: The gain of a paraboloidal antenna is directly proportional 

 to its area. Therefore, the antenna gain is proportional to the 

 square of the diameter. Increasing the antenna diameter by 

 /To = 3.16 will increase its area and hence its gain by a numerical 

 factor of 10. This is equivalent to a lOdB increase. ) 



If an uncoolcd parametric amplifier is used instead of a premium 

 grade transistor amplifier, the receiver and antenna noise 

 temperatures are now 50 K +75 K respectively = 125 K. The noise 

 power in a ] 00-Hz bandwidth is now -157.6dBtn instead of -153dBm. 

 This represents an improvement of 4.6dD and a reduction in antenna 



56 



