As receiver temperatures get better, we may reach a point in which atmospheric and spillover noise dominate system noise such that further reductions in receiver noise result in insignificant improvements in sensitivity. In terms of the equations presented above, we can prescribe a practical performance goal, at least parametrically. The DSB noise temperature of the ultimate receiver when using the Planck equation to express physical temperatures as equivalent radiation temperatures is given by Kerr, Feldman, and Pan in MMA Memo 161 as
The question is how close do we need to get to this limit
before further improvements are insignificant in terms of integration
time. To parameterize the problem, let us define an ``acceptable''
integration time (
) representing the time necessary to achieve an
arbitrary sensitivity and define an ``ultimate'' integration time
required for a quantum-limited receiver (
), but in the presence
of atmospheric and spillover noise. Let ``n'' be the performance
degradation we consider acceptable. An appropriate value for this
factor might be 2.
From the system temperature equation (Equation 1) and the radiometer equation (Equation 13),
where we are assuming that the observation is made in SSB
mode but that 
is a DSB receiver noise temperature. Solving
for 
, we find
