Inverse Square Law: Explaining Reduced Data Rate w/ Distance

[Drakkith]

Quoting from Wiki, bolded section mine:

Because of the inverse-square law in radio communications, the digital data rates used in the downlinks from the Voyagers has been continually decreasing the farther that they get from the Earth. For example, the data rate used from Jupiter was about 115,000 bits per second. That was halved at the distance of Saturn, and it has gone down continually since then. Some measures were taken on the ground along the way to reduce the effects of the inverse-square law. In between 1982 and 1985, the diameters of the three main parabolic dish antennas of the Deep Space Network was increased from 240 feet to 270 feet, dramatically increasing their areas for gathering weak microwave signals.

What exactly is going on here with the data rate? Is it just the strength of the signal that is falling off as distance increases? If so, how does that reduce the data rates that can be used? If not, what limits the data rates?

 

[Vanadium 50]

The farther away a source is, the weaker its signal, and the longer one needs to listen to determine whether a 1 or 0 is sent, so the slower the data rate has to be.

 

[Drakkith]

The farther away a source is, the weaker its signal, and the longer one needs to listen to determine whether a 1 or 0 is sent, so the slower the data rate has to be.

Can you elaborate on this?

 

[Vanadium 50]

What part is unclear?

 

[Drakkith]

What part is unclear?

How listening longer helps you tell if it's a one or a zero. Something to do with how the carrier frequency is modulated?

 

[Baluncore]

This is a statistical sampling effect. The further the signal is below the noise floor, the longer you must integrate to raise the signal or lower the noise. Integration time is a square law. To change the Signal to noise ratio by a factor of two takes four times longer. This is compounded by the range inverse square law.

 

[Drakkith]

Ok, I see what you're getting at.