Listening slowly

The phrase “too faint to hear” hides several different problems. Perhaps the receiver cannot distinguish a carrier. Perhaps it can detect the carrier but cannot recover the data reliably. Perhaps it can do both, just not at the rate somebody would like.

Those are different entries in a link budget. There is no single volume knob marked deep space.

The part a large dish buys you

NASA’s Deep Space Network includes 70-metre and 34-metre antennas. The larger diameter is not just a visual statement. For comparable aperture efficiency at the same wavelength, collecting area scales with diameter squared. ^[1]

That is my idealised area comparison, not a specification for the relative performance of two actual DSN receivers. Feed losses, efficiency and system noise temperature matter. Still, the calculation explains why building a bigger receiving aperture is useful when the transmitter is inconveniently far beyond the reach of a maintenance visit.

Distance works against you in the familiar inverse-square way in a free-space link with fixed antenna gains. Double the range and received carrier power falls by a factor of four, or about 6 dB. Do not confuse that with propagation delay. A signal can be weak and quick, or strong and late. Deep-space missions get the inconvenient combination.

Spend longer on each bit

For received carrier power C, bit rate R_b, and noise spectral density N₀, energy per bit relative to noise density is:

Holding the other terms fixed, halve the bit rate and you double the energy available per bit: a 3 dB improvement. Whether that is enough depends on modulation, coding, the required error rate and implementation losses. This equation does not promise you can decode any arbitrarily faint signal merely by waiting.

It also assumes the receiver can acquire and track the link. Pointing errors, frequency uncertainty and changing conditions can make that an engineering problem of its own. A lovely number for energy per bit is of limited comfort if you are looking in the wrong place.

I like the fact that patience has a numerical value here. There are days when engineering advice amounts to “do less, more carefully”, and radio communications has at least had the decency to put units on it.