I think that's specifically true when you're pointing a radar at an aircraft, but is not true for radar altimeters.

When you're pointing a radar at an aircraft, the angular size of the aircraft is 1/r^2, so 1/r^2 of the emitted radiation hits the aircraft. Once emitted from the aircraft, the angular size of radar receiving dish is 1/r^2, so 1/r^2 of that radiation is detected.

With a radar altimeter, you're pointing the radar at the ground. The angular size of the ground is 50% of the sphere, whether you're one foot above the ground or 100,000 feet. (...ok, maybe it's like 49.5% of the sphere...) As long as you're pointing it down-ish, 100% of the emitted radiation hits the ground. There is only one 1/r^2 relationship, on the return leg.

This fixed angle paints a larger and larger circle as altitude increases. If you double your altitude, you quadruple the size of the surface that's reflecting radar back at you.

A bunch of stuff cancels out and you end up with 1/r^2 at the receiver, which is what we started with.

But they’re not broadcasting to the whole sphere either, because the radar instrument is not an isotropic radiator. That antenna has gain. It’s louder / more sensitive in a specific direction. Probably by a lot. You can’t make perfect antennas, but you don’t need any signal at all from most of the sphere, so you can gain many decibels.

The angle of the beam you do have is probably fixed, and being fixed would imply that the area swept by the core of the beam is indeed proportional to the square of the altitude. But I don’t think two trips through an n^2 distance is n^4 unless I’m missing some of the physics. Shouldn’t it be (2n)^2 and this still proportional to the square of the altitude not to the hypercube? (And affected by scattering and bad reflectivity from the terrain, which seems likely to be independent of altitude?) This is different for detecting random entities in free space where most of the first n^2 trip really is lost.

So it’s like you say but for different reasons??!?!

As I keep repeating here, if excessive or debilitating interference is being experienced between services under normal operating conditions then there has been a failure of Spectrum Management planning - absolutely no question about it.

OK, we know such interference has happened, so who was responsible for the planning fuck-up?

I've no argument about filters, RFI etc., what most are saying about the engineering issues makes sense.

My argument is that the spectrum planning has failed and that much of the reason can be put down to deregulation in the 1980s when many governments essentially washed their hands of Spectrum Management (succumbed to commercial pressures and overly loosened engineering standards and now we're paying the penalty).

It seems to me (given the international nature of the problem with non-US registered aircraft flying into US airspace, etc.) that we need to go back to the core of the problem and acknowledge these past 'regulations' errors before the problem can be fixed properly.

Perhaps all radar altimeters will have to be changed (respecified with much tighter filters, better intermod figures, etc.) but given the fuck-up who should pay? After all, it's not the FAA's fault nor that of the aircraft industry (see my comments in other posts about the ITU and WRC).

As I see it, this is a political issue, not a technical one.