Say, some alien just wanted to mess with us, but doesn’t invade, or even care enough to want to kill us, but seeing how everyone is on their phone all the time, they decided to just jam all our radios to watch us suffer. Their transmitting power they use is so powerful, its jamming signals are 1000 times stronger than the strongest radios we have, so there’s no way we can overpower the jamming.
What does the immediate aftermath look like?
What does it look like in the long term?
(Please don’t say “kill the aliens” they have tech so advanced, its impossible to do it)
Strongest (declassified) radio transmitter is (likely) the Eglin AFB Site C-6. https://en.wikipedia.org/wiki/Eglin_AFB_Site_C-6. Peak radiated power is 32 megawatts, it operates at a bandwidth of 10MHz.
32MW is about 105dBm. Times 1000 will add 30 dB, so the alien transmitter will be at least 135dBm, which corresponds to 32GW.
Given the Friis Transmission Equation, 135dBm with a transmit antenna gain of 1dBi, at a distance of 12,756km (diameter of earth), a receive antenna with a gain of 1dBi, will receive a signal of: 22.44dBm at 1MHz, 2.44dBm at 10MHz, -17.56dBm at 100MHz, -37.56dBm at 1GHz, -57.56dBm at 10GHz, adding an additional 20dB of loss per decade. This is completely ignoring all effects like atmosphere and ionosphere, signal traveling through or around the earth, reflections, any funky propagation, or constructive/deconstructive interference patterns that may occur. Also ignoring antenna gain.
A rule of thumb is that the signal-to-noise ratio (SNR) should be at least 5x (or about 7dB) in general and some digital modes will tolerate it. 20dB is usually the minimum recommended in general, with 25dB or more being recommended for voice.
AM radio at about 1.5MHz will still work- but only for about 1km from the tower. At this point the AM signal from a 100kW transmitter would be about 46.03dBm for a specially designed antenna and receiver, but the noise level would be about 22.44dBm. Realistically, AM will not work and may even blow out a receiver front-end. Television at about 88MHz will be usable for only about 1km using a specially designed receiver, normal TV likely won’t work at all.
GPS is around 1.5GHz and the typical levels received are about -130dBm. Our noise is about 90dB or 1,000,000,000 times stronger than the received signal. No chance of GPS working at all. Wifi is around 2.4GHz or 5GHz and a “perfect” signal is about -30dBm. The received noise at 2.4GHz would be about -45.17dBm, and at 5.6GHz this would be -52.53dBm, so feasible that wifi could still work if you are close to your router/antennas.
Cell Phones have an extremely wide range of frequencies. On the lower frequency end, they likely won’t work. For something like K band at 10GHz, the phone itself would be transmitting about 33dBm. At a distance of 2 km, the cell tower will be seeing about -83dBm from your phone, while the the noise received will be far higher at about -57dBm.
Lastly, Submarine communication is typically done at ELF (3-30kHz). They typically need about a whole power station dedicated to powering it, and the effective transmitted power will be something like 5 watts or less. A submarine at 100km might pick up a signal of -2.99dB on the surface (realistically, far far less when submerged due to sea-water attenuation). The noise level on the surface from noise would be 52.9dBm.
This is all assuming that somehow, the aliens have a perfectly efficient wide-band transmit antenna. And have landed on earth with their super transmitter. And all of these numbers assume that max transmit power takes up the same bandwidth as the signal of interest.
In practice, the aliens would want to be far away from us. No closer than the moon, let’s say. And they probably will want an array surrounding the earth to maximize line-of-sight. To maintain the previous numbers, they would need an additional 25dB of transmit power. And probably an additional antenna on a ship, opposite to earth from where the moon is. So that’s an additional 3dB of power required (x2 for 2 antennas).
They could probably knock off about 20dB if they used high-gain antennas. But let’s say they use that power to further overwhelm earth’s ability to use radios, even for edge-cases.
They would require 163dBm- about 20TW of power. To jam a single frequency listed above.
Let’s say to jam the TV station, they were broadcasting over a bandwidth of 6MHz. That gives a power-spectral-density of 3.4MW/Hz. To cover the entire spectrum at the same time, say 10kHz to 300GHz, they would need just over 1 exawatts. 10^18 watts. That’s a lot of power! They could use a partial dyson sphere with the sun, but we could say the aliens are nice enough to still allow the sun to illuminate the earth and other planets to keep everything else the same.