[skew]

Have any of these articles included hard numbers?

These slides say GPS received power is around -160dBm http://www.ima.umn.edu/talks/workshops/8-16-18.2000/van-dier...

I see unsourced claims LightSquared signals would be around -70dBm, which is at least roughly consistent with LTE.

If so, that's a signal 1,000,000,000 stronger than the satellite-to-ground signals LightSquared's band was allocated for, immediately adjacent to the GPS band (10 or 20 Mhz apart, near 1.5Ghz).

Is there some reason it's not totally ridiculous to expect GPS receivers to be engineered for that kind of noise?

[jacquesgt]

A first order filter will attenuate at a rate of 20 dB per decade away from its cutoff frequency. For example, at a frequency 1000 times higher than its cutoff frequency, a first order filter will attenuate by 60 dB.

An n-th order filter will attenuate at 20*n dB per decade.

Let's assume based on your numbers the GPS band is 20 MHz away from LightSquared's 1.5 GHz-ish band. That's log(1.52/1.5) = 0.00575 of a decade.

We need 180 - 70 = 110 dB of attenuation to push the LightSquared signal amplitude well below the GPS signal amplitude. Solving for n above, 1/0.000575 x 110/20 = 956.

An order 956 filter is not something you can design for a buck or two. It's certainly not something you would design if you expected to filter out other space-based -160 dBm signals. Plus, the numbers above are very aggressive. You're going to need to do even better if you don't want to distort the signal you care about.

[ec429]

According to the article, the interference is 86dB above the GPS signal (400mn.×). Wikipedia gives figures of 60-80dB. The LightSquared band is from 50MHz to 16MHz below the GPS L1 band, which as a percentage of 1.5GHz is from 1% to 3%. This is not very far away, and 86dB is a lot. I don't think it's reasonable to expect any equipment to have that kind of selectivity; after all, high-Q filters are not only expensive, they are often also heavy and bulky.

Also there is an upper bound on filter sharpness given by the latency constraints (GPS needs accurate timing, and a brick wall filter has infinite latency) but that bound's probably not even being approached here; I don't have hard data on GPS signal latency requirements nor a simple formula relating rejection to latency.

[jleader]

From the 2nd page of the article, quoting from the "Technical Working Group" (which supposedly included representatives from both LightSquared and the GPS industry):

"the interfering signal at a distance of 500 feet from the [cell] tower [was] up to 800 billion times more powerful than the distant GPS signals being received from space,"

and a mile away power levels were "400 million times those of the GPS signals."

That's a difference of ~87 to 120 dB, which seems consistent with the 90 dB difference you cite.

(edited: s/LightSpeed/LightSquared/)