I tinker with software radio as a hobby and I am stuck solving a very basic problem. But first, a background exposition.
Bdale, what have you done to me
Many years ago, I attended an introductory lecture on software radio at a Linux conference we used to have - maybe OLS, maybe LCA, maybe ALS/Usenix even. Bdale Garbee was presenting, who I mostly knew as a Debian guy. He outlined a vision of Software Defined Radio: take what used to be a hardware problem, re-frame it as a software problem, let hackers hack on it.
Back then, people literally had sound cards as receiver back-ends, so all Bdale and his cohorts could do was HF, narrow band signals. Still, the idea seemed very powerful to me and caught my imagination.
A few years ago, the RTL-SDR appeared. I wanted to play with it, but nothing worthy came to mind, until I started flying and thus looking into various aviation data link signals, in particular ADS-B and its relatives TIS and FIS.
Silly government, were feet and miles not enough for you
At the time FAA became serious about ADS-B, two data link standards were available: Extended Squitter aka 1090ES at 1090 MHz and Universal Access Transciever aka UAT at 978 MHz. The rest of the world was converging quickly onto 1090ES, while UAT had a much higher data rate, so permitted e.g. transmission of weather information. FAA sat like a Buridan's ass in front of two heaps of hay, and decided to adopt both 1090ES and UAT.
Now, if airplane A is equipped with 1090ES and airplane B is equipped with UAT, they can't communicate. No problem, said FAA, we'll install thousands of ground stations that re-transmit the signals between bands. Also, we'll transmit weather images and data on UAT. Result is, UAT has a lot of signals all the time, which I can receive.
Before I invent a wheel, I invent an airplane
Well, I could, if I had a receiver that could decode a 1 megabit/second signal. Unfortunately, RTL-SDR could only snap 2.8 million I/Q samples/second in theory. In practice, even less. So, I ordered an expensive receiver called AirSpy, which was told to capture 20 million samples/second.
But, I was too impatient to wait for my AirSpy, so I started thinking if I could somehow receive UAT with RTL-SDR, and I came up with a solution. I let it clock at twice of the exact speed of UAT, a little more than 1 mbit/s. Then, since UAT used PSK2 encoding, I would compare phase angles between samples. Now, you cannot know for sure where the bits fall over your samples. But you can look at decoded bits and see if it's garbage or a packet. Voila, making impossible possible, at Shannon's boundary.
When I posted my code to github, it turned out that a British gentleman by the handle of mutability was thinking about the same thing. He contributed a patch or two, but he also had his own codebase, at which I hacked a bit too. His code was performing better, and it found a wide adoption under the name dump978.
Meanwhile, the AirSpy problem
AirSpy ended collecting dust, until now. I started playing with it recently, and used the 1090ES signal for tests. It was supposed to be easy... Unlike the phase shift of UAT, 1090ES is much simpler signal: raising front is 1, falling front is 0, stable is invalid and is used in the preamble. How hard can it be, right? Even when I found that AirSpy only receives the real component, it seemed immaterial: 1090ES is not phase-encoded.
But boy, was I wrong. To begin with, I need to hunt a preamble, which synchronizes the clocks for the remainder of the packet. Here's what it looks like:
The fat green square line on the top is a sample that I stole from our German friends. The thin green line is a 3-sample average of abs(sample). And the purple is raw samples off the AirSpy, real-only.
My first idea was to compute a "discriminant" function, or a kind of an integrated difference between the ideal function (in fat green) and the actual signal. If the discriminant is smaller than a threshold, we have our preamble. The idea was a miserable failure. The problem is, the signal is noisy. So, even when the signal is normalized, the noise in more powerful signal inflates the discriminant enough that it becomes larger than the discriminant of background noise.
Mind, this is a long-solved problem. Software receiver for 1090ES with AirSpy exists. I'm just playing here. Still... How do real engineers do it?
UPDATE: I bought the Pearson book, but found nothing in it about correlators. So, I tried everything I could come up with on my own, including a correlator that subtracted (thus computing the area under the difference). Absolutely nothing worked. I guess I just suck at applied mathematics. In the end, I gave up on math and programmed a high-low water comparator and that worked beautifully. The final version is split between the main loop in main.c and the comparator in pre.c.