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Radios
It is entirely possible to do this with just an RTL-SDR dongle and nothing else. You may struggle with LRPT a bit, but APT is a doddle. Sometimes the dongles are a little lacking in gain for LRPT unless it’s a really good pass.
Moving up to a better, more sensitive SDR with higher bit resolution would definitely help. The Airspy kit looks good, MM3IIG and M7SMU swear by their RSP1As which seem to do a better job of picking the weaker low-angle signals out of the noise than the dongles with their poor front ends.
If you’ve got a hardware receiver that can do this then great! Especially if you’ve got CAT control for Doppler. Beyond the scope of this guide, though.
And finally remember: you can’t do this with a handheld and out to an audio jack as the 25 kHz bandwidth won’t be wide enough for even APT. MM3IIG tried it, and got a discernible image but without all of the required information for enhancements and using the full sensor data.
Low Noise Amplifiers
For APT if you have a good line of sight and decent antenna you really, really don’t need an LNA. For LRPT: maybe. With overhead passes from about 60-90 degrees you shouldn’t need one. The signal has a lower power density because of the wider bandwidth and similar power to APT. Overhead passes should give you an SNR of around 10-15 dB and up with an RTL-SDR dongle, which should easily be enough for demodulation. For lower passes you may find you lose data and sync occasionally unless you have a decent LOS and a well-tuned/aimed antenna.
If you move away from VHF to higher bandwidth/frequency signals later on then you’ll definitely need to look into one, (as well as bandpass filters appropriate for the band) and don’t forget they’ll need power (through whatever method required). Check the current draw and that your power method or SDR can actually provide enough.
The Nooelec stuff is all great and well-supported, and if you're feeling lucky there are suppliers on AliExpress who do clones of the combined LNA/BPF boards. Remember to check how you'll power the LNA (USB or Bias-T) and that you have enough current to do it.
Bandpass Filters
These can be useful, particularly if you are plagued by intermod on your SDR. LRPT works best with a decent amount of gain, so by suppressing those signals out-of-band you’ll get less issues when you turn it up. You can buy some that work between 136-138 MHz or build your own if you’re savvy. Also useful if you have other RFI in the area and can’t operate from the middle of a big empty field. Just check the specs first and make sure they do what you need.
This also applies to those weaker signals at lower angles (for both APT and LRPT). Sometimes you’ll want the gain up to help and that lets the intermod in. Filtering before gaining up will mean your radios front end won’t have as many issues with other signals interfering.
Here's a good resource on making a filter with the kind of materials you may have lying around (standard capacitor values, etc): https://lucasteske.dev/2016/11/137mhz-bandpass-filter-for-noaa-meteor-satellites/
You may well decide that a certain signal is so powerful that you want to use a notch filter to remove it instead, of course.