Hi Ralf
I don't think the Arduino UNO has the performance to carry out the DSP required to demodulate, AGC, etc of the IQ signals.
I did experiment a couple of years ago with using a Teensy 3.2, together with the Teensy Audio Adapter with the Elektor SDR as the RF front end to make a standalone Elektor SDR Receiver. The Teensy has the horsepower required for the demodulation and much more, but I have to say I lost interest and let the project slide, so it never got completed or even close to a public release.
You should take a look at Frank, DD4WH's Github Repository for a Teensy 3.1 based SDR ?
73
Peter