It's been 3 years since I wired mine, but let me see if I can help. You didn't mention if you're using the standard European ISO connectors or some proprietary OEM wiring, and didn't mention if your radio has a Aux detection circuit like mine. This would help troubleshooting the wiring configuration.
- When playing a blank sound, I can hear that the left channel is lower and more noisy than the right one. I've rewired the parrot line-out to the radio line-in twice, no change. Since the signal/noise ratio is good when playing media stuff, this is not the biggest problem.
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- Parrot line-out to car line-in. I wired the radio line-in ground to a car bolt as the parrot don't give explicit ground. It's maybe a mistake, I should remove or change this wire.
Your line in ground is absolutely wrong and should be undone immediately. "Ground" is always relative; the audio signal is the relative difference between the positive and negative/ground wires. Connecting to a different ground will result in either louder or quieter audio. Connecting to a random car bolt will definitely add noise and engine whine. It is probably the source of the left/right problem. Worst case is that you're shorting something and going to fry your Parrot.
Just so we're clear, the Parrot line in has 4 wires: a black/red pair and a brown/white pair. Your radio's line in should have either (1) 4 matching inputs, either separately or as a left/right pair of RCA plugs, or (2) only 3 inputs, being a left, right, and shared ground, like you find in an Aux jack or headphones. If you only have 3, then join both L/R grounds from the Parrot (IIRC, the black and the brown) to the radio's line in ground.
The ground for the Parrot's power is a different black wire running along side the red and orange 12V power lines. These 3 wires go from the black male Parrot Molex connector to the gray male power ISO connector. If you're using these standard ISO power connectors, then your Parrot should already grounded. If not, then that's the ground you need. You can connect it to a car bolt, just be sure to remember your article about ground loop.
- Phone call is not really working, I can launch a call using voice recognition but during call, I hardly hear the other people, even with all sound volumes to the max. I can hear huge whine (not surprising). In the same time the other people won't hear me, even if I shout.
I have absolutely no idea on this one. If streaming music is working OK, then calls should work, too, especially the mic. The only thing I can think is that pulling the line in to ground is shorting the call/mic circuitry. Fixing line in ground
might fix calls.
- parrot's mute : anyway, I don't see how this cable could be useful, as I doubt the car will switch to the aux input when the mute signal is fired... On the parrot's schema the mute is wired for the "line-in setup", but I wonder how it works.
The yellow mute coming from the Parrot connector is what I used to tie into the Aux connect/disconnect circuit, which automatically switches to Aux for me. I got lucky in that the Parrot mute pulls to ground when active, and so does my detection circuit.
If you don't have a similar detection circuit
and you're using your radio's line in, then you should
not hookup the mute. With the line in wiring, the Parrot uses the radio to play audio, but if radio mutes whenever the Parrot sends it audio...
As you were talking about ignition, in my case the big problem is that my 12v lighters are powered only when the engine is on, so it's very very annoying to make tests (during first install I used a custom extra wire, but now everything is secured). I'd like to get an ignition coming from the radio, as you suggested.
Most modern car radios should have a remote power. Just Google for your radio's wiring diagram.