How to convert from power signal received by Antenna to voltage signal?
The antenna has a design output impedance, usually 50 ohms, it is NOT a voltage source, but appears to be a voltage source in series with a resistor equal to its designed output impedance.... All RF work is better thought of as power transfer rather then voltage transfer as impedance is so easy to change. 

For maximum power transfer you need to have a load that matches the output impedance of the antenna (Graph the power in a load for a voltage source in series with a resistor driving a variable load and you will find that maximum power transfer occurs when the source and load impedance are equal, seriously worth taking the time to do this).
For sources having a complex source impedance the maximum power transfer occurs when the load is the complex conjugate of the source impedance. 

Now one probably could design an antenna to match into 1 ohm, or 0.1 ohm, or 0.01 ohm (But things are getting VERY lossy because of secondary effects), but in all cases the power delivered will be equal (apart from the losses due to poor antenna efficiency), you will see much less voltage and more current as the system impedance drops. 

Consider an antenna with a design output impedance of 1 ohm (Unlikely for all sorts of reasons, but go with it), model it as say a 1.414V voltage source in series with a 1 ohm resistor. Into a matched load (1 ohm) you get 0.707V (Voltage divider) and 0.707A, multiplying these gives you your 0.5W.
If you load this up into 0.1 ohms you get ~0.13V @ 1.3A = 0.169W, hardly an improvement.

Now a free space path loss of only 20dB seems unlikely to me, with a 1m separation and isotropic antennas for example you have ~40dB of path loss at 2.4GHz, and you can add 20dB for every decade of path length, so you might want to look at your numbers.