Well, you want the series capacitor to pass RF at 1.6 GHz with as little 
attenuation as possible, while you want the choke to have the highest 
impedance possible at 1.6 GHz.  Obviously just about any capacitor would 
block DC, and any choke would pass DC, so it's the AC characteristics that 
matter.  However, no components are ideal, so the capacitor has inductance 
and the inductor has capacitance, and these can be important at 1.6 GHz.

First, the capacitor.  It needs to have an impedance at 1.6 GHz that is 
significantly lower than the 50 ohm characteristic impedance of the 
transmission line.  Considering capacitance alone, anything from about 47 pF 
or larger should do.  But as the capacitance increases, the parasitic 
inductance usually increases too, and you want to minimize that.  So the 
smaller the capacitor the better - physically smaller.  That's why I suggest 
47-100 pF surface-mount ceramic, for minimal inductance.

Now, the absolutely *ideal* pass capacitor would have just the right 
capacitance *and* inductance to be series resonant at 1.575 GHz.  This 
perfect capacitor would have near-zero impedance at that frequency because 
of the resonance.  It would have *lower* impedance than a larger capacitor. 
And that's why I suggested 47 pF, because some guesses about inductance 
suggested that it would be closer to being series resonant than a 100 pF cap 
would be.  On the other hand, I have no test equipment to measure this.  If 
a larger cap passes more signal for you, then it's clearly a better choice.

You do want to make sure that the self-resonant frequency of the cap is 
*above* the operating frequency, if you can't put it *at* the operating 
frequency.  A capacitor behaves like a capacitor below resonance (i.e. 
impedance decreases with increasing frequency), but it behaves like an 
inductor above resonance (increasing impedance).  This shouldn't be hard if 
you stick to ceramic chip caps in the 100 pF range.

The inductor should have enough inductance not to load the RF signal, 
ideally 500 ohms or more at 1.575 GHz.  The inductor I described should meet 
that.  Again, the *ideal* choke would have just enough parasitic capacitance 
to be parallel resonant at 1.575 GHz, giving nearly infinite impedance at 
that frequency, and that's what I aimed for when choosing diameter and turns 
and spacing (as well as easy construction, of course).  But again I just 
have some mathematical models of chokes to work with, no test equipment.

Again, you want the choke's self-resonant frequency to be above the 
operating frequency, since it behaves like a choke below resonance and like 
a capacitor above resonance.  You probably want to avoid commercial chokes 
because they all have inductances much higher than needed (i.e. 1 mh).  
These probably have resonant frequencies in the MHz, and are capacitive at 
1.6 GHz.

All the active antennas I've taken apart don't use a discrete coil for the 
RF choke at all.  They just use a narrower trace than the signal (so the 
characteristic impedance is 100 or 150 ohms just from that, and most signal 
is reflected at the junction with the 50 ohm path).  Then the designer adds 
a number of zig-zags in the trace to increase its inductance.  If you have a 
reasonable way of designing and etching PC boards, that's a simpler way to go.

        Dave