[time-nuts] Truetime XLi sat signal levels (dBW to dBc/SNR conversion question)

[David I. Emery]

On Fri, Jun 14, 2019 at 01:05:21AM +0000, Mark Sims wrote:
 
	Since nobody else has stuck their neck out to speculate... I
will.

	I do not pretend to know for sure exactly what TrueTime means.

> Pretty much all GPS receivers report sig levels in dBc or SNR type
> values in the range of around 20 .. 50.   The Truetime XLi reports them
> in dBW with a range of around -196 to -145 dBW). 

	That of course is -166 dBm to -115 dBm

	But you know that.

>    Does anybody know how to convert the dBW values into something more
> in line with standard dBc or SNR values?  The conversion does not need
> to be exact, it just needs to be reasonable looking...

	As I understand the dBc values,  they are the signal power after
despreading of the 50 symbol per second underlying 50 baud BPSK almanac
in the appropriate approximately 50 Hz bandwidth it occupies compared
to the thermal (or also spread interference) energy in that same
bandwidth. Thus 20 dBc would be despread 50 baud BPSK energy 20 db over
the noise in the relevant approximately 50 Hz BW (depending on filter
rolloff).

	This is probably actually calibrated as Eb/No of the despread 50
baud almanac signal.

	This of course is a ratio of signal to noise and interference
and not directly related to actual signal power coming out of the
antenna which depends on antenna gain, and feed losses and cable losses
and so forth.

	There is also absolute power per square meter (flux density),
but any measurement of that would depend on antenna, LNA, filter, cable,
GPS receiver front end  gains and losses and noise temp which would not
in general be the same from installation to installation and a measure
of this would require calibration of those things for that installation.

	One possible interpretation of what Truetime is using is the
noise density per root Hz compared to that from a 50 ohm termination at
room temperature.   Obviously a 50 ohm system terminated in a 50 ohm
load has -174 dBm/Hz at 290K and the lower end of their scale at -166
dBm is 8 db above this, which I understand is about the theoretical
threshold (BER of 10**-5) for the 50 baud BPSK in Eb/No.   What this
implies is that despread, the input signal power density/Hz  inside the
despread signal bandwidth would be -166 dBm/Hz (8 db Eb/No with No being
-174 dBm).

	Now in actual reality the effective noise temp of antenna and
filter, and sky and environment and LNA is probably not 290K exactly... 
I'm not familiar enough with this as respects GPS to be sure what would
be considered normal for a typical or even theoretical deployed antenna.

	I would however expect that the True time dBW numbers would track
Eb/No measures on other receivers starting at some base offset...
and it seems likely perhaps that the 8 db Eb/No point for other receivers
is -166 dBm or -196 dBW on their scale.

	This would be related to actual power density/Hz across the signal
at L1 (or whatever)   by the process gain.. 50/1023000 or 43.1 db.

	In other words at the point where the BER of the 50 baud almanac
gets up to around 1 error in 10**5 bits the effective signal power/Hz from
the spread GPS signal on a zero gain hemispheric antenna would be (-166
- 43.1) dBm/Hz or -209.1 dBm/Hz 

	But what do I know.   Perhaps someone who does will answer.


-- 
  Dave Emery N1PRE/AE, die at dieconsulting.com  DIE Consulting, Weston, Mass 02493
"An empty zombie mind with a forlorn barely readable weatherbeaten
'For Rent' sign still vainly flapping outside on the weed encrusted pole - in 
celebration of what could have been, but wasn't and is not to be now either."