Now we can say that for a digital accumulator, with a DUMP cycle of 1 ms and input sinewaves with frequencies above 1 kHz, theaverageresults in accumulator contents are zero. And we can say that for sinewaves with frequencies below about 500 Hz, theaverageresult in the accumulator follows the amplitude of the applied sinewave. It should be clear now that the digital accumulators in the GP2021 are acting like lowpass filters with a cutoff frequency of about 500 Hz.
WAVEFORMSSHOWNWITHNEARLYZEROPHASEANDFREQUENCYERRORONVCOWITHRESPECTTOINPUTSIGNAL 0DEG. 90DEG.
I Q LOWPASS CUTOFF~500Hz
LOWPASS CUTOFF~500Hz IFIN@ 1.405MHzVCO
tt
t t RECOVERED50HzDATAININPHASEARM t t
NEARLYZEROOUTPUTINQUADRATUREARM
0DEG. 90DEG.VCO Fig.9.7AnalogmodelofI/Qprocessing
9.4 An Analog Model of the Doppler Loop 181
integer as read from accumulator). By reading the accumulator contents of the Inphase arm, the host computer can recover the 50 Hz data from the GPS SV being tracked.
Now, it is clear that the In-phase arm of our model will demodulate the 50 Hz data as long as we keep zero error on the VCO inphase and frequencywith respect to the incoming signal from the SV. It is not trivial to get from a situation where there are large frequency and phase errors to one where they are quite small, as we shall see.
9.4.2 Adjustable Baseband Bandwidth for Track
Its no coincidence that the accumulators are dumped every 1 ms. As we now know, this results in an equivalent lowpass operation on the mixer output of the Quadra-ture and Inphase arms of the GP2021. Baseband lowpass filters of 500 Hz band-width are equivalent to 1 kHz wide bandpass filters if they are shifted in the frequency domain away from DC.
1 kHz is the bandwidth used in the GPS100SC receiver at the 10.7 MHz crystal IF filter. A 1 kHz bandwidth Bandpass filter or equivalently 500 Hz for baseband processing is a good bandwidth for capture of the GPS signal. But it is not the optimum bandwidth once the GPS signal is captured and tracked in Code and Doppler.
Once tracking is achieved it is quite desirable to “tighten up” the receiver bandwidth. With the GPS100SC, this not possible as the IF bandwidth is fixed.
With the GP2021, it is possible to reduce the bandwidth of the equivalent lowpass filters implemented by the 16-Bit accumulators. Adding two successive accumula-tor results together can do this. If this is done, we have halved the bandwidth of the equivalent lowpass filters. This illustrates how easy it is to adjust the bandwidth of the GP2021 signal processing at least at the level of the host-computer processing.
9.4.3 Doppler, Code Scan, and Threshold Detects
As with the GPS100SC receiver, the GP2021 must scan the possible Doppler offsets until the signal falls inside its 500 Hz lowpass filter. Commanding ramp type frequency values to the Doppler DCO does the scan operation. The software monitors the combined signal level in the I and Q arms while scanning Code and Doppler. If a predetermined threshold is exceeded, then C/A Code and Doppler tracking are initiated. This process is essentially identical to that of the GPS100SC.
The thresholds are set in software, which is an advantage as it allows them to be adjusted for changing signal conditions if needed.
182 9 The Zarlink 12-Channel GPS Receiver
9.4.4 Doppler Acquisition and Track
Previously, we assumed the Doppler loop was “locked on” to the applied GPS signal. But how can we use our model to explain how the VCO can be commanded to the correct frequency and phase?
This is not an easy question to answer. The methods used to “pull in” the VCO are usually different than those used to command the VCO once track is established.
Looking at Fig.9.8, we can see that when the VCO frequency is significantly off the output of the lowpass filters in each arm are fairly complex signals. And we have simplified them by assuming an analog model and that the C/A code was not present!
Generally speaking, in “lock” the energy in the Inphase arm is at a maximum while the energy in the Quadrature arm is at a minimum. By steering the VCO such that this condition is achieved the phase and frequency of the VCO will move toward synchronism with the applied signal. But this can be problematic.
Another approach is to use the lowpass filter outputs to estimate the angle between the VCO sinewave and the applied GPS signal sinewave. The inverse tangent function can be used to estimate the angle between the two sinewaves. The ratio of the accumulator values in the Inphase and Quadrature arms provide input to the arctangent function. This results in a computed, estimated angle. From the angle information, an error signal is derived and applied to the VCO so as to drive this angle toward zero.
These two methods rely on the host computer to read the accumulated data every 1 ms and properly process it. The most difficult part of this process is transition between SCAN and TRACK particularly for the Doppler loop. We will return to this discussion after a more detailed look at the waveforms of Fig.9.8.