Interference, Multipath, and Scintillation - Understanding GPS: Principles and Applications - page 251

flash ADC, then the digital sampling process can follow the A/D quantization pro-
cess. If the quantization process is sequential (time-consuming), as in a successive
approximation ADC, then an analog sample-and-hold (zero-order-hold) process
must precede the A/D quantization process in order to hold the sampled analog sig-
nal constant until the quantization process completes.
The sampling process always introduces aliasing noise into the digitized signal
because it is impossible to completely filter out higher frequency components to
fully comply with the Nyquist sampling theorem. The Nyquist sampling theorem
says that all information is contained in the sampled data if the continuous analog
data is sampled at twice the highest frequency content of the data. For example, if
there is no frequency content beyond B S -Hz bandwidth of a given signal, then sam-
pling this signal at 2 B S Hz preserves all of its information and there is no aliasing.
Obviously antialiasing filtering can only “reduce” the levels of the higher frequency
signal components outside of B S Hz to an RMS level that is small but not zero. These
low-level out-of-band signal components are all aliased (folded back) into the
in-band signals by the sampling process. Once aliased, no postprocessing technique
can remove this noise.
A common misunderstanding is the belief that B S Hz is the passband B P of the
desired GNSS signal (buried in noise), when, in fact, B S Hz is the (much wider)
stopband (i.e., the bandwidth at which the undesired higher frequency signals,
which may or may not be buried in noise, have all been reduced by the antialiasing
filter to a low level). For P(Y) code, the usual assumption is that the front-end band-
width B P should be about twice the spreading code rate, or 20 MHz. Since there is
zero P(Y) code energy at the spreading code rate frequency nulls, there is less than
0.1 dB loss of additional signal-to-thermal-noise ratio incurred by using a very
sharp cutoff bandpass filter of 17 MHz. Assuming the stopband, B S , for the
antialiasing filter is achieved at 25 MHz, this implies a sample rate of R S = 50 MHz,

not 34 MHz. Contrast this with the 20-MHz passband case with the same
antialiasing filter roll-off rate, resulting in a stopband of 28 MHz and R S = 56 MHz,

not 40 MHz. The 17-MHz bandwidth design choice is an excellent tradeoff to
reduce the ADC sampling rate with negligible increase of antialiasing filter imple-
mentation loss.
It is common practice in high-end commercial C/A code receiver designs to
widen the front-end bandwidth in order to operate them with narrow correlators
for improved pseudorange accuracy in thermal noise as well as to mitigate
multipath effects. In this case, the front-end bandwidth and ADC sample rates must
both be increased to include multiple C/A code sidelobes.
Misunderstanding of the fundamental requirement for ADC sampling rate based
on the stopband of the antialiasing filter can result in tens of decibels of aliasing
noise. For a well-designed GNSS receiver, the antialiasing filtering and the sampling
rate are both appropriately designed so that the effect of aliasing noise is negligible.
The quantization process introduces additional interference into the signal in
the form of quantization noise and clipping noise. The quantization noise is caused
by the finite amplitude resolution as defined by the least significant bit in the ADC.
The clipping noise is related to that portion of the analog signal amplitude that is
beyond the peak-to-peak value of the reference voltage range of the ADC. If digital
frequency excision or frequency domain search techniques are used following the