# sampling frequency of GPS

Now I am trying to design FIR based adaptive filter for rejection of Jamming in GPS device. (just self-learning purpose, Jamming is simple tone)

I've designed NOT-BAD performance adaptive filter for low sampling frequency. (~44100 Hz)

But when I use this adaptive filter for high sampling frequency (16 MHz), transient width of filter is greatly increased. (I think it is sure because transient width is proportional to 1/degree)

Since it is self learning purpose, I just want to know how big sampling frequency of normal GPS signal for digital filtering is.

If it is not so high as above, I'll quit this design and concentrate on other issues(quantization error etc).

If sampling frequency of normal GPS signal is high as above, I'll study more about that issue.

So, my question is :

How high sampling frequency of normal GPS is ?

Thank you.

• Why adaptive filter? Just use a band pass around the center frequency of the GPS signal before getting the phase difference. The sampling frequency in your case, since you assume a jamming tone, need to be twice the jamming tone frequency (assuming it could be higher that the GPS frequency). This will allow you to nicely filter the jamming out. Your filter is designed based on how close you anticipate the jamming frequency to the GPS one.
– Moti
Aug 8, 2015 at 3:03
• @Moti Thank you for your comment. I've already use BPF for getting signal with center freq = 4MHz, band width = 2MHz. Since Jamming frequency can be in this band [3MHz, 5MHz], I used adaptive filter. (Jamming frequency is totally unknown). Aug 8, 2015 at 3:11
• Do you know the specific carrier you look for? As far as I understand a GPS signal is very narrow frequency. You want to filter out the jamming with a simple filter around the specific GPS carrier.
– Moti
Aug 8, 2015 at 7:10

C/A code (the main civilian channel as of now) has a main lobe of around 2MHz and depending on how much processing you want to do, it is normally sampled in the low MHz range, which you are in. (you could pull it off with 2-5MHz).

Do know that the signal must be mixed down to a lower frequency before you sample it. The original signal is at 1.57GHz.

The frequency response of a BPSK signal is a sinc and therefore it's infinite. Most of the energy though is concentrated in the first null-to-null lobe. Here in this picture you can see the a rectangle representing a BPSK pulse and its transform. The rectangle in this example lasts 200 samples and the sampling frequency is 1000. So the amplitude of the first lobe is 5Hz at (complex) baseband and 10Hz at (real) IF. If we sampled only at 5Hz at baseband (or 10Hz at IF), that would be like applying a window of 5Hz in the frequency domain, in red in the second picture. The effect in the time domain would be a smoothing of the original rectangle and a loss of signal power. Because GPS signals are autocorrelated in the receiver, the result of the correlation is also affected by the small sample rate. Instead of being a triangle (see 4th picture), what we get is a smooth sinc. The result is a weaker signal (with a loss in the order of 1.8dB) but potentially also a loss of precision in the computed pseudorange.

For GPS L1 C/A, the BPSK modulation has a frequency (aka chipping rate) of 1023 chips/ms. Therefore the first null is at 1.023MHz and the bandwidth of the first lobe is 2.046MHz at IF. A sampling rate of exactly 2.046Mhz would be sufficient to capture the energy from the first lobe. That particular number (an integer multiple of the chipping rate) though would be a poor choice for other reasons.

• This actually isn't true. That's the minimum sample rate to intake the DSSS signal's main lobe without any aliasing, but I've seen (successful) GPS receiver designs that first lowpass filter the signal to a somewhat smaller bandwidth (e.g. 1.6 MHz) to reduce the required computational load (with the loss of a bit of performance). Sep 27, 2017 at 11:44
• Thank you for the downvote. I've personally acquired satellites at 1.024MHz complex sampling rate in an actual commercial product. Sep 27, 2017 at 14:59
• I didn't downvote your answer, but the fact is that it isn't accurate for the reason I cited above. To be completely pedantic, there is no "bare minimum" sample rate at all, given good enough SNR and a sophisticated enough receiver. Sep 27, 2017 at 15:00
• Sorry for assuming that then :-) Sep 27, 2017 at 15:01
• Anyway, to the downvoters, feel free to edit the answer if you think it's worth correcting. My point of view is practical, while theoretically there is no "bare minimum", I haven't come across anybody sampling the GPS signal at a rate<1.024MHz. Sep 28, 2017 at 8:37