I wil try to cover some basic concepts regarding GNSS signals in this post. I will start with GPS and GALILEO (Which of now is in stage 2 – IOC “Initial Operation Capability” with 10 available Satellites). The problem with these 2 systems is that they are sharing the carrier frequency of L1 block (154*10.23MHz = 1575.42MHz). Because of this, a new modulation scheme was invented for GALILEO – the BOC (Binary offset modulation),moving the GALILEO spectrum away from the GPS spectrum,thus allowing both systems to cooperate. The BOC modulation is simply a modulation,where the PRN is multiplied by a rectangular clock signal of  a specified frequency. For example BOC(10,5) means, that the binary carrier has 10 times of a speed of a base GPS system (Which is 1.023MHz) and also that the PRN sequence is repeated 5 times faster than in the GPS system. In other words, within 1ms, the PRN is repeated 5 times. In fact, GALILEO doesnt use the BOC modulation itself, but rather a modification to it – the altBOC modulation, which has somewhat sharper correlation peak and will not be discussed here. The BOC and BPSK spectrums are shown in the featured image while their autocorrelation properties are shown on the next picture:

As we can see, the BOC Modulation has a sharper correlation peak resulting in improved accurancy of ranging. The number of minimums and maximums around the BOC peak depends on the modulation as can be seen in a different modulation scheme:


The first BOC parameter specifies the offset to a given carrier (in fact the Binary Carrier should be probably renamed to subcarrier) while the PRN spreading speed (Second BOC parameter ) affects the width of the spectrum. The higher the spreading speed,the more bandwidth of a spectrum is occupied. these both properties can be as well seen in the featured image of BOC(10,5) modulation and BPSK (GPS) spectrum.

Now that we have talked about the spreading speed, there is an important note to take about the PRN, which is not only used as a ranging signal, but also as a kind of protection against detectability and narrowband interference. Both of these properties will be discussed soon, however I was rather lazy to simulate a standard narrowband signal (Well not that lazy to just add a sine wave) , so in my example a LFM pulse was used. This pulse is rather popular in RADAR technology than anywhere else, but important for me was to simulate a narrowband signal with a specified bandwidth. I have simulated a situation as follows:


In the first subplot, we can see a standard spectrum of a LFM pulse with a bandwith of 1MHz and duration of 1ms (Which is somewhat too long for RADAR systems at least). The more interesting part is the second plot of a BPSK (GPS) spectrum with a lot of noise and even with a narrowband intereference from a LFM pulse. Please just note, that all signals are in baseband (Around zero frequency) complex envelope. As we can see, we cannot see the GPS spectrum, its hidden in the noise around, which is why it is a bit harder to detect these kind of signals with Spread Spectrums. Eventhough we cannot see the signal, believe it or not, we can still calculate the autocorrelation function of such a signal and even measure the pseudodistance from it! See yourself:

The correlation peak is not extra sharp,but the important thing is,that we can still locate it correctly. Try to play with the SNR of both the noise and the LFM pulse (And its bandwidth) to see what happens with the correlation peak :) Quite interesting would be for example to compare the influence of noise and narrowband signals both for BPSK and BOC modulation. My quess is, that BOC might be a bit more vulnerable due to its complexity. Anyway, lets take a look on the GLONASS system. 

GLONASS unlike both GPS and GALILEO is an FDMA (Frequency division multiple access) system. Each satellite transmits on a bit different frequency, which is specified as k*df + FL1. Where k is an integer ranging from -7 to 6, FL1 is the center frequency (1602MHz) and df is the channel separation (0.5625 MHz for L1). All satellites use the same spreading PRN sequence with half the speed of a GPS system (511KHz). We can obtain the PRN sequence quite easily with a linear shift register:


As always, the initial state is all ones filling and then reading data, shifting and feedbacking. Quite simple even for matlab :D … Ok, well now that we have the PRN and the FDMA scheme, lets take a look on the GLONASS spectrum (Simplified with a center frequency of 10MHz) :

As we can see, there is nothing special about the GLONASS spectrum, in fact the scheme is similar for example to OFDM (Orthogonal Frequency Division Multiplexing) systems. If there was a comparison between the GPS and GLONASS (Single PRN) spectrum,we would see that the width of GLONASS spectrum has half the bandwidth of a GPS spectrum, which is nothing really new :)

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