# The Potential of LEO Satellite-Based Opportunistic Navigation for High Dynamic Applications
## 3 Simulation and Signal Processing Tools
### Iridium Signal Processing Tool  
Iridium Next downlink signals come in discontinued bursts transmitted by 75 satellites that orbit the Earth at an altitude of 780 km. A downlink burst is transmitted in the band 1616-1626.5 MHz using one of the several frequency channels available following the FDMA multiple access. The system has simplex and duplex channels; we used the simplex channels (1626-1626.5 MHz) because they are broadcast regularly worldwide on fixed carrier frequencies (the ring alert and the messaging channels). Bursts have a common structure composed of a tone over \(T_{tone}=2.56\) ms, followed by a BPSK word over a short period, then followed by QPSK data until the end of the burst. The data rate is \(Rs=25\) ksps. The burst duration of a simplex channel does not exceed \(T_{burst}\leq 20.32\) ms [6; 27]. Based on the Iridium signal structure, we designed an Iridium signal processing tool to detect Iridium bursts and measure their carrier frequencies. The tool shown in Figure 3 works as follows. We perform burst detection by comparing the power level of the incoming signal \(r\) to a threshold \(T\) that is supposed to represent the noise power level (i.e., without the useful signal)  
\[\tilde{y}[n]=N^{-1}\sum_{i=0}^{N-1}\lvert r[n-i]\rvert^{2}\quad\overset{<}{ \geqq}T \tag{26}\]  
where \(N\) is the size of the averaging window. When the signal average power exceeds the threshold, the burst start epoch \(k_{start}\) and the burst end epoch \(k_{end}\) are determined. Then, for each detected burst \(s=r[k_{start}:k_{end}]\), we compute the spectrum of the burst tone. The frequency of the maximum of the spectrum yields a coarse estimation of the burst carrier frequency \(\hat{f}_{c}\) as  
\[\hat{f}_{c}=argmax_{f}\big{\{}\ DFT(r[k_{start}:k_{start}+T_{tone}F_{s}])\big{\}} \tag{27}\]  
where \(DFT(. )\) is the discrete Fourier transform and \(F_{s}\) is the sampling frequency. We then use this approximate frequency to down-convert the burst \(s\) to baseband  
\[s_{bb}=s\times exp\Big{(}j2\pi\Big{(}\hat{f}_{c}t\Big{)}\Big{)},\ \text{with}\ t=\Big{[}0:\frac{1}{F_{s}}:T_{burst}\Big{]} \tag{28}\]  
Finally, the baseband burst \(s_{bb}\) enters a phase lock loop (PLL) where its carrier frequency estimation is refined. The PLL is composed of a numerical controlled oscillator (NCO), an integrate-and-dump over \(Ti\), \(\sum_{Ti}(. )\), an arctangent phase detector and a first-order loop filter. At this stage, the Doppler frequency is given by the difference between the carrier frequency estimated by the PLL and the transmitter frequency. We processed real life Iridium signals captured in a static location by means of a USRP-N310. We used an active right hand circular polarized antenna with a \(\sim\)37 dB gain in the Iridium frequency band. The antenna was located on the roof of our building  
Figure 3: Block diagram of the Iridium signal processing tool. to maximize signal reception. This solution provides Iridium bursts and their Doppler shift measurements with a timestamp capability better than 1 s. The digitizer has been configured with a sampling frequency of 2 MHz around \(Fo\) = 1626.25 MHz. The processing tool is configured as follows. During the burst detection, the average signal power is computed over a duration of 1 ms. The PLL coherent integration time \(Ti\) is set to 10 \(\upmu\)s, the PLL equivalent noise bandwidth \(Bn\) is set such that \(Bn\times Ti=0.02\). Figure 4 illustrates the processing results of a single burst. As bursts are very short, the PLL requires a large loop bandwidth and thus a small integration time that leads to high noise frequency estimates. In order to improve the frequency precision, we averaged the frequency estimated by the PLL over time. Figure 5 shows the expected PLL frequency thermal noise standard deviation (std) as a function of the carrier-to-noise density ratio (CNR) as well as the frequency thermal noise std obtained after averaging over the last \(Ta\) = 0.5 ms of the burst tone.