# A High Dynamic Weak Spread Spectrum Signal Acquisition Strategy Based on Iterative Local Search
## 3 ILS Acquisition Strategy
### Acquisition Success Probability Analysis  
The acquisition success probability is an important indicator to measure the acquisition algorithm. Acquisition success means that when the signal parameters (including the Doppler and code phase) captured by the acquisition algorithm are transmitted to the tracking loop, the error with the real signal parameters is within the tolerance range of the tracking loop. On the one hand, successful acquisition requires that the acquired signal parameters are accurate and, on the other hand, that the acquisition time is within the tolerance range. Figure 5: Parallel code phase search process. Figure 6: The process of parallel code phase search after ILS improved acquisition strategy. The tolerance range of the tracking loop to the carrier frequency error depends on the frequency-locked loop. Reference [2] pointed out that the frequency-locked loop in the classical tracking loop uses Equation (9) as the frequency discriminator. \[\omega_{e}(t_{k})=\frac{\Phi(t_{k+1})-\Phi(t_{k})}{t_{k+1}-t_{k}} \tag{9}\]  
where \(\Phi(t_{k+1})\) is the phase difference at \(t_{k+1}\); \(\Phi(t_{k})\) is the phase difference at \(t_{k}\); \(\omega_{e}\) is the angular frequency error; the result of \(t_{k+1}-t_{k}\) is the coherent integration time \(T_{coh}\) of the tracking loop. The frequency pull in the range of the tracking loop is \(\pm\frac{1}{2T_{coh}}\). In addition, there is code phase deviation in the tracking loop \(\pm\tau_{t}\). Under the background of the satellite-ground microwave link of the space station, when using the traditional parallel code phase search for the acquisition, the SNR of the signal is low and the acquisition time is long. At this time, due to the influence of the high dynamic characteristics of the signal, the signal parameters obtained by the acquisition and the signal parameters received by the tracking loop greatly deviate. Therefore, the acquisition result of the traditional parallel code phase acquisition algorithm cannot be used as the initial value of the tracking loop, and its acquisition success probability is extremely low. The error \(x_{fe}\) between the searched Doppler frequency transmitted to the tracking loop and the actual Doppler signal Doppler frequency can be given by:  
\[x_{fe}\approx x_{f_{bin}}+f_{v}T+\frac{1}{2}f_{a}T^{2} \tag{10}\]  
where \(x_{f_{bin}}\) is the Doppler search accuracy; \(T\) is the acquisition time. According to Equation (6), the error \(x_{te}\) between the searched code phase transmitted to the tracking loop and the actual code phase can be given by:  
\[x_{te}\approx\frac{f_{c}}{f_{IF}}(x_{f_{bin}}T+\frac{1}{2}f_{v}T^{2}+\frac{1}{6 }f_{a}T^{3}) \tag{11}\]  
The parallel code phase acquisition with the ILS strategy gradually reduces the acquisition time through multiple rounds of searches, reduces the error between the acquisition result and the signal parameters of the tracking loop, makes the error within the tolerance range of the tracking loop, and greatly improves the acquisition success probability. According to the transfer model shown in Equation (8), in the iterative local search strategy, when the single search time is sufficiently small, the Doppler change is approximately linear. The range of \(x_{fe}\) can be given by:  
\[\left|x_{fe}\right|\leq\frac{x_{f_{bin_{-}k}}+x_{f_{bin_{-}k-1}}}{T_{o}}T+x_{ f_{bin_{-}k}} \tag{12}\]  
where \(x_{f_{bin_{-}k}}\) is the \(k\)th Doppler search accuracy; \(x_{f_{bin_{-}k-1}}\) is the \((k-1)\)th Doppler search accuracy. \(T\) is the elapsed time for the \(k\)th search; \(T_{o}\) is the elapsed time for the \((k-1)\)th search.