## 4 Experiments and Discussion
### Performance Analysis of the Resampling Strategy
The carrier-to-noise ratio was set to vary from 25 to 45 dB-Hz with a step of 1 dB-Hz and circular correlation time of signal acquisition was set as \(L_{x}=20\) ms. The experiments of signal acquisition were repeated for 200 times for each carrier-to-noise ratio. Detection probabilities are evaluated and compared for signal acquisition without/with the resampling strategy. From the experimental results of sensitivity illustrated in Figure 10, it can be found that the signal could be acquired successfully with the resampling strategy when the carrier-to-noise ratio was bigger than 32 dB-Hz, and detection probability had reached 100% with the carrier-to-noise ratio of 38 dB-Hz. Compared to the detection probability without the resampling strategy (the blue plot), the sensitivity of the resampling strategy had a loss of nearly 1 dB. It can be attributed to the bandpass sampling filter that filters out some powers of the side lobe signals from the received broadband signal. However, the significant computational cost reduction obtained can make up for the sensitivity loss, as longer circular correlation time and non-coherent integration can be adopted to increase the sensitivity. In order to validate the effects of the proposed strategy on computation and time cost of signal acquisition, comparative experiments without/with the resampling strategy were conducted on all the datasets. Experimental results are presented in Table 3 and Figure 11. Meanwhile, the circular correlation time was fixed as \(L_{x}=20\) ms to eliminate the effects of variable circular correlation time. With respect to the comparison in Table 3, the resampling frequency was reduced to about 10% of the conventional sampling frequency by applying the resampling strategy to Dataset 1, 2, and 3. In Figure 11, computations (multiplication and summation operations) of all the datasets are linearly related to the amount of frequency bins and the data size of the sampled signal. The amount of frequency bins was set as a constant, based on the width of frequency search range and the bandwidth of each frequency bin. And the data size of the sampled signal was exactly determined by the resampling frequency. Resulting from the reduced sampling frequency, the computation cost of signal acquisition with the resampling strategy was greatly decreased, nearly 90-94% of that without the  
Figure 9: Correlation ratios of Satellite PRN12 acquired using the resampling strategy. proposed strategy, as shown in Table 3 and Figure 11. Besides, the received broadband signal in Dataset 4 was an 8-bit complex signal with negative intermediate frequency. The bandpass filter of the proposed resampling strategy was removed since it was not applicable to extract the main lobe signal of Dataset 4. Additionally, the conventional sampling frequency of Dataset 4 was low enough. Thus, the resampling frequency reduced to about 59%, not as nearly 10% for other datasets. Correspondingly, the computation reduction of 43% was gained by applying the resampling strategy to signal acquisition of Dataset 4. Meanwhile, for all experimental datasets, the time cost of signal acquisition with the resampling strategy reduced to about 7.7 \(\sim\) 65% of that with the conventional acquisition algorithm, accompanying with the reduced computation. Experimental results in Table 3 and Figure 11 prove that the adoption of the resampling strategy directly resulted in the significant reduction on the resampled signals, which were used for FFT, correlation, and convolution operations. It makes the dominated contribution to the improved performance of computation and time cost of signal acquisition. Moreover, it is concluded that the resampling strategy can demonstrate better performance for the received broadband signal of higher conventional sampling frequency. Figure 10: Sensitivity of the resampling strategy for weak signals.