## 4 Experiment Results and Analyses
Applying the time-frequency tool to map the remaining signal onto the time-frequency plane, the resulting spectrogram is shown in Figure 11. It is important to note a characteristic of sinusoid wave is observed around the Doppler frequency of -1,500 Hz, which matches the acquired information of PRN 18 in Table 2. Although the strength of the characteristic of the sinusoid wave is not as obvious as that of the typical strength satellite signal in Figure 9, the PRN 18 signal is detectable around the corresponding Doppler frequency on the spectrogram. The attenuation is expectable for a satellite signal with a low received power. That is, although the satellite information is despread with a spreading gain, it might be close to the noise floor. In other words, the proposed approach could provide evidence to show that the satellite signal of PRN 18 is present. In reality, the satellite signal of PRN 18 is in view according to the acquisition result of the collected roof GPS signal, as shown in Table 1. The SEV process further provided evidence that the PRN 18 is present, although it was previously categorized as noise by the acquisition process. After applying the proposed SEV process to the others satellite signals, which were previously declared as signal absent in Table 3, five additional satellites (PRNs), which are marked in red in Table 4, are now declared as signal present. As a result, the SEV process increases the number of acquired satellites from one to more than four, that is, it meets the basic requirements (_i.e._, at least four satellites in-view) for continuing the navigation service under indoor environments. Consequently, the proposed SEV process is effective for detecting the satellite signals with low received power. \begin{table}
\begin{tabular}{||c|c|c|c||} \hline IRN & Code delay & Doppler frequency & CPPR (\(\Omega\)R) \\  & samples & (1 Hz) & \\ \hline
22 & 1,419 & 1,000 & 0.85 \\ \hline
30 & 2,543 & 2,500 & 7.55 \\ \hline
14 & 2,954 & 1,500 & 1.14 \\ \hline
26 & 15,588 & –1,500 & 1.52 \\ \hline
18 & 10,815 & –1,500 & 2.20 \\ \hline
12 & 7,445 & 500 & 1.17 \\ \hline
31 & 6,178 & 3,000 & 2.61 \\ \hline \end{tabular}
\end{table} 
Table 2: The acquisition result of the collected indoor signal by the conventional acquisition method with the integration time of 1 millisecond. Figure 10: (a) The correlation distribution _versus_ the code delay samples at the frequency bin with maximum correlation peak. (b) The correlation distribution _versus_ the frequency bin at the code delay sample with maximum correlation peak. (c) The search pattern of the PRN 18 of the collected indoor signal in the acquisition process. \begin{table}
\begin{tabular}{||c|c|c|c|c||} \hline IRN & Code delay & Doppler frequency & CPPR (\(\Omega\)R) \\  & samples & frequency & (\(\Omega\)R) & (\(\Omega\)R) \\  & (Hz) & by Coherent & by non-coherent \\
22 & 6,923 & –1,500 & 1.24 & 1.17 \\ \hline
30 & 2,541 & 2,500 & 8.05 & 8.04 \\ \hline
14 & 16,183 & 2,500 & 1.97 & 2.01 \\ \hline
26 & 16,172 & 1,000 & 2.68 & 2.67 \\ \hline
18 & 1,845 & 2,000 & 0.35 & 0.32 \\ \hline
12 & 15,207 & 1,000 & 0.55 & 0.50 \\ \hline
31 & 14,774 & 2,500 & 0.53 & 0.49 \\ \hline \end{tabular}
\end{table} 
Table 3: The acquisition result of the collected indoor signal by the conventional acquisition method with the coherent and non-coherent integration time of 2 milliseconds. For the satellite signal with low received power, the code delay sample of the maximum correlation peak estimated in the acquisition process might not be exactly correct. The miss-alignment between the code delay of the local C/A replica and that of the incoming satellite signal would result in the imperfect removal of C/A code effect, and the maximum correlation value and its resulting SNR would be therefore degraded. This paper also investigates the performance of the proposed approach if the estimated code delay sample has an offset from the correct one.