# A Channel Compensation Technique Based on Frequency-Hopping Binary Offset Carrier Modulated Signal
## 4 Simulation Results  
This section will mainly provide the numerical results of the Type I and Type II errors and uncoded bit error rate (BER) for the AWGN channel with relative movement between satellite and UAV. Based on the Doppler effect formula  
\[\xi=\frac{\Delta f}{f}=\frac{v_{r}}{c}\cos\theta, \tag{28}\]  
where \(\theta\) represents the relative angle, \(v_{r}\) is the relative velocity, and \(c\) is the speed of light, from which we can figure out the Doppler frequency shift \(\Delta f\) and relative shift \(\xi\). Supposing \(\theta=0\) in the occasion of maximum relative velocity, that \(v_{r}\) equals to 12.5 km/s larger than low earth orbit (LEO) velocity 7.8 km/s as trying to enter or leave the orbit, which is gradually accelerating and causes a stepping Doppler shift from a random small number up to about 640 Hz. Additionally, since I/Q modulation is adopted, intending to overlap signals' power spectrum in the frequency domain, Figure 13 suggests that the majority of both PSDs limited to the boundary as nearly 10 MHz with shape peaks almost blending, in order to efficiently exploit valuable bandwidth resources, which, meanwhile, leads to the necessity of the designing signals' power allocation, according to the fact that the original generated power of FH-BOC signal surpasses over 10 dB/Hz of the OFDM signal for the majority power distribution part. Type I and Type II errors, also referred to false positive error and false negative error, are usually introduced to examine the probability of correctness in statistical testing. In our proposed system, the validity of the signal detection scheme denotes an important characteristic, since not only is taking several two-dimensional searches within anterior failures is unacceptable coming to realistic communication system, but also demodulating contemporary OFDM symbols is not feasible without code phase alignment and frequency  
Figure 13: Power spectral density distribution of combined signals. compensation. The inspected results on our designed signal acquisition procedure performance over different \(Eb/No\) and power ratio, which represents power of OFDM signal over power of FH-BOC signal, are demonstrated in Figure 14.  
It can be noticed that the Type I in Figure 14a or II in Figure 14b error rates gradually go down, along with the increment of \(Eb/No\). Additionally, we can identify that the general performance on the signal acquisition gradually falls as the value of the power allocation ratio increases, which means the one with a higher power allocation to FH-BOC signal outperforms others. As a result, the one power ratio of \(m^{2}\):\(m^{2}\) = 3:1 is the most prominent, as when \(Eb/No\) = 12 dB, and either error rate has nearly reached the level of \(10^{-4}\). Based on the reliability of acquisition procedure, the performance on the stability of the tracking loop is demonstrated in Figure 15. Through the estimated parameters of phase, code delay, or frequency condition,in accordance to the real imposed interference, the difference between for every milli-second period is suggested intuitively. Either estimated parameter undergoes a short period of measuring the adjustment as tracking of the phase \(\phi\) in Figure 15a, code delay \(\tau\) in Figure 15b, or spur occurred as frequency \(\Delta F\) in Figure 15c, then turning into a plain and stable condition with little fluctuation, such as an absolute difference limited to a near 0.05 length of a single PRN code chip in the code delay tracking. Therefore, the power distribution shown in Figure 13 guides that a well-balanced allocation of power towards the in-phase signal and quadrature signal should be taken into consideration because the former is certainly capable of measuring the carrier frequency and providing sampling time localization for the OFDM signal, while trying not to inflict excessive influence on its demodulation as possible.