## 3 Performance Evaluation  
At present, the acquisition tracking technology is relatively mature, and it can accurately capture the carrier frequency with the residual frequency within 100 Hertz at low SNR easily. The compensated residual Doppler frequency offset might fully meet the requirements of Doppler diversity. It is well-known that contradiction exist between capture accuracy and speed, the lower the capture accuracy, the faster the capture speed, and the larger the residual Doppler offset of the Doppler diversity processed. This paper focuses on the ability of Doppler diversity and the selection of its parameters. At the same time, considering the strong ability of coarse capture, the simulation results of coarse capture are not given here. In the Doppler diversity module, the simulation system applies the BPSK (Binary Phase Shift Keying) modulation method and the shifting branches are \(Q\) = 3. Artificial shift frequency \(f_{x}T\) = 0.75 according to the authors of [8]. The bit error rate (BER) performance when \(T\) = 10\({}^{-4}\), \(F_{D}T\) = 0.1 (\(F_{D}\) = 1 kHz) and \(F_{D}T\) = 0.5 (\(F_{D}\) = 5 kHz) is shown in Figure 4. The BER performance is poor when \(F_{D}T\) = 0.1 and it has not reached 10\({}^{-2}\). When \(F_{D}T\) = 0.5, the ideal known channel state and MMSE (Minimum Mean Square Error) equilibrium are compared, which discovers mistakes of diversity combination due to inaccurate estimation of state information of channels, thus resulting in a high error rate of signal demodulation. This conforms to the conclusion drawn by the authors of [11]. There is a trade-off relation between Doppler diversity and channel estimation error. With the increase of Doppler frequency offset, the fast time-varying performance of channel is strengthened, accompanied with increase of interference power and decrease of signal to interference ratio. All of these are disadvantageous to the communication system. Due to the estimation error of channel, the system performance drops dramatically. Therefore, the system performance cannot be improved whether or not the diversity reception method is adopted when \(F_{D}T\) > 0.1 (\(F_{D}\) > 1 kHz), thus failing to meet requirements on telemetry and communication. The BER performances with and without Doppler diversity when \(F_{D}T\) = 0.01, 0.05 and 0.1 under T = 10\({}^{-4}\) are shown in Figure 5. The normalized Doppler frequency offset is decreased continuously. Generally, the system achieves good performance when \(F_{D}T\) < 0.1. When \(F_{D}T\) = 0.1 (\(F_{D}\) = 1 kHz), it is impossible to realize accurate demodulation when no Doppler diversity reception method is used. When \(F_{D}T\) = 0.05 (\(F_{D}\) = 500 Hz), BER performance under no Doppler diversity reception method is about 6 dB lower than that under the use of the Doppler diversity reception method. However, the BER performance under the use of diversity reception method is poorer than that without the diversity reception method when \(F_{D}T\) = 0.01 (\(F_{D}\) = 100 Hz). This shows that under a very small Doppler frequency offset, the system is slightly influenced by the Doppler offset, but the Doppler diversity reception method might strengthen interferences rather than offsetting interference signals mutually. It can be seen from Figures 4 and 5 that when the residual Doppler frequency offset is too large, channel estimation is not accurate enough and the system performance is too poor, but conversely, the system cannot get evident gains when the diversity is too small. Hence, the diversity system might achieve the best performance when the residual Doppler frequency offset is around 1 kHz. In a previous simulation analysis, the \(f_{x}T\) = 0.75 is determined according to [8], when the normalized Doppler frequency offset is higher than 0.25. It can be seen from Figures 4 and 5 that the BER performances are not good when the normalized Doppler frequency offset is higher than 0.25.