Integrated design of ranging and DOR signal for China's deep space navigation

2.1 PN ranging signal

The PN ranging proposed by CCSDS adopts the weighted-voting, balanced Tausworthe code, which is obtained by combining six periodic component codes (CCSDS 2022). According to the weight of the ranging clock component, referred to as T4B ( ν = 4 ) or T2B ( ν = 2 ), it respectively provides greater ranging accuracy or shorter acquisition time. The PN code is phase-modulated on the carrier at a specific chip rate F chip , which is coherent with the uplink carrier, as given by the following expression (for X-bands):

where f X is the uplink frequency, and l and k are specific numbers. For interoperability, l and k should be preferably selected to be 8 and 6, respectively, at a chip rate of ∽2 Mchip/s (CCSDS 2022).

Figure 1 shows an example of the power spectrum of the signal obtained by performing linear phase modulation on the carrier by using the T4B code with a modulation index 0.70 rad. The horizontal coordinates denote the radio frequency of the signal, where f represents the carrier frequency. The vertical coordinates denote the power spectrum of the signal in decibels (dB). Note that several spectral lines are located at ± 0.5 F chip , ± 1.0 F chip , ± 1.5 F chip , etc., owing to the alternating +1 and − 1 chips of the clock component. For a chip rate that is approximately equal to 2 Mchip/s, the frequencies of the first-, second-, and third-order tones are approximately equal to ± 1, ± 2, and ± 3 MHz, respectively.

Figure 1

Power spectrum of the signal phase-modulated by the T4B code.

2.2 DOR signal

Delta-DOR is an application of differential VLBI to spacecraft tracking. That is, an interferometric measurement (referred to as a delay) of a quasar with accurate coordinates, is subtracted from that of the spacecraft. The result of a Delta-DOR measurement provides knowledge of the spacecraft’s angular position in the inertial reference frame defined by the quasars (CCSDS 2019).

To conduct interferometric spacecraft measurements, a set of sinusoidal tones called DOR tones are phase-modulated on the downlink carrier. That is,

where P T is the downlink signal power, ω = 2 π f is the downlink carrier angular frequency, N is the number of DOR tone pairs, ω i is the angular frequency of the i th pair of DOR tones, and m i is the modulation index. According to the CCSDS recommendations, two pairs of DOR tones should be utilized for the X-band: the outer DOR tones, which are approximately located at f ± 20  MHz for obtaining high-precision delay observations, and the inner DOR tones, which are approximately located at f ± 4  MHz for resolving the ambiguity of the outer DOR tone. Figure 2 is a schematic of the X-band DOR signal spectrum; the carrier and two pairs of DOR tones shall be collected and recorded by five channels, and the VLBI channel bandwidth is usually 2, 4, or 8 MHz and is centered on the DOR tones. In fact, the accuracy of Delta-DOR measurements depends on the spanned bandwidth of the outer DOR tones. As the inner DOR tones are only utilized to assist the ambiguity resolution, CCSDS does not constrain strictly the specific frequency of the inner DOR tones and can be selected and designed according to the actual situation.

Figure 2

Downlink spectrum and VLBI channels for DOR measurements.

3.1 Basic principles

The integrated design of the signal adheres to the following principles:

1. Multiplexing: to improve the power efficiency;

2. Compatibility: compatible with CCSDS recommendations for interagency cooperation;

3. Reality: can be implemented within the current capabilities of spacecrafts and ground stations;

4. Inheritance: to avoid implementation risks induced by state changes of technologies;

5. Advancements: to improve the measurement accuracy.

3.2 Overall design

Note that the single tones of the PN ranging power spectrum (Figure 1) and the DOR tones are all spectral lines whose spectral characteristics are the same. In addition, their frequencies (approximately equal to ± 1, ± 2, ± 3 MHz, etc.) are also close to the inner DOR tone frequency recommended by CCSDS. Therefore, there is no need for additional, dedicated modulation of the inner DOR tones. The spectral lines of the PN ranging power spectrum can act as the inner DOR tones to resolve the ambiguity of the outer DOR tones. As the power of the tones on the PN spectrum decays rapidly as a function of frequency, the tones at ± 20 MHz would be too weak for interferometry. Therefore, to maintain the accuracy of the interferometric measurement, it is necessary to retain the outer DOR tones.

On this basis, an integrated signal based on PN ranging and the outer DOR tones is expressed as follows:

where the two-phase modulation items are the PN codes and the outer DOR tones, respectively, m PN and m DOR are their modulation indices, c k is the PN code sequence, h ( t ) is the impulse response of the baseband shaping filter, T c is the chip width (the reciprocal of the chip rate F chip ), and ω DOR is the angular frequency of the DOR tone.

3.3 Parameter set

According to the principles of compatibility, inheritance, and advancement, the undetermined parameters in Eq. (3) are designed as follows:

1. Chip rate: l = 8 , k = 6 (2 Mchip/s)

2. This is the highest chip rate for interagency cooperation. The higher the chip rate is, the higher the achieved accuracy of range. In addition, a higher chip rate results in a larger spanned bandwidth of the PN spectral lines, which helps attain higher-precision delay measurements for ambiguity resolution of outer DOR tones.

3. Uplink PN code modulation index: 0.95 rad and regenerated PN code modulation index: 0.70 rad

4. As the uplink margin is always sufficient, increasing the modulation index of the uplink ranging signal can effectively reduce the jitter of the uplink PN ranging without affecting the quality of uplink communications. Furthermore, a large modulation index for regenerated PN code can improve further the ranging accuracy and enhance the power of the single tones; effectively, the latter improves the accuracy of delay measurements from the PN spectral lines and benefit the ambiguity resolution of the DOR tones.

5. DOR tone: ± 1/440 of the downlink carrier frequency and modulation index: 0.40 rad

6. The frequency of the DOR tones complies with the CCSDS recommendations (approximately equal to ± 20 MHz for the outer tones), and is also consistent with the current design of China’s lunar and Mars missions. The modulation index is the same as the current value of the DOR tones in China’s lunar and Mars missions.

3.4 Power spectrum

Based on the above models and parameters, a novel design of ranging and DOR signal is obtained, whose power spectrum is shown in Figure 3(a). The horizontal coordinates denote the radio frequency F of the signal relative to the carrier frequency f . In addition, the vertical coordinates denote the power spectrum of the signal in decibels (dB). For comparison, Figure 3 also shows the power spectrum of the downlink signals of PN ranging and two pairs of DOR tones in panel (b) (hereinafter referred to as the normal design); the currently utilized signal of tone ranging (based on ± 500 kHz sidetones) and two pairs of DOR tones are shown in the bottom panel (hereinafter referred to as the classic design). Spectral lines in the figure are ranging signals, DOR tones, and their intermodulation components. The red circles denote the effective components that can be used for interferometry. It can be observed that the power distribution of the novel design is more concentrated, while those of the normal and classic designs have more spectral components owing to the intermodulation of ranging tones and the two pairs of DOR tones. Although the spectral structures appear to be quite different, the main power remains in the residual carrier, the first-order of ranging tones, and the first-order of DOR tones. In fact, the downlink signals from deep space are weak, and many of the spectral structures in the figure are corrupted by noise.

Figure 3

Power spectra of the novel (a), normal (b), and classic (c) designs.

4.1 Link budget

The main parameters and results of the link budget are listed in Table 1. Compared with the classic case, the novel design contains no residual command or turnaround noise and omits the inner DOR tones, thus resulting in the residual carrier, telemetry subcarrier, and DOR tones with a higher intensity (by 1.8 dB). That is, the supported telemetry data rate could be increased by approximately 50%. More importantly, the ranging signal is 4.9 dB stronger than that of the classic signal case, thus indicating a much higher accuracy. The power efficiencies of the novel and classic signals are approximately equal to 87 and 54%, respectively, thus demonstrating a 33% increase in the effective utilization of downlink power. Compared with the normal signal case, the novel one omits the inner DOR tones, thus resulting in the residual carrier, telemetry subcarrier, and DOR tones with a higher intensity (by 0.35 dB). This improvement is meaningful in deep space communication. Alternatively, this means that for solar system boundary explorations, communications amounting to several months’ flight can be further supported without decreasing data rates.

4.2 Error analysis

For ranging and Doppler measurements, the thermal noise error dominates the total error. Thus, only this error is considered here. Regarding the Delta-DOR measurements, there are many determining factors for the delay error, all of which should be accounted for.

4.2.3 Delay accuracy

The delay error of Delta-DOR measurements is induced by a number of factors, including radio source thermal noise, spacecraft thermal noise, clock instability, phase dispersion, station location error, earth orientation parameter (EOP) error, zenith tropospheric delay error, tropospheric jitter, ionospheric delay error, ionospheric jitter, solar plasma, radio source coordinate error, and others (CCSDS 2019). The observation scenario here is based on the current system architecture. Two widely separated stations simultaneously observe a spacecraft/quasar for Delta-DOR measurements. Quasars are angularly close to the spacecraft. The same spanned bandwidth and VLBI channels are assumed for both spacecraft and quasar observations to achieve the best cancellation of the instrumental effects.

For Delta-DOR measurements, the delay accuracy depends on the precisions of both the spacecraft and quasar delay measurements. To estimate delay errors, all parameters relevant to the measurement geometry, and random and systematic effects must be assigned. Table 3 lists the nominal parameter values for the delay error budget. It is worth mentioning that the only difference among the novel, normal, and classic signals in Delta-DOR measurements pertains to the power-to-noise spectral density of the DOR tones ( P / N 0 of outer DOR in Table 1). The parameters in this table are utilized to evaluate all the delay error components mentioned above, according to the error models and equations provided by the CCSDS technical report on Delta-DOR measurements (CCSDS 2019). The delay error component results for all types of signals are shown in Figure 4. Note that the delay errors induced by radio source thermal noise, spacecraft thermal noise, clock instability, phase dispersion, tropospheric jitter, ionospheric jitter, and solar plasma are random, while delay errors induced by the other factors are systematic. The total error (1 σ ) is the sum of all systematic error components and the RSS of all the random error components. This method of total error calculation is different from that in CCSDS (CCSDS 2019), which uses the RSS of all systematic and random error components as the total error. In other words, the method used for total error calculation in this study is considered to be more conservative and reasonable.

Table 3

Nominal parameter values for evaluation of delay error budget

Parameter	Value
Quasar (Q) integration time	300 s
Spacecraft (S) integration time	5 s
Q–S angular separation	0.2 rad
Q elevation angle	25°
S elevation angle	20°
Min. angle between Sun and Q/S	20°
Spanned bandwidth	38.32 MHz
G/T for antenna	49.0 dB/K
Channel sampling rate	4,000,000 samples/s
Q correlated flux density	1 Jy
System loss factor	0.8
Radiofrequency wavelength	0.0356 m
P / N 0 of outer DOR	39.72/39.37/37.92 dBHz
Time between Q/S-scan centers	360 s
Station frequency stability at 600 s	1.0 × 1 0 − 14
Phase ripple	0.2°
Baseline coordinate	0.05 m
Baseline orientation	0.02 m
Zenith wet troposphere	0.005 m
Zenith dry troposphere	0.002 m
Fluctuating troposphere (10°)	0.01 m
Daytime ionosphere model	0.04 m
Nighttime ionosphere model	0.01 m
Fluctuating ionosphere (10°)	0.01 m
Separation of ray paths	2000 km
Solar wind velocity	400 km/s
Q coordinate uncertainty	7.5 × 1 0 − 10 rad
Baseline onto plane-of-sky	3,000 km

Figure 4

Error budget for Delta-DOR measurements of three types of signals.

Based on this, the delay measurement accuracies ( 1 σ ) for the novel, normal, and classic designs are estimated to be approximately equal to 0.19 ns. The accuracy results are listed in Table 2. In fact, the DOR tone is slightly improved in the novel design case, resulting in a slightly smaller spacecraft thermal noise. As the other error sources dominate, the total error is almost the same, as observed in Figure 4.

4.3 Summary

Although the accuracy is based on theoretical analyses, it is consistent with data from real mission situations when multiplied by a factor in the range of 1.5–3. Table 2 summarizes the results presented above. It can be observed that the improvement of the ranging accuracy is the most remarkable owing to the better PN ranging scheme and the minimization of power loss. Compared with the classic signal, the intensity of the residual carrier in the novel design case was increased by 1.8 dB, which supports a 50% higher telemetry data rate. The delay measurement error caused by the spacecraft thermal noise was also reduced, which contributes slightly to the overall delay measurement accuracy. Compared with the normal design case, the novel signal achieved a downlink signal with higher intensity of 0.35 dB. Although this does not correspond to profound improvements in measurement accuracy, it is meaningful for deep space communications, especially for solar system boundary explorations. A higher power efficiency of the downlink signal is achieved for the novel design, which supports a more energy-efficient design of the spacecraft.