Ranging Module

The ranging module provides ranging and timing analysis capabilities for space communications systems.

Calculations related to two-way sequential or pseudo-noise (PN) radiometric ranging.

This module provides functions for calculating range ambiguity and power allocations between residual carrier and modulated components.

References

[1] 810-005 203, Rev. D “Sequential Ranging”

[2] 810-005 214, Rev. C “Pseudo-Noise and Regenerative Ranging”

[3] CCSDS 414.1-B-3 “Pseudo-Noise (PN) Ranging Systems Recommended Standard”

[4] CCSDS 414.0-G-2 “Pseudo-Noise (PN) Ranging Systems Informational Report”

class spacelink.core.ranging.PnRangingCode(value, names=None, *, module=None, qualname=None, type=None, start=1, boundary=None)[source]

Bases: Enum

The type of PN ranging code used.

DSN = 1
CCSDS_T4B = 2
CCSDS_T2B = 3
class spacelink.core.ranging.DataModulation(value, names=None, *, module=None, qualname=None, type=None, start=1, boundary=None)[source]

Bases: Enum

The type of data modulation used alongside ranging.

BIPOLAR = 1
SINE_SUBCARRIER = 2
spacelink.core.ranging.CODE_LENGTH = 1009470

The length of the full PN ranging sequence.

The DSN and CCSDS PN ranging codes all have the same length.

References

[2] Equation (9).

[3] Sections 3.2.2 and 3.2.3.

Type:

int

spacelink.core.ranging.COMPONENT_LENGTHS = {1: 2, 2: 7, 3: 11, 4: 15, 5: 19, 6: 23}

The lengths of the six components of the PN ranging codes.

The DSN and CCSDS PN ranging codes all have the same component lengths.

The key is the component index (1-6). The value is the length of the component in chips.

References

[2] Table 2.

[3] Sections 3.2.2 and 3.2.3.

Type:

dict[int, int]

spacelink.core.ranging.pn_sequence_range_ambiguity(ranging_clock_rate)[source]

Compute the range ambiguity of the standard PN ranging sequences.

Parameters:

ranging_clock_rate (Frequency) – Rate of the ranging clock \(f_{RC}\). This is half the chip rate.

Returns:

The range ambiguity distance.

Return type:

Distance

References

[2] Equation (11).

[4] p. 2-2.

spacelink.core.ranging.chip_snr(ranging_clock_rate, prn0)[source]

Compute the chip SNR \(2E_C/N_0\) in decibels.

Parameters:

  • ranging_clock_rate (Frequency) – Rate of the ranging clock \(f_{RC}\). This is half the chip rate.

  • prn0 (DecibelHertz) – The ranging signal-to-noise spectral density ratio \(P_R/N_0\).

Returns:

The chip SNR \(2E_C/N_0\).

Return type:

Decibels

References

[4] p. 2-3.

spacelink.core.ranging.carrier_to_total_power(mod_idx_ranging, mod_idx_data, modulation)[source]

Ratio of residual carrier power to total power \(P_{C}/P_{T}\).

This applies under the following conditions:

  • The ranging clock (chip pulse shape in the case of PN ranging) is a sinewave.

  • Uplink or regenerative downlink.

This does not apply to the downlink case when a transparent (non-regenerative) transponder is used.

Parameters:

  • mod_idx_ranging (Angle) – The RMS phase deviation by ranging signal; \(\phi_{r}\) for uplink or \(\theta_{rs}\) for downlink.

  • mod_idx_data (Angle) – The RMS phase deviation by data signal; \(\phi_{cmd}\) for uplink or \(\theta_{tlm}\) for downlink.

  • modulation (DataModulation) – The data modulation type.

Returns:

The ratio of residual carrier power to total power \(P_{C}/P_{T}\).

Return type:

Dimensionless

References

[1] Equation (10) for sequential ranging uplink.

[2] Equation (19) for PN ranging uplink, (50) for regenerative downlink.

spacelink.core.ranging.ranging_to_total_power(mod_idx_ranging, mod_idx_data, modulation)[source]

Ratio of usable ranging power to total power \(P_{R}/P_{T}\).

This applies under the following conditions:

  • The ranging clock (chip pulse shape in the case of PN ranging) is a sinewave.

  • Uplink or regenerative downlink.

This does not apply to the downlink case when a transparent (non-regenerative) transponder is used.

Parameters:

  • mod_idx_ranging (Angle) – The RMS phase deviation by ranging signal; \(\phi_{r}\) for uplink or \(\theta_{rs}\) for downlink.

  • mod_idx_data (Angle) – The RMS phase deviation by data signal; \(\phi_{cmd}\) for uplink or \(\theta_{tlm}\) for downlink.

  • modulation (DataModulation) – The data modulation type.

Returns:

The ratio of usable ranging power to total power \(P_{R}/P_{T}\).

Return type:

Dimensionless

References

[1] Equation (11) for sequential ranging uplink.

[2] Equation (20) for PN ranging uplink, (51) for regenerative downlink.

spacelink.core.ranging.data_to_total_power(mod_idx_ranging, mod_idx_data, modulation)[source]

Ratio of usable data power to total power \(P_{D}/P_{T}\).

This applies under the following conditions:

  • The ranging clock (chip pulse shape in the case of PN ranging) is a sinewave.

  • Uplink or regenerative downlink.

This does not apply to the downlink case when a transparent (non-regenerative) transponder is used.

Parameters:

  • mod_idx_ranging (Angle) – The RMS phase deviation by ranging signal; \(\phi_{r}\) for uplink or \(\theta_{rs}\) for downlink.

  • mod_idx_data (Angle) – The RMS phase deviation by data signal; \(\phi_{cmd}\) for uplink or \(\theta_{tlm}\) for downlink.

  • modulation (DataModulation) – The data modulation type.

Returns:

The ratio of usable data power to total power \(P_{D}/P_{T}\).

Return type:

Dimensionless

References

[1] Equation (12) for sequential ranging uplink.

[2] Equation (21) for PN ranging uplink, (52) for regenerative downlink.

spacelink.core.ranging.pn_component_acquisition_probability(ranging_to_noise_psd, integration_time, code, component)[source]

Compute the acquisition probability for one component of the PN ranging code.

Successful acquisition means that the correct phase of the component code is identified by the receiver. The number of possible phases is equal to the component length.

This calculation assumes that the received signal is correlated against all possible cyclic shifts of the component code in parallel and that the shift with the maximum correlation output is selected. See [4] Section 2.6.2 for details.

This function uses equation (91) from [2]. [4] has an equivalent equation in Section 2.6.3.2, but it uses slightly different values for the cross-correlation coefficients which leads to slightly different acquisition probabilities.

Parameters:

  • ranging_to_noise_psd (Frequency) – The ranging-to-noise power spectral density \(P_R/N_0\).

  • integration_time (Time) – The integration time \(T\).

  • code (PnRangingCode) – The PN ranging code type.

  • component (int) – The component index in [1, 6].

Returns:

The acquisition probability for the given component.

Return type:

Dimensionless

References

[2] Equation (91).

spacelink.core.ranging.pn_acquisition_probability(ranging_to_noise_psd, integration_time, code)[source]

Compute the overall acquisition probability for the PN ranging code.

This is the product of the acquisition probabilities for all components.

This calculation assumes that correlations for all component codes are performed in parallel. See [4] Section 2.6.2 for details.

Parameters:

  • ranging_to_noise_psd (Frequency) – The ranging-to-noise power spectral density \(P_R/N_0\).

  • integration_time (Time) – The integration time \(T\).

  • code (PnRangingCode) – The PN ranging code type.

Returns:

The overall acquisition probability for the PN ranging code.

Return type:

Dimensionless

References

[2] Equation (90).

spacelink.core.ranging.pn_acquisition_time(ranging_to_noise_psd, success_probability, code)[source]

Compute the acquisition time for the PN ranging code.

Successful acquisition means that the correct phase of the full PN ranging sequence is identified by the receiver. For the same receiver architecture, higher probability of successs requires either higher \(P_R/N_0\) or more time.

This calculation assumes that correlations for all component codes are performed in parallel, which is typical for ground station receivers. [3] and [4] refer to this as “station acquisition,” though it could also apply to a regenerative transponder that uses the same parallel correlation architecture. The See [4] Section 2.6.2 for details.

Keep in mind that this only accounts for the acquisition time of a single PN ranging receiver. If a regenerative transponder is used, the ground station receiver’s acquisition processing can’t begin until the on-board transponder has completed its acquisition processing.

Parameters:

  • ranging_to_noise_psd (Frequency) – The ranging-to-noise power spectral density \(P_R/N_0\).

  • success_probability (Dimensionless) – The desired probability of successful acquisition.

  • code (PnRangingCode) – The PN ranging code type.

Returns:

The minimum integration time required to achieve the desired probability of successful acquisition.

Return type:

Time

References

[2] Inverse of Equation (90).